Special Topics in Structural Dynamics, Volume 5

This work treats the lateral harmonic forcing, with spatial dependencies, of a two-segment beam. The segments are compact so Timoshenko theory is employed. Initially the external transverse load is assumed to be spatially constant. The goal is the determination of frequency response functions. A novel approach is used, in which material and geometric discontinuities are modeled by continuously varying functions. Here logistic functions are used so potential problems with slope discontinuities are avoided. The approach results in a single set of ordinary differential equations with variable coefficients, which is solved numerically, for specific parameter values, using MAPLE^®. Accuracy of the approach is assessed using analytic and assumed mode Rayleigh-Ritz type solutions. Free-fixed and fixed-fixed boundary conditions are treated and good agreement is found. Finally, a spatially varying load is examined. Analytic solutions may not be readily available for these cases thus the new method is used in the investigation.

The success or failure of a structure can hinge on the proper selection of its fasteners. A predominant failure of a fastener during random vibration is that of fatigue. This generally occurs after the loss of the bolt pre-tension. Time domain methods for fatigue assessment of fasteners are used for typical environments in the Aeronautics industry. Also explored is if the multiaxial loading of random events creates proportional or non-proportional loading in the fasteners. This work finds that if the applied loads at a fastener jointed interface from a random vibration environment are such that the preload is greatly reduced, then it is essential to analyze fasteners with a multiaxial fatigue method.

Electromagnetic shakers and closed loop control systems are commonly used in qualification tests for environmental vibration conditions. However, at high frequencies shakers have resonances and anti-resonances. Resonances can be beneficial in that the shaker needs to exert less force to achieve the desired environment, but they can make it more challenging for the control system to match the desired environment. Anti-resonances are more problematic because they represent frequencies where the voltage input to the shaker causes little motion (at some locations on the slip table or adapter plate). Hence, these can cause the system to require driver voltage levels above the controller capacity and cause the test to abort. Furthermore, an anti-resonance is in essence a motion that is unobserved at the point(s) of interest, and hence they may lead to damage if internal components experience much higher vibration levels than the control accelerometer. This paper proposes and characterizes a hybrid shaker system that would use a piezoelectric actuator in addition to the electromagnetic shaker to create a MIMO control system. It is hoped that the additional control effort introduced by the piezoelectric actuator could be used to expand the frequency range over which the desired environment can be achieved.

Experimental modal analysis via shaker testing introduces errors in the measured structural response that can be attributed to the force transducer assembly fixed on the vibrating structure. Previous studies developed transducer mass-cancellation techniques for systems with translational degrees of freedom; however, studies addressing this problem when rotations cannot be neglected are sparse. In situations where rotations cannot be neglected, the apparent mass of the transducer is dependent on its geometry and is not the same in all directions. This paper investigates a method for correcting the measured system response that is contaminated with the effects of the attached force transducer mass and inertia. Experimental modal substructuring facilitated estimations of the translational and rotational mode shapes at the transducer connection point, thus enabling removal of an analytical transducer model from the measured test structure resulting in the corrected response. A numerical analysis showed the feasibility of the proposed approach in estimating the correct modal frequencies and forced response. To provide further validation, an experimental analysis showed the proposed approach applied to results obtained from a shaker test more accurately reflected results obtained from a hammer test.

Frequency response functions (FRFs) of thin workpieces, which are typically clamped step-thickness cantilever plates, are needed at every stage in order to avoid chatter (cutting-related instability). Due to variability of machining procedure, FRF estimation is proposed to be carried out at the embedded computer at machine tool, which has limited computing power. A combination of Reissner-Mindlin plate theory and Rayleigh-Ritz method are used to form small system matrices to estimate FRFs. Mode shapes of uniform-thickness Timoshenko beams are taken as the admissible functions. Example shows that a system with approximately 500 DOFs, which is much smaller than a full finite-element model with 10,000’s of DOFs, can estimate the first four natural frequencies with a similar error level during every step of cut. Additionally, experimental natural frequencies are used to estimate the contact stiffness at the vice. As a result, the change in those natural frequencies during machining are determined accurately.

