Topics in Modal Analysis & Testing, Volume 8

Over the past 50 years, great advances have happened in both analytical modal analysis (i.e., finite element models and analysis) and experimental modal analysis (i.e., modal testing) in aerospace and other fields. With the advent of more powerful computers, higher performance instrumentation and data acquisition systems, and powerful linear modal extraction tools, today’s analysts and test engineers have a breadth and depth of technical resources only dreamed of by our predecessors. However, some observed recent trends indicate that hard lessons learned are being forgotten or ignored, and possibly fundamental concepts are not being understood. These trends have the potential of leading to the degradation of the quality of and confidence in both analytical and test results. These trends are a making of our own doing, and directly related to having ever more powerful computers, programmatic budgetary pressures to limit analysis and testing, and technical capital loss due to the retirement of the senior demographic component of a bimodal workforce. This paper endeavors to highlight some of the most important lessons learned, common pitfalls to hopefully avoid, and potential steps that may be taken to help reverse this trend.

Many devices use vibration to provide sensory cues to a human user. In applications, such as smart phones, the vibratory sensory cue is somewhat simple and needs only to exceed a known threshold to signal the user; however, applications that require an individual to control or manipulate an instrument while being given a vibratory sensory cue must also consider the excitation, whose primary purpose is to provide vibrotactile feedback, which can alter the user’s ability to properly control or maneuver the instrument. Another consideration for many handheld instruments is that a user’s grip pressure can drastically alter the instrument’s dynamic response. To this end, predicting the instrument’s response is made difficult, because the relationships between grip pressure and the equivalent interfacial damping and stiffness is complex. To address this research gap, this paper explores the idea of performing experimental vibration tests on a laparoscopic instrument while being held at varying grip pressures. This research is motivated by the idea of providing vibratory feedback through laparoscopic surgical instruments. A gap in the literature exists in understanding how surgeon grip characteristics impact the optimal frequency for which this excitation should be supplied. Results from this study indicate that excitation frequencies should be greater than 175 Hz for both weak and strong grip configurations. Lower frequencies result in a larger amplitude response at the instrument tip for all grip pressures, which could result in patient harm as the instrument tip oscillates uncontrollably.

Vibration testing spaceflight hardware is a vital, but time consuming and expensive endeavor. Traditionally modal tests are performed at the component, subassembly, or system level, preferably free-free with mass loaded interfaces or fixed base on a seismic mass to identify the fundamental structural dynamic (modal) characteristics. Vibration tests are then traditionally performed on single-axis slip tables at qualification levels that envelope the maximum predicted flight environment plus 3 dB and workmanship in order to verify the spaceflight hardware can survive its flight environment. These two tests currently require two significantly different test setups, facilities, and ultimately reconfiguration of the spaceflight hardware. The vision of this research is to show how traditional fixed-base modal testing can be accomplished using vibration qualification testing facilities, which not only streamlines testing and reduces test costs, but also opens up the possibility of performing modal testing to untraditionally high excitation levels that provide for test-correlated finite element models to be more representative of the spaceflight hardware’s response in a flight environment. This paper documents the first steps towards this vision, which is the comparison of modal parameters identified from a traditional fixed-based modal test performed on a modal floor and those obtained by utilizing a fixed based correction method with a large single-axis electrodynamic shaker driving a slip table supplemented with additional small portable shakers driving on the slip table and test article. To show robustness of this approach, the test article chosen is a simple linear weldment, whose mass, size, and modal parameters couple well with the dynamics of the shaker/slip table. This paper will show that all dynamics due to the shaker/slip table were successfully removed resulting in true fixed-base modal parameters, including modal damping, being successfully extracted from a traditional style base-shake vibration test setup.

Acoustoelastic structures are a complex dynamic system that exhibit modal coupling between a structure and its enclosed acoustic fluid. Common structures that exhibit this phenomenon in the aerospace industry are pressure vessels such as a solid rocket boosters or advanced solid rocket motors. When a structural analyst simulates the structural modes of these pressure vessels with shell finite elements, they often apply an internal pressure force in their model to represent the acoustic fluid. In a model free of boundary conditions, the application of this internal pressure force produces modal results that ground some rigid body modes, often going from six to three zero-frequency modes. Therefore, since the finite element modal simulation inappropriately grounds the structure and thus is unable to accurately predict the rigid body modes, it calls into question whether the elastic or flexible modes predicted by the same modal analysis are accurate. This paper presents an experimental study to address this question by designing, analyzing, fabricating, and testing a simple cylindrical pressure vessel. A free-free steel cylindrical pressure vessel was modeled with finite elements and modal tested with and without pressure. Modal tap testing was used to extract the structural response and compute frequency response functions which were compared to analytical results to discern the accuracy of the predicted elastic modes of the pressure vessel.

A fixed base correction method that uses acceleration constraint shapes as references to transform flexible or dynamically active boundary conditions into fixed boundaries has been recently implemented for modal tests. The method uses test data directly to generate constraint shapes associated with accelerometer measurements at the test article and test fixture interface that are then used as references when calculating corrected fixed base frequency response functions (FRFs). The main challenge with the method is that at least one disturbance source, such as a modal shaker, must be applied to the boundary structure for each constraint shape used, so it is advantageous to understand how many constraint shapes may be required to fix a boundary for test planning purposes. This paper outlines a procedure that uses multipoint constraint equations in an analysis model of an integrated test article and its test fixture to determine the number of exciters necessary to apply the fixed base correction method. The method is verified by comparing mode shapes of the fixed base test article to the system model with a number of multipoint degrees of freedom constrained.

Modal tests are performed to validate analysis models of structures, and it is important to support a test article use fixtures that allow an engineer to focus his time and effort on updating the analysis model instead of the supports. Oftentimes, however, inadequate boundary condition fixtures are used in modal surveys because the design and manufacture of a proper boundary condition may be too expensive for a program. An alternative approach of creating appropriate boundary conditions by using accelerations as references to fix degrees of freedom is presented in this paper and is demonstrated using test results from a tap test on an aluminum beam. Frequency response functions (FRF) are generated directly and indirectly using a partial inversion of the FRF matrix for several different boundary condition cases using the same set of test data. Modes are extracted from the resulting FRF and are compared to an analysis model.

Bridge system identification is recently studied using mobile sensing network data. As one possible solution, the data collected by moving sensors are to be mapped to some predefined virtual stationary locations and then, using estimated stationary data, various system identification methods can be applied. The mapping function, however, has not been studied thoroughly so far. STRIDEX, which is a recently proposed platform for bridge SID using mobile sensing, assume sinc function as an estimator for the mapping function. Despite its effectiveness under certain conditions, the function cannot accurately estimate stationary time responses from mobile data in more realistic cases of moving sensors with random presence over the bridge. In this paper, an alternative solution based on low-rank matrix completion problem is proposed and motivations for this choice are discussed. This method attempts to complete the matrix as accurate as possible by convex optimization, given a sparse matrix of acceleration values with various time and space coordinates. A comprehensive comparison between sinc and matrix completion approaches is performed and the results are evaluated in terms of the response prediction accuracy in both time and frequency. Results show that the proposed matrix completion signals are a very good match to the actual signals, while the reconstructed signals using sinc are sometimes not as accurate.

This paper expands on the ideas presented in two previous papers (Schwarz et al., Curve fitting analytical mode shapes to experimental data, IMAC XXXIV, 2014; Schwarz and Richardson, Linear superposition and modal participation, IMAC XXXII, 2014). Here, we again show with examples how all vibration, whether it is represented in the form of time waveforms, frequency spectra, or ODS’s, can also be represented as a summation of mode shapes. The title of this paper is actually a universal law which is used for all modal analysis, Fundamental Law of Modal Analysis (FLMA): All vibration is a summation of mode shapes.The modal parameters of a structure can be obtained in two ways, 1. Experimental Modal Analysis (EMA): Extracting EMA mode shapes by curve fitting a set of experimentally derived time waveforms or frequency spectra that characterize the structural dynamics 2. Finite Element Analysis (FEA): Solving for the FEA mode shapes from a set of differential equations that characterize the structural dynamics In this paper, it will be shown how the benefits of analytical FEA mode shapes can be combined with experimental data to yield more robust dynamic models (Richardson and Richardson, Using photo modeling to obtain the modes of a structure, Proceedings of the International Modal Analysis Conference, 2008; Richardson, Sound Vib Mag, 2005). FEA mode shapes will be used to “decompose” and then “expand” experimental data to include DOFs that cannot or were not determined experimentally (Schwarz et al., Using mode shapes for real time ODS animation, IMAC XXXIII, 2015).A unique advantage of this approach is that only mode shapes themselves are required. Modal frequency and damping are not required. Another unique advantage is that mode shapes from an FEA model with free-free boundary conditions and no damping can be used.It usually requires a great deal of skill and effort to modify an FEA model and its boundary conditions so that its modal frequencies and mode shapes accurately match EMA modal frequencies and mode shapes. In addition, adding accurate damping to an FEA model is usually so difficult that damping is left out of the model altogether. The approach presented here circumvents both of these difficulties.

Conventional broad-band modal testing is done by acquiring a single-reference or multiple-reference set of FRFs and curve-fitting them to obtain modal parameters. Since a (fixed) reference sensor is required throughout the data acquisition process, testing a large structure requires that a (potentially) long wire be used to connect the reference sensor to the acquisition system.In a previous paper (McHargue et al., ODS & modal testing using a transmissibility chain, IMAC XXXVI, 2017), a new modal testing method was introduced which does not require the use of a fixed reference sensor. This method is based on the calculation of a series of Transmissibility’s, called a TRN chain. This method has several important advantages, 1. Excitation forces need not be acquired 2. Only two response sensors are required for data acquisition 3. The two sensors can be physically close to one another throughout data acquisition Since the excitation forces need not measured, data for calculating a TRN chain can be acquired from an operating machine, or during any test where excitation is provided by impacting or by using one or more shakers.A Slinky test is a unique way of acquiring a TRN chain. In a Slinky test, one sensor is merely “hopped over” the other sensor with each new acquisition, as shown in Fig. 9.3. As the two sensors are moved over the surface of the structure in this manner, a “chain” of Transmissibility’s is calculated from the acquired data.A TRN chain can be “seeded” with an Auto spectrum, Cross spectrum, Fourier spectrum, or FRF to yield a single-reference set of measurements, from which experimental modal parameters can be extracted. A Slinky test is much faster, easier, and less costly than a conventional modal test.