Up to date concerns of automotive authorities are environmental sustainability, fuel efficiency and CO₂ emission. Lightweight component design is a key solution for those concerns. In a passenger vehicle, total weight of the seat structures is comparably high due to their quantity per vehicle. Therefore, seat structure has been chosen for lightweight design. Moreover, seat structure, seat belts and seat-belt anchorages are vital components of vehicles considering passenger safety in case of an accident. Thus, these components have to pass safety tests defined in European regulation ECE-R14. In order to reduce the number and cost of the regulation tests, a virtual test model is carried out using nonlinear finite element methods. Additionally, thickness and topology optimizations are performed to investigate light weighting opportunities on seat structure. Explicit and implicit methods are used to obtain virtual test model by using Radioss and ANSYS, respectively. The required validation process is carried out by performing seat pull test according to ECE R-14 regulations. Seat back displacement data is collected during the experiment. After comparison of the experiment result with both implicit and explicit analyses results, the proper virtual test model is chosen by taking computation time and accuracy into account. The validated model is used to optimize thickness and topology. The final design after optimization is evaluated in virtual test environment per ECE R14 regulation.

In this paper, we show how Operating Deflection Shapes (ODS’s) and mode shapes can be obtained experimentally from measurements that are made using only two sensors and two short wires to connect them to a multi-channel acquisition system. This new test procedure is depicted in Fig. 7.1. Not only is the equipment required to do a test much more cost effective, but this method can be used to test any sized test article, especially large ones.

A “round trip” example is used to show how an original set of modal parameters can be recovered by curve fitting a single reference set of output-only Cross spectra, and a single reference set of FRFs.

The use of the Bayesian tools in system identification and model updating paradigms has been increased in the last 10 years. Usually, the Bayesian techniques can be implemented to incorporate the uncertainties associated with measurements as well as the prediction made by the finite element model (FEM) into the FEM updating procedure. In this case, the posterior distribution function describes the uncertainty in the FE model prediction and the experimental data. Due to the complexity of the modeled systems, the analytical solution for the posterior distribution function may not exist. This leads to the use of numerical methods, such as Markov Chain Monte Carlo techniques, to obtain approximate solutions for the posterior distribution function. In this paper, a Differential Evolution Markov Chain Monte Carlo (DE-MC) method is used to approximate the posterior function and update FEMs. The main idea of the DE-MC approach is to combine the Differential Evolution, which is an effective global optimization algorithm over real parameter space, with Markov Chain Monte Carlo (MCMC) techniques to generate samples from the posterior distribution function. In this paper, the DE-MC method is discussed in detail while the performance and the accuracy of this algorithm are investigated by updating two structural examples.

Rollovers are recognized as the most dangerous type of road accident. Among all accidents, they are the most challenging to analyze due to the complex nature of rollover accidents. The aim of this paper is to analyze the influence of the structural components, more specifically skin parts, on the safety of occupants during rollover crashes. Full scale experiments and components testing are needed to evaluate the safety of the passengers. As part of this study, full rollover test according to ECE R66 test procedure was conducted. Additionally, series of Finite Element (FE) analyses using LS-Dyna were performed to evaluate capabilities of skin parts to absorb the crash energy and its influence on the crush mechanism. Along with structural assessments, Anthropometric Test Devices (ATD) were used to evaluate the severity of the rollover crashes. Injury parameters such as Head Injury Criteria (HIC), chest acceleration, pelvic acceleration, and neck forces were measured for different rollover scenarios. The results showed that for the bus with high deformation of skin-cage structure the injury outcomes were lower than the injuries from the stiffer passenger compartment. Preliminary Results of this study are in conflict with the of UN ECE R66 safety assessment results, which indicate that stiffer buses are safer. Hence, further work needs to be carried out to find the links between an intrusion of skin and cage, and severity of injuries.