It has been recently proposed to incorporate a tendon in a rotorcraft blade to introduce a means of controlling its dynamics properties. This has been shown as an effective resonance avoidance mechanism that should allow rotorcraft to operate with shape adaptive blades or with variable rotor speed, thereby increasing their performance and efficiency. In the previous studies, the tendon was attached to the blade’s tip, passed freely through its whole body and was fixed at the root of the blade. The tendon was therefore free to vibrate unrestrictedly inside the blade. This, despite delivering the required changes to dynamics, may not be the most optimal and viable design. In this paper, a modification of this concept is investigated. Unlike in the previous studies, the tendon does not pass freely through the blade, but it is connected to it in a single spanwise location using a mechanical attachment. This coupled blade-tendon system is studied both numerically and experimentally. The blade is modelled as the Euler-Bernoulli beam, the tendon as a taut string, and the attachment point as a concentrated mass. The boundary and connectivity conditions are used to ensure the required coupling between the beam and the tendon. Free vibration analysis is conducted using a boundary value problem solver and a bench-top experiment is used for validation of the numerical results. The variation of modal properties with the applied tendon tension and the location of the attachment point is investigated. It is found that many features observed in the previous studies, such as the frequency shift and frequency loci veering, are still exhibited by the modified system, but they are manifested under different loading conditions. In this way, the attachment points may influence the ability to control the beam’s dynamic properties. The implications of these phenomena for the application of an active tendon in rotorcraft are discussed.

This chapter introduces some principles and methods for designing modal test plans based on finite element method (FEM) results. The number of points in FEM is closed, generally in the thousands. From the FEM results, many orders of modal frequencies and vibration shapes can be obtained. However, in a modal test, only the foremost orders are concerned; thus, the number of measured points is limited, generally in the tens. There are 2–4 exciting points for a multi input multi output (MIMO) test, whereas 1 exciting point is practical for a single input single output (SIMO) test when the modes are not closed. When the number of foremost orders and measured points are fixed, it is not practical to automatically compute the position of the total measured points from the FEM results for several reasons. First, the computing work is very complex and time-consuming. Second, for the best mathematical results, some key points may be lost and some points that cannot be measured are included. Most importantly, none of these point are able to construct a regular plane, so the result is unacceptable aesthetically. The practical approach is to design an initial plan in which the position is measured manually according to common experience and the space is evenly distributed. By computing the maximum value of the un-diagonal elements of the modal assurance criterion (MAC) matrix and observing the modal shape animation of the simplified results, some measured positions can be modified. If some points need to be deleted in the initial base, this task can be completed automatically by dividing all measured positions into two groups: points that are allowed to be deleted and points that cannot be deleted. After the positions of all measurements are fixed, the number of exciting points and their positions can be obtained automatically according to the exciting energy distribution of different orders in each position.

The promise of extracting fixed base modes from structures mounted on shake tables is enticing since doing so allows a testing organization to save a considerable amount of schedule and money by reducing two traditionally separate tests into one. Oftentimes, however, the modal analysis results are not of high quality because the test planning and conduct of base shake environmental tests are not conducive to performing a high-quality modal survey.This paper will discuss test planning and test conduct methods that can be used to maximize chances for successfully extracting high-quality mode shapes from structures mounted on shake tables. These methods are the same for any modal survey test; sensors should be placed to adequately observe and differentiate modes of a structure, and the excitation must be long enough in duration to adequately define high-quality frequency response functions (FRFs). Finally, methods to separate closely spaced modes by using multiple references, either with multiple-degree-of-freedom shake tables or a single-axis base shake test supplemented with modal shakers, will be discussed.

In many contexts the modal properties of a structure change, either due to the impact of a changing environment, fatigue, or due to the presence of structural damage. For example during flight, an aircraft’s modal properties are known to change with both altitude and velocity. It is thus important to quantify these changes given only a truncated set of modal data, which is usually the case experimentally. This procedure is formally known as the generalised inverse eigenvalue problem. In this paper we experimentally show that first-order gradient-based methods that optimise objective functions defined over a modal are prohibitive due to the required small step sizes. This in turn leads to the justification of using a non-gradient, black box optimiser in the form of particle swarm optimisation. We further show how it is possible to solve such inverse eigenvalue problems in a lower dimensional space by the use of random projections, which in many cases reduces the total dimensionality of the optimisation problem by 80–99%. Two example problems are explored involving a ten-dimensional mass-stiffness toy problem, and a one-dimensional finite element mass-stiffness approximation for a Boeing 737-300 aircraft.

Modal testing of large structures such as wind turbine blades poses several challenges. Applied test setup configuration, test specimen mounting and measurement equipment are known to affect the test results. This paper presents a comparison study of the modal tests of nominally identical 14.3 m long blades. Blade A was supported in free-free boundary conditions and tested with the Experimental Modal Analysis using accelerometers. Blade B was clamped to a concrete block and tested with Operational Modal Analysis and strain gauges. The modes and corresponding natural frequencies obtained from both test cases were compared and correlated with the numerical models of the blades.

Metallic structures like circular plates or turbine discs feature special mode shapes that can be classified by nodal diameters and nodal circles. It is often desirable to experimentally examine just one mode shape with its distinct nodal diameter and nodal circle. To excite just one mode shape at a certain eigenfrequency the circumferential spectrum of the excitation force must not have other frequency content than the desired frequency and additionally have to resemble the mode shape itself. A device capable of creating such a single mode shape excitation has not existed yet. Here, a patented device is presented which is able to excite a single distinct mode shape of a rotating metallic circular structure. To achieve this the device features a toroidal horseshoe electromagnet with a variable gap geometry. By using the variable gap geometry and variable inductor current any modeshape of a metallic circular rotating structure can be excited. It is also possible to excite a combination of modeshapes by linear superposition of the necessary gap geometries. A brief explanation of the device is given followed by experimental results.