Automatic impact modal testing is a technique gaining momentum in recent years thanks to the popularization of Scanning Laser Doppler Vibrometry. These systems allow automatizing the output measurement of thousands of degrees of freedom in a short time. The use of automatic impact modal hammers allows automatizing the excitation input and broadband excitation without loading a structure with an extra mass or other drawbacks. However, the impact force repeatability is a prominent concern among test engineers, especially those who work with materials with non-proportional force/response ratios. Assessing the impact force repeatability of a given automatic modal hammer or test rig is necessary in order to ensure the right response level is measured impact after impact.

The assessment procedure can be misleading if not done right. Studying the automatic modal hammer repeatability under typical modal test conditions invariably leads to impact signals strongly distorted by the so called picket fence effect. This results in impacts sampled by only 3–4 data points; insufficient to accurately describe the actual impact force signals and the short contact times between hammer tip and structure. In the reality, the impacts are of larger magnitudes and shorter contact times than what is shown by the analyzer in typical test conditions.

This work studies the influence of the sampling frequency and the test structures used on the repeatability assessment of automatic impact modal hammers. Impact force signals are acquired in this work with enough resolution to eliminate the picket fence effect and truly evaluate how repeatable and reproducible automatic impacts are. The practicality of the procedure, which involves very large datasets and long testing times, is discussed. Guidelines are offered at the end of the paper for a successful repeatability and reproducibility assessment of automatic impact modal hammers.

The emergence of systematic condition monitoring of railway infrastructure has the potential to reduce the cost of providing a safe network. The traditional ‘inspect and rectify’ style of maintenance planning is being increasingly complemented by a ‘monitor, predict and prevent’ approach. In order to facilitate this, the frequency of track measurement must be increased from the current periodic measurements using specialised instrumented vehicles. In recent years there has been an increased interest in the challenge of finding railway track longitudinal profile using the response of passing instrumented vehicles as a by-product of regular service. A method is presented where the inertial response of a train bogie is used as input to an optimisation technique that infers the track longitudinal profile. The method finds the track profile that generates a numerical output from a vehicle-track interaction model that best fits a measured response. Experimental data is used to validate the longitudinal profile estimation algorithm. An Irish Rail InterCity train was instrumented to capture in-service vehicle responses. During the testing period, the longitudinal profile of a section of this line featuring a known settlement issue was surveyed by traditional means, for reference. A calibrated vehicle is used in the optimisation algorithm to find the longitudinal profile that generates a numerical vehicle response best fitting the measured data. The known track settlement is found quite well using the calibrated vehicle, thereby validating the method. The reproducibility of the method is assessed. While improvements in accuracy and reproducibility are required to bring the method up to best practice standards, the information provided demonstrates the ability to find localised changes in track profile.

The existence of free boundary conditions is frequently assumed for Experimental Modal Analysis (EMA) of a structure. However, free-free conditions can only be approximated because the structure must be supported in some manner. Therefore, comparing simulated data with experimental data can be deceiving, because these suspensions falsify modal parameters especially structural damping and stiffness. The current scenario of structural analysis is more towards focusing on modal updating or correlation, rather than the simulation results (FE) or the experimental results. So it is imperative to bridge the gap between FE and EMA, by carefully studying various parameters.

To overcome these drawbacks, levitation is suggested as a truly free-free suspension method. The levitation method was developed to allow a non-destructive, adaptable, and completely contactless approach for material testing: the structure under test is suspended on a thin film of pressurized air providing an aerodynamic bearing, levitating the specimen. Two suspension devices were constructed. Pressurized air is circulated into a casing with a single outlet (“air cushion”) or a fine grid of outlets (“air bed”).

A study was performed to investigate the influence of the support conditions on the modal parameters eigenfrequency and damping. Tested specimens were a brass plate, a stainless steel plate and two composite material probes. The tested suspension methods were (a) foam mat, (b) air cushion and (c) air bed. Modal tests were performed using a Scanning Laser Doppler Vibrometer (SLDV) and an automatic modal hammer for excitation. Evaluations of the measurements were performed manually.