Modal Analysis is a well-established key tool used to analyze the dynamic behavior of a structure. A robot manipulator consists of mechanical structures, like the body links between the joints and gears, and mechatronic components, like motors and their control system. The dynamic behavior of all subcomponents making up the robot arm are individually well understood. However, their respective influence on the dynamic behavior of the entire robot system is still a matter of research. Understanding the dynamics of the manipulator and setting up a validated model of its full dynamics is essential, in order to devise proper control strategies. One specific challenge comes from the fact that the vibration properties (modes, damping and frequencies) depend on the overall pose and thus change during the operation of the robot. Further, non-linearities from the joints and the action of the joint controller can significantly influence the dynamics of the system. In this paper, the influence of these effects on the overall dynamic behavior of a 7 DOF robot manipulator developed for automated sweet pepper harvesting is analyzed, using Modal Analysis.

Additive manufacturing (AM) presents engineers and manufacturers with unprecedented design freedom compared to conventional manufacturing techniques. This freedom comes with its own challenges. The wide variety of AM techniques, machines, and design geometries introduces difficulties in building consistent parts with known material properties. Of particular interest is the anisotropic nature introduced in the AM process. While AM is being adopted for applications in a variety of industries, the uncertainties introduced in manufacturing are slowing its implementation for critical parts such as structural members and jointed elements. As part of the ongoing effort to alleviate these issues, this paper aims to quantify the dynamic response of AM parts built using a variety of build orientations and internal structures. Multiple parts with theoretically identical external geometries are excited by a shake table while high-speed data are collected using digital image correlation (DIC). A finite element model is developed and calibrated using the DIC data to characterize the material property changes due to selection of build orientation and internal structures.

Often, when testing structures, engineers assume the experimental system only exhibits linear behavior. This linear assumption means that the modal frequency and damping of the structure do not change with response level. In many assembled structures, components are connected through bolted joints. These systems behave in a weakly nonlinear fashion due to frictional contact at these interfaces, but often these structures are still treated linearly at low excitation levels. This work contains a case study where an assumed linear system exhibits nonlinear behavior. Because of this nonlinearity, if the force applied to the structure during linear testing is not sufficiently low then the test may capture a nonlinear frequency or damping instead of the true linear parameters. The errors associated with this linearization causes inaccuracy when simulating a system response. In particular, a linear substructuring problem is presented in which true linear frequencies and damping ratios are compared to slightly nonlinear counterparts to observe the error caused in the assembled response. This paper documents lessons learned and heuristics to be considered when capturing true linear parameters from a weakly nonlinear structure.

Force appropriation testing has long been used for ground vibration testing of aircraft, where it is critical to estimate the modal parameters and especially damping accurately. Recently, extensions were presented that allow systematic identification of the nonlinear normal modes (NNMs) of conservative and non-conservative nonlinear structures. While this method provides accurate results with high confidence, it is unfortunately quite slow and so the structure may be subjected to significant damage over the course of a test. This work proposes a new approach in which the test is performed more quickly by simply acquiring measurements near the nonlinear resonance, but without the time consuming tuning required to reach the resonance precisely. Then, the recently proposed single nonlinear resonant mode method is used to interpolate between test points in order to estimate the NNM from each set of forced responses. The method is first evaluated numerically using a reduced model of a curved clamped-clamped beam that exhibits both softening and hardening response due to geometric nonlinearity. Then the method is employed experimentally to measure the first two NNMs of a curved beam that was manufactured from plastic using a 3D printer and the results are compared to the traditional tuning approach.

Measured infield accelerometer data is very useful when evaluating the structural dynamics of any mechanical system. Researchers have great difficulty to make measurements from all particular regions where they are interested in due to shortage of measurement channels and difficulty of instrumentation. Thus the vibrations on the rest of the structure should be estimated with limited measured data.In this study a response acceleration estimation method based on input force estimation is employed. For estimation of applied forces and acceleration data form unmeasured locations of the structure, an accurate model of the system is required. Thus at first stages of the study, FE model is established and updated using experimental modal analysis results. Having the accurate dynamic model, vibration measurements of the structure are done under unknown forces to simulate operational conditions. To estimate applied load location, a state space model (SMM) of the structure is established using updated FE model. By employing augmented Kalman filter (AKF) approach, the location of the applied force is estimated from candidate force input locations, and the force signal is reconstructed.Knowing the force input location and the transfer function (TF) matrix of the structure, response acceleration power spectral density (PSD) data of the unmeasured locations can be estimated from measured locations. Employing Frequency Response Functions (FRFs) between excitation and measured location, PSD of the input force is obtained. Using input force PSD and FRF between excitation and unmeasured location, the unmeasured PSD data can be predicted.The methodology presented in this study is applied to the GARTEUR structure which is an internationally accepted de facto model. The FE model of the GARTEUR structure is set up first and subsequently the FE model is verified by modal tests. In the laboratory tests, GARTEUR structure is excited by impact hammer from an arbitrary location. Using the SMM of the GARTEUR and AKF approach, the location of the excitation force is estimated from candidate locations. After this step, PSD for the unmeasured locations are estimated from TF matrix of the structure and measured vibration data. Finally, both estimated and measured acceleration and force data are compared and satisfactory results are obtained.