The results showed that the detected eigenfrequencies of the metallic specimen have a variation below ±0.3% for the tested suspension methods. This variation is 10 times higher for the composite plates and lies between ±3%. The damping ratios of the levitation suspensions show the different material behavior of metallic and composite specimen: damping ratios of metallic specimen lie between 0.05–0.5% whereas damping ratios of composite plates are ten times higher and lie between 0.3% and 3%. The damping ratios measured with the air cushion are smaller than the damping ratios for the air bed supporting the hypothesis that a laminar air film under the specimen leads to less additional damping.

The study shows that EMA can be performed on metallic and composite specimens using contact-less suspension methods. Especially for light-weight material specimens where EMA cannot be performed or where the results are not reliable, the contact-less suspension (levitation method) can be used.

A critical issue for structural health monitoring (SHM) strategies based on pattern recognition models is a lack of diagnostic labels for system data. In an engineering context these labels are costly to obtain, and as a result, conventional supervised learning is not feasible. Active learning tools look to solve this issue by selecting a limited number of the most informative data to query for labels. This article demonstrates the relevance of active learning, using the algorithm proposed by Dasgupta and Hsu (the DH active learner). Results are provided for applications of this technique to engineering data from aircraft experiments.

This work proposes the implementation of a multimodal and fully passive piezoelectric tuned vibration absorber that mitigates several resonances of a nonlinear structure. By extending a principle of similarity, an analogous electrical network is designed in order to reproduce the dynamics of the mechanical structure. Several electrical resonances are simultaneously tuned to the mechanical resonances, thus providing the equivalent of a multimodal vibration absorber from electromechanical coupling through an array of piezoelectric patches. Furthermore, the use of a nonlinear capacitor in the analogous network generates an autonomous adjustment of the electrical resonance frequencies when the structure reaches the nonlinear domain. The interest of this method is proved experimentally by mitigating vibration over a wide frequency range that covers the first three modes of a beam with cubic nonlinearity.

Random vibration under preload is important in multiple endeavors, including those involving launch and re-entry. In these days of increasing reliance on predictive simulation, it is important to address this problem in a probabilistic manner – this is the appropriate flavor of quantification of margin and uncertainty in the context of random vibration. One of the quantities of particular interest in design is the probability distribution of von Mises stress. There are some methods in the literature that begin to address this problem, but they generally are extremely restricted and astonishingly, the most common restriction of these techniques is that they assume zero mean loads. The work presented here employs modal tools to suggest an approach for estimating the probability distributions for von Mises stress of a linear structure for the case of multiple independent Gaussian random loadings combined with a nonzero pre-load.

Currently, structural health monitoring (SHM) represents one of the main areas of interest in engineering, being applied both for maintenance cost reduction and operational safety. In this contribution, a hybrid SHM system is proposed as a complementary methodology for the damage diagnosis of a typical aeronautical material panel (aeronautical aluminum plate 2024-T3), through the integration of two SHM techniques, namely the electromechanical impedance technique and the Lamb waves. For the diagnosis, a damage metric extracted from the impedance signatures of the structure was used in conjunction with an algorithm for localization of the damage by considering Lamb waves. In addition, temperature compensation techniques were systematically employed to avoid false diagnoses and a statistical model was developed to establish threshold indices according to a predefined confidence level. Thus, this work presents an evaluation of the sensitivity of the proposed techniques, considering a success rate. Finally, the results show the great potential for the integration of the two techniques together with statistical approach.

Many industries are moving toward the opportunities afforded by additive manufacturing (AM) techniques as a primary manufacturing method for components. Additionally, AM continues to be an effective option for rapid prototyping in many applications. Some advantages AM processes have over traditional manufacturing include the ability to create highly complex and multi-material parts with little or no restriction on the geometry of the object at a relatively low price point. However, one of the main challenges that from AM techniques is the relatively high variation, in both material properties and exact geometry, from part to part. This variation calls for structural health monitoring of each individual part. In this paper, fiber Bragg gratings (FBGs) -- chosen because they can be embedded with minimal effect on the desired structure -- are inserted into AM geometries between layers, allowing for strain readings to be taken in situ. These measurements provide empirical data of incipient failure as AM parts tend to fail between layers. Fused deposition modeling (FDM) is used, as it is relatively common and inexpensive, to create parts into which the FBGs are embedded. Measurements taken under a variety of tests are compared to analogous finite element as well as analytical models allowing for model accuracy evaluation for AM parts. This work provides experimental data to validate models, in addition to forming a better understanding of the validity and procedure of embedding FBGs into FDM parts. Additionally, this work serves as a proof of concept and calls for more work to be done in the field.

In mechanical testing for system qualification, test engineers often face the challenge of representing a multi-axis vibration environment using a single-axis shaker table with only one degree of freedom for control. On large, complicated systems, the target environments are often defined as power spectral densities (PSDs) of a random vibration signal at multiple locations. These PSDs are almost invariably defined such that they are not physically realizable in any boundary condition. If one location responds with exactly its target PSD, another location will respond with a PSD that is different from its respective target. This paper presents a control strategy that minimizes an error between the responses and their respective targets, given a single actuation input. By estimating a model in real-time, an optimal input can be solved for each iteration of the control loop to adjust the excitation input and properly track responses. Implementing this control algorithm on a linear time invariant system by filtering the feedback sent to standard shaker controller hardware, there was a 4.3 dB and 3.5 dB variance in filter magnitude when using a 2.5 s model history and 5 s model history respectively. When applying this scheme to the LTV model, we noticed a stable change in filter magnitude. This paper has been approved for release as LA-UR-17-29695.

Multiple-Input Multiple-Output (MIMO) vibration control testing is nowadays recognized, in the environmental testing community, as an effective test methodology to accurately replicate the vibration environment a structure needs to withstand during its operational life. For these applications, the control process typically takes place in the frequency domain, within the data acquisition hardware’s embedded processor. Multiple analog voltages (the so called drives) are computed and streamed to the exciters in order to obtain a controlled response of a Unit Under Test (UUT) for a set of multiple control channels (the so called Controls, typically acceleration recordings). The multi-input excitation can be simultaneously applied with a set of multiple independent shakers or with multi-degrees of freedom (DOFs) shaking tables. In this case the drives are translated in the shaking tables DOFs in the three dimensional space. Advanced state-of-the-art hydraulic and electrodynamic multi-axis shakers are nowadays available to excite the UUT in all the six DOFs. On the other hand six DOFs motion platforms are widely used in motion simulation, where the aim is to use the platform to replicate the motion of an object in the three dimensional space. This is typically performed with dedicated algorithms, running on real time hardware that communicates with the platforms internal controller via Internet Protocol. Theoretically, the only step to combine this type of hardware with a data acquisition system and a vibration control software is to translate the drives in actuator displacements. However, adding layers to the communication chain, brings practical challenges. First of all, in order to establish any communication, it is mandatory to cope with the platforms protocol and real time requirements. Then, for any environmental testing application, it is fundamental to guarantee that the information sent is not inconsistently distorted or delayed in the communication process. This work aims to show the challenges and the solutions to combine a six DOFs motion simulation platform with an advanced off-the-shelf MIMO vibration control software and data acquisition hardware. Case studies will show the possibility of effectively using the motion simulation platform for both multi-axis random vibration control (MIMO Random) testing and time waveform replication (TWR).

This paper provides a summary of the various vibration tests that have been recently conducted on the test frame that has been used for various studies, starting from the IASC-ASCE benchmark for vibration damage identification technologies created in the early 2000s. The tests conducted include ambient-vibrations of various configurations of the test frame, which simulate different levels of structural damage. A detailed description of the conducted tests, as well as modal analyses of selected damage scenarios are included in the paper. This system will be online by mid-2018, and will allow interested parties to acquire real-time data from ambient vibration tests. Long term damage detection studies are also possible to be conducted.