Railway vehicle is a complexity dynamic system, vibration characteristics of flexible hanging equipment directly affects the dynamics of vehicle, especially coupled vibration between car-body and equipment. This paper was based on test bench f which supported excitation for the car. Solving method for the dynamic parameters were put forward. Meanwhile, modal parameters identification and coupling relationship analysis between car-body and flexible hanging equipment were carried out, which played an important role to the design of car.

In this work we explore the use of emerging full-field, high-resolution, modal identification techniques from video to characterize the viscoelastic properties of a material. Currently, there are no cost-effective methods to directly measure viscoelastic material properties at intermediate strain rates. These properties can be measured at low strain rates using quasi-static loading techniques, while Split-Hopkinson’s bar tests are used at high strain rates. Determining material properties at the intermediate strain rate regime is challenging as it requires large, expensive testing apparatuses and involves complex experimental protocols. An imager-based technique would provide a simpler, more affordable method for measuring viscoelastic material properties at these strain rates. To obtain measurements for intermediate strain rates of viscoelastic materials, we develop a testing protocol that involves creating a simple structure from the material-under-test and measuring its vibrational response using an imager. A finite-element model of the viscoelastic testing structure is also constructed. We extract full-field, high resolution mode shapes and modal coordinates from the video measurements of the structure as it vibrates in the desired strain regime. The frequencies of oscillation and the damping ratios are then identified. This information is intended to be used to perform model updating on the viscoelastic material properties of the finite-element model, resulting in an improved estimate of the material properties. Imager-based techniques are particularly attractive for explosive testing applications because the optics can be adapted to address the small sample sizes necessary for explosive testing. In addition to advancing viscoelastic material modeling, this work points toward the development of an imager-based modal analysis technique for identifying the structural dynamics of micro-scale structures. At this small scale, conventional contact-based sensors would result in mass-loading effects, yielding inaccurate measurements. As a solution, our full-field, high-resolution imager-based technique provides a method to characterize viscoelastic material properties while also demonstrating potential for future work in identifying structural dynamics of micro-scale structures.

The modal identification of large and dynamically complex structures (e.g. aircrafts) often requires a multiple-input excitation. Sine sweep excitation runs are applied in order to concentrate more energy on each line of the frequency spectrum. The work is aimed at developing a new data processing technique for aircrafts Ground Vibration Testing when a multi-point sine sweep excitation is used. The Virtual Driving Point method cancels out the necessity of performing as many sweeps as shakers in order to compute the system’s FRFs. Each single sweep can be individually performed and the measured data can be independently analyzed. As a result, modal analysis is more easily carried out and each single sweep leads to different modes, whose symmetric or antisymmetric nature depends on the relative phase between inputs that has been adopted during that run (mainly 0∘ and 180∘). This procedure allows to obtain more defined mode shapes and, more generally, reliable results in terms of modal parameters. New data processing techniques, as the ones object of this work, always require to be validated through their application to different data sets. It is indeed important, in order to asses the reliability of the method, to analyze and compare its outcome when applied to different data and to find a constant improvement with respect to results provided by conventional methods. For this reasons, different GVT measurements were performed and post-processed to validate the proposed approach. Before applying the method to a physically acquired data set, it has been tested on a numerically simulated three DOFs system in order to identify the possible results to which it could lead and the advantages that it could bring. Then, three GVT data sets, during which a two points excitation has been used, have been analyzed: a data set acquired during a measurement campaign on an airplane mockup; a data set related to a scaled airplane model, the Garteur model, which is bigger than the previous one and is characterized, like large aircrafts, by close modes; a data set acquired during a measurement campaign on a real aircraft, the eFusion Magnus electric aircraft developed in cooperation with Siemens.

The use of self-organizing maps and artificial neural networks for structural health monitoring is presented in this paper. The authors recently developed a nonparametric structural damage detection algorithm for extracting damage indices from the ambient vibration response of a structure. The algorithm is based on self-organizing maps with a multilayer feedforward pattern recognition neural network. After the training of the self-organizing maps, the algorithm was tested analytically under various damage scenarios based on stiffness reduction of beam members and boundary condition changes of a grid structure. The results indicated that proposed algorithm can successfully locate and quantify damage on the structure.

Extracting accurate material modal damping from a specimen can be very challenging due to the potential influence of the excitation and measurement system, and the required support of the specimen. This becomes particularly challenging if large amplitudes are required to determine nonlinear behavior, or large damping is present due to the material under investigation. An improved approach is proposed here to enable large amplitude, single harmonic, free decay damping extraction of a flat test specimen. It is based on a setup that uses the inertia of two large, free hanging end masses to enforce a pinned-pinned boundary condition with predetermined nodal locations, ensuring minimum effect of the support structure on the damping behavior. Excitation is achieved with the help of a removable electromagnetic shaker system that enables large amplitude single harmonic excitation, and smooth transition to a free, single harmonic decay. A Laser Doppler Vibrometer is used to measure the free decay, from which amplitude dependent damping can be obtained for individual modes via logarithmic decrement. Initial results of the approach show its great potential to provide reliable, amplitude dependent parameters with minimum impact of the test setup.

Structural connections are a crucial component of any structural system. The connection stiffness can impact the static and especially the dynamic behavior of a structure. Therefore, reliable finite element modeling of the structural systems involves accurate estimation of their connections stiffness parameters. Accurate representation of connection stiffness parameter is one of the most challenging steps in model verification as connections are physically small parts of a structure and some parameter estimation procedures may lack the sensitivity to change in connection behavior to capture the stiffness parameter of connection elements. One of the most well-known experimental structures which has been extensively used in the model updating research field in recent years is a structural frame set up in the University of Central Florida which is known as the UCF Grid. This experimental structure is an instrumented planar grid comprised of several steel members interconnected by gusset plates. The grid is instrumented by eight uniaxial accelerometers to capture the accelerations of the specific nodes of the structure when the grid vibrates due to an excitation. In this paper, the modal data of the grid obtained experimentally by an impact test are used for estimation of the stiffness parameters of the grid joints. A modal based error function method is employed to update the finite element model of the grid built in SAP2000® environment. For the model updating computations, an optimization MATLAB® code is linked to the SAP2000® Open Application Programming Interface to facilitate the parameter estimation procedure. The updated finite element model of the grid based on new estimations for its joints’ stiffness parameters could represent the structural behavior of the grid in a more reliable scheme.

The Brandenburg industrial landscape is characterized by heavy industry sectors such as metallurgy and mining. Most of these industrial plants (ironworks, refineries, mines, etc.) have their origin in the state-planned rapid industrialization the German Democratic Republic underwent during the 1950s. Therefore, many critical constructive parts of these industrial plants have already surpassed their life expectancy or its remaining life expectancy can no longer be clearly determined due to poor documentation.Heavy duty bridge cranes are an essential part of heavy industries or warehouses. During the course of their lives, these cranes and their rails are exposed to many different loads, damages and material fatigue processes during operation. Runway beams, those where the bridge crane runs on, are especially prone to the generation of cracks due to material fatigue. Condition monitoring and early damage detection can ensure the long-term load capacity and serviceability of bridge cranes, and contribute to a more cost-effective maintenance.This paper presents the results of a feasibility study for a vibroacoustic damage detection procedure on bridge crane runway beams. A segment of a railway beam has been studied with experimental modal analysis and the results used to correlate and validate a FE model, generated by means of optical scanning. The modal analysis was performed by means of automatic impact excitation and Scanning Laser Doppler Vibrometry. Several damage cases were later simulated in the FE model, evaluating this way the development potential for a vibroacoustic method for damage detection in bridge crane railway beams.

Noise, vibration and harshness (NVH) problems are critical issues to be tackled by automotive industry to ensure comfort of people. The key role of this problem is played by the susceptibility of the structure to vibrations. Therefore, design values such as the modal parameters (i.e. eigenfrequencies, damping ratios, mode shapes and modal scaling factors) are essential and their experimental validation is of high interest. At this purpose, both Experimental and Operational Modal analysis (EMA and OMA) represent a powerful approach. Previous works have investigated and implemented a completely automated OMA technique for continuously tracking the modes of machines under normal operating conditions. In this work the automatic modal parameter estimator is used to perform automated experimental modal analysis on data acquired from a car body-in-white excited by means of multiple shakers. Fully automated modal analysis is performed with special focus on damping value and mode shape validation. The results obtained with the manual and automatic modal parameter estimators are compared in order to show the validity and performance of the implemented method. Modal parameters estimation is based on the state-of-the-art pLSCF algorithm. To make it suitable for continuous analysis, the algorithm is improved by eliminating all the required human interactions.

Design and development of tires require accurate characterization of their dynamic response. For this purpose, Experimental Modal Analysis (EMA) techniques have been heavily utilized. However, as the focus shifts from stationary to rotating tires, testing solutions become limited and more challenging. Conventionally, cleat excitation with force measurements on the fixed spindle has been the standard approach for testing tires in rotation. However, the limited control on the input excitation has hindered the characterization of rotating tires, especially at high frequency.In this work, EMA of rotating tires mounted on a free-spindle rotating modal rig is investigated. Testing is conducted in stationary and rotating frames-of-reference. In the former configuration, electrodynamic shakers attached to the free-spindle are used to excite the tire and a Scanning Laser Doppler Vibrometer (SLDV) is used to measure the response at the sidewall. For the later frame-of-reference, piezoelectric actuators mounted inside the rotating tire are utilized for excitation, whereas accelerometers mounted on the sidewall are used for response measurement. The capabilities and limitations of both testing configurations are investigated at several rotational speeds. The effects of contact patch excitation and the frequency range of interest on EMA of rotating tires are also addressed.

Operational Modal Analysis (OMA) is one of the branches of experimental modal analysis which allows extracting modal parameters based on measuring only the responses of a structure under ambient or operational excitation which is not needed to be measured. This makes OMA extremely attractive to modal analysis of big structures such as wind turbines where providing measured excitation force is an extremely difficult task. One of the main OMA assumption concerning the excitation is that it is distributed randomly both temporally and spatially. Obviously, closer the real excitation is to the assumed one, better modal parameter estimation one can expect. Traditionally, wind excitation is considered as a perfect excitation obeying the OMA assumptions. However, the present study shows that the aeroelastic phenomena due to rotor rotation dramatically changes the character of aerodynamic excitation and sets limitations on the applicability of OMA to operational wind turbines. The main purpose of the study is to warn the experimentalists about these limitations and discuss possible ways of dealing with them.