Sound waves enter the outer ear and pass into the ear canal where the waves cause the eardrum to vibrate. Those acoustics are transmitted to the middle ear, and then pass through the innermost part of the ear, called the cochlea. The basilar membrane (BM), the main structural element of the cochlea, analyzes the waves propagating through it much like a biological Fourier analyzer. The waves travel from the base of the cochlea through the BM and get absorbed at the apex of the cochlea. These latter feature of the human auditory system is the inspiration to study waves propagating from one end of a beam to the other without reflections at the boundary.

Inspired by this the work herein numerically studies the dynamics of a uniform beam connected to a spring-damper system, in order to study some of the observed phenomenological behaviors of the basilar membrane. The location of the spring-damper system divides the beam into two dynamic parts: one which exhibits traveling waves and the other with standing waves. The various structural parameters of the setup have effects on the frequency bandwidth of the absorber and the portion of the beam with traveling waves. These parameters are numerically studied in this paper. These results lead us to new applications of the linear vibration absorber and possible explanation of the functionality of the Helicotrema in the cochlea.

Operators of construction trucks (such as wheel loaders, excavators, etc.) are often exposed to severe whole body vibrations induced by road/soil unevenness. Most of construction trucks are not equipped with any cabin suspensions unless seat and tires. Especially these latter are of paramount importance since they also govern the natural frequencies and the modes of vibration of the vehicle. Specific care has thus been paid to tires during the years and different technologies were adopted for their construction.

The present paper compares different methodologies to assess comfort of construction truck operators. In particular, outdoor tests prescribed by the standards to evaluate whole body vibrations experienced by operators are compared with ad hoc designed indoor tests carried out using a four-post test rig. Four sets of tires having the same dimensions but differing for type of construction. Tires were selected to evaluate potential differences, advantages and drawbacks of applied methodologies.

In industry, highly frequent inspection of tooling used to machine safety critical components is common place. Worn or damaged tools produce undesirable surface finishes leading often to early failure of the part due to fatigue crack growth. In the development stages of polycrystalline boron nitride tools, the tool wear inspection technique is an off-line run-to-failure method. This approach interrupts the cutting process intermittently, to measure the tool wear using optical and scanning microscopy. This method is time consuming and expensive, causing bottlenecks in production. The overall aim in industry is to develop an on-line, automated system capable of informing the operator of the tool’s imminent failure. This paper focuses on treating this process as a preventative maintenance problem by studying whether acoustic emission can be used as an indirect measurement of tool wear at any given time. Acoustic emission measurements taken from the machining process of face turning are investigated here. Basic analysis in the frequency domain using principle component analysis reveals a number of interesting insights into the process. Relationships between the sharpness of the tool and the magnitude of the frequencies suggests promising link between acoustic emission and tool wear.

A multi-span beam structure carrying multiple moving oscillators is seen in a variety of engineering applications, including highway bridges, elevated guideways and railways with moving vehicles, and tubes conveying fast-moving pods. With the oscillators having different speeds and varying inter-distances, the dynamic interactions between the supporting structure and the moving oscillators are usually complicated. Indeed, the number of moving oscillators on the structure is time-varying, and as such, a conventional solution method must frequently check the number of oscillators on the structure and adjust the numerical algorithm accordingly. Because of this, most investigations have been limited to just one or a few moving oscillators. Proposed in this paper is a new semi-analytical method that can systematically handle a beam structure with an arbitrary number of moving oscillators, without tedious number checking and algorithm adjustment. In the development, an extended solution domain (ESD) is firstly defined and a generalized assumed-mode method is then developed based on the ESD, which eventually yields a set of time-varying state equations. Solution of the state equations by a standard numerical integration algorithm gives the dynamic response of the coupled beam-oscillator system. Because the proposed method makes use of the exact eigenfunctions of the multi-span structure that are obtained by a distributed transfer function method, it is highly accurate and efficient in computation, as shown in a numerical study.