Over many years, members of the experimental modal analysis community have been challenged over the use of modal orthogonality and cross-orthogonality criteria for validation of experimental modal vectors and for assessment of test-analysis correlation, respectively. At the heart of the challenge is the role played by the potentially inaccurate TAM mass matrix, which is derived from a mathematical model. Recent work that exploits left-hand eigenvectors, estimated by the SFD technique, provides a promising way out of the TAM mass matrix impasse. Modal orthogonality, defined as the product of left- and right-handed experimental eigenvectors (real or complex) is mathematically an identity matrix. This guarantees that SFD estimated modes are always perfectly orthogonal. Modal cross-orthogonality, defined by product of analytical left-hand eigenvectors and experimental right-hand eigenvectors (after consistent “mass” normalization of both sets) does not possess the desired “unit maximum coefficient magnitude” property. Therefore, an alternative cross-orthogonality definition, based on weighted complex linear least-squares analysis, is evaluated and found to possess the desired property. Employment of (1) the left- and right-handed experimental eigenvector based orthogonality matrix and (2) the weighted complex linear least-squares based cross-orthogonality matrix represents a “game changer” that potentially frees the experimental modal analysis community from the potentially inaccurate TAM mass matrix.[Test FEM Correlation Left Eigenvectors]

The goal of this work is to understand the generation and propagation of one-dimensional steady state traveling waves in a finite medium with a two-force excitation methodology. The solution to the second order partial differential equation describing the equation of motion for a string is theoretically solved considering a fixed-fixed boundary condition. The parameters that affect the generation and propagation of waves should be well understood to control and manipulate the desired system’s response. The string equation is solved by rearranging it based on linear wave components and phase difference components needed to generate steady-state traveling waves in a string. Two excitation forces are applied to a string near the boundaries to understand the generation and propagation of traveling waves at various frequencies. Determining the quality of the traveling waves and understanding the parameters on the wave propagation of a string can lead to further understand and leverage various engineering disciplines such as mechanical actuation mechanisms, propulsion of flagella, and the basilar membrane in the ear’s cochlea.

Tuned vibration absorbers (TVA) provide passive energy dissipation from their primary structure but are limited to only having significant impact on a single frequency. Many researchers have theoretically determined optimal TVA parameters to build an array of varied sized TVAs to absorb a range of frequencies and ultimately flatten an entire peak of a structure’s frequency response function (FRF). These theoretical approaches often only considered the primary structure to have a single degree-of-freedom and did not consider material and spatial constraints that would normally arise in physical implementation. This study provides the method and results of designing and implementing multiple arrays of TVAs to flatten the FRF at and around both modal frequencies of a two-degree-of-freedom (2DOF) structure. The host 2DOF structure is comprised of two small wooden blocks supported by four thin aluminum posts in a two-story setup with base excitation. A total of 20 TVAs were attached to each primary mass—ten targeting frequencies around the low-frequency mode and ten targeting frequencies around the high-frequency mode. The TVAs were cantilever beams made of varied length dry fettuccini pasta with some including modeling-clay tip masses. The final design successfully reduced the original 2DOF structure’s first natural frequency response by more than 9 dB and second natural frequency response by more than 19 dB for both primary masses.

Tire-pavement induced vibrations are among the main sources of vehicle exterior noise. Its dominant spectral content is approximately within 500–1500 Hz. For these frequencies, previous studies have proposed the existence of travelling waves along the tire’s circumferential direction, as opposed to a modal behavior. This distinctive structural response generates acoustic waves that propagate into the environment. Unfortunately, no noise measurements above 500 Hz that can be used to validate this assumption have been conducted. In this work, a methodic measurement approach for tire vibrations and noise within the frequency range of interest is presented. Two tires of different size and construction were horizontally suspended over a test rig inside an anechoic room. In order to avoid the interference with the rig’s rigid body modes, they were hanged with low stiffness cords. The tires were then excited with an impulse input by using an impact hammer. Noise was measured using a 19 microphone arc array. The array formed a semi-circle around the tire’s cross section, thus providing noise levels induced by both sidewall and tread band vibrations. The arc was then rotated around the tire in order to capture tire noise directivity patterns. On the other hand, vibrations measurements were performed by using accelerometers on a set of 35 equally spaced points along the mid-tread line of the tires. A chirp signal was implemented as an input in order to fully characterize the tire response within the frequency range of interest. Noise measurements show the expected levels decay along the circumferential direction, whereas structural tire responses suggest the existence of waves that propagate along this direction.

This work deals with the application of a robust adaptive vibration control scheme on a flexible crane-type structure, which is based on Positive Feedback Control and on-line algebraic identification strategies of the most important modal parameters of the mechanical structure submitted to changes on mass, viscous damping and/or stiffness, common under variable payloads, as well as the estimation of exogenous excitation forces. For active vibration control the flexible structure employs a PZT stack actuator. Moreover, the modal parameters are estimated using on-line algebraic identification algorithms, which lead to fast estimations of those critical natural frequencies and modal damping on a given frequency range. This information is then used to synthesize and tune an adaptive Positive Position Feedback control scheme, for robust active damping injection tasks on certain specific mode shapes of the flexible structure. Some experimental results are provided to describe the fast and effective vibration attenuation on an experimental setup.

This work considers the experimental evaluation on a two-wheel tractor, employed for small agricultural practices, to characterize the human-structure-soil interaction under typical activities into small greenhouses (e.g., tillage). First, the two-wheel tractor is evaluated to get its modal parameters and, then, the machine is tested for endogenous excitation due to different engine speeds and for several working scenarios (operational modal analysis). In particular, the modal testing is focused on the human-structure-soil interaction to verify how the vibrations and noise affect to the human operator and, thus, propose passive solutions to reduce adverse effects caused on humans via passive damping injection and/or proper structural modifications. The results are used to evaluate the overall dynamic performance in a system-theoretic approach for decision-making during the design and evaluation of this machinery.

Impact excitation is a common technique used for modal testing of structures. The quality and bandwidth of the dynamic model of a structure obtained through impact testing directly depends on the characteristics of the impact excitation. However, applying optimal, or even satisfactory, impact excitation to structures manually (using impact hammers) requires considerable experience. Indeed, even experienced personnel may have much difficulty in applying single-impact, repeatable (force magnitude, impact location, impact orientation) excitations with a required frequency bandwidth. As such, impact testing can become very time consuming, necessitating very large number of repetitions to obtain acceptable coherence values and an accurate dynamic model of the structure in the form of frequency response functions (FRFs).To address these challenges, in this work, an impact excitation system (IES) is implemented, where the excitation is provided by a flexure-based system. In this system, the motion of the instrumented hammer is controlled by a custom-made flexure. By modifying the flexure geometry, initial displacement of the hammer (dictated by an electromagnet), the initial distance between the hammer tip and the sample surface, and the added mass at the hammer tip, a broad range of impact forces and frequency bandwidths can be obtained in a highly reproducible fashion. To demonstrate the repeatability and reproducibility of the presented system, impact testing is performed on a solid cast iron block with different force levels. The results between the automated and manual testing are compared by doing several repetitions. Finally, the given system is used in testing of a turbine blade to obtain its dynamics in the form of FRFs. As a result, it is concluded that the flexure-based impact excitation system enables applying controllable force levels and required frequency bandwidth to obtain accurate dynamic models of structures.

The ability to simulate the aeroacoustic and thermoacoustic loading typically experienced by space access vehicles and hypersonic flight vehicles is accomplished through the use of a progressive wave tube (PWT) housed in the Combined Environment Acoustic Chamber (CEAC). Simulating these types of acoustic loading requires the test article be mounted flush with the wall of the PWT, exposing the test article to the propagating pressure wave. This mounting capability is achieved through the use of a strong-back fixture, referred to in this work as a test cart, whose initial design was to withstand static pressure loading on the front face where a test article is mounted. However, this test cart experiences dynamic loading during these acoustic tests. Preliminary modal evaluations of test articles mounted to the cart have indicated that the test cart has several natural frequencies in the testing frequency range of interest (0–1000 Hz). The interaction between the test cart and test article is undesirable because it contradicts the analytical rigid boundary conditions and could also lead to unrealistic failure as a result of over excitation of the specimen if the same mode exists in the test cart and test article. The goal of this work is to characterize the test cart using experimental modal analysis and evaluate the need for modification or complete redesign of the test cart to eliminate modes below 1000 Hz and maintain the intended functionality of the cart.

For fatigue estimation of many large structures the damping coefficients of the first couple of modes are the most essential. These modes can often be identified, by Operational Modal Analysis (OMA), by using a low number of sensors. However, it is not well known how the number of sensors and their locations are affecting the damping estimates provided from OMA. In this paper it is investigated how the damping estimates from OMA depend on the number of sensors and their locations. In addition, the so-called reference-based OMA methods using quadratic Hankel matrix, where only a few DOFs are used for calculations of the non-parametric functions (e.g. correlation functions), is compared to using the squared (full) Hankel matrix. All the results are presented based on experimental data.

This paper describes a series of ambient and forced vibration tests conducted on an old 44 story reinforced concrete building; Empire Landmark Hotel, located in Downtown Vancouver, Canada. The structure of the building consisted of reinforced concrete frames with concrete core walls, shear walls and concrete slabs. Three series of sensors were used to measure the ambient and forced vibrations of the building in multiple locations. Modal response analysis was performed to identify the dynamic properties of the building. As results, the natural frequencies, damping ratios and mode shapes of the building were presented.

This paper describes a series of ambient vibration tests conducted on a full scale wood frame building specimen to determine the dynamic properties of the typical wood frame school buildings in British Columbia, Canada. The specimen was subjected to the shake table tests to simulate the magnitude 8.8 earthquake and its aftershocks on the building. A set of sensors were used to measure the ambient vibration of the specimen before and after the main shock and after the sequent aftershocks. Modal response analysis was performed to identify the dynamic properties of the specimen. As the results, the natural frequencies, damping ratios and mode shapes of the specimen before and after each shake table test were presented.

Determining the dynamic characteristics of rotor suspensions is needed to make accurate predictions of rotor behavior. If direct measurements are unavailable, a method for estimating them is needed. This paper describes a method for estimating suspension characteristics from rotor runout data measured by proximity probes in a rotor test stand. Comparison of measured critical speeds with values predicted using the estimated rotor suspension parameters for a test rotor show good agreement, indicating that the method is valid.