Topics in Modal Analysis & Testing, Volume 8

Health and athletic performance models can be used to prescribe an individualized training regimen to maximize improvement over a given period (e.g., preparing for a peak event). The Banister impulse-response (IR) model is a popular approach to describe the cumulative dynamic effects of training on athletic performance. The model describes both positive and negative training effects (PTEs and NTEs, respectively) that occur from a single training impulse, each having magnitude and decay parameters determined via testing of individual athletes. This work proposes that PTE and NTE responses from a single training impulse can similarly be described by the response of a single degree of freedom (SDOF) viscoelastic system. Cumulative training effects can then be modeled using the discrete form of the convolution integral in a manner similar to the IR model. The pedagogical advantage of this approach is to offer students studying mechanical vibrations a physical sense for how cumulative impulses relate to the response of a system. The other advantage of this approach is to initiate the discussion on how concepts from structural dynamics can be used to solve problems in exercise physiology.

In this context a parameter-free detection of significant frequencies during the test procedure was developed. To achieve this goal, the vibration data is recorded by a triaxial structure-borne sound sensor during the test. The evaluation is used for online crack detection, so that an early shutdown of the testing machine and thus a meaningful result over the life cycle of a mechanically joined joint is guaranteed.

For this purpose, time series are described in the frequency domain at each function value by a novel feature vector. The characteristics used are independent of external test parameters, such as the test frequency or force level. This makes it possible to change test parameters without additional algorithmic effort and without expert knowledge.

An experimental demonstration is presented highlighting the ability of low-cost, mass-produced, Bragg-grated fiber optic strain sensors to be used in response-only modal analysis. For the demonstration, a lightweight carbon fiber testbed instrumented with a single optical fiber containing 59 fiber optic strain sensors was mounted in a cantilever configuration. The dynamic strain response of the beam to impact excitation of an unknown magnitude and direction were recorded for five impacts. The resulting strain response time-history data was processed into sensor-to-sensor power spectral density information to allow for modal parameter estimation using ATA’s IMAT^™ software. The information for each of the derived power spectral density functions was combined into a power spectral mode indicator function to identify the poles of the system and extract the modal frequencies and damping ratios for the first seven flexible modes of the testbed. A scanning laser vibrometer was used to validate the modal parameters obtained by the fiber optic strain sensing system using conventional frequency-response-function-based experimental modal analysis techniques.

The vibration-based damage detection of structures has been an active topic among many research fields for, at least, the past four decades. In its early years, great effort has been devoted towards developing damage indicators computed from experimental data. Recently, as this problem is increasingly studied with a data science perspective, efforts are shifting towards finding highly meaningful features in experimental vibrational data, which is key to Machine Learning success. The present work had the objective of analysing how the performance of a Machine Learning approach compares to and may benefit from early-developed damage indicators. A performance comparison is presented between some early-developed damage indicators, based on both frequency and mode shapes, and an Artificial Neural Network (ANN) supplied with vibrational data. Also, the use of the early-developed damage indicators as inputs in the ANN was investigated. A two-span simply supported beam was used as the numerical experiment for the tests. The performance of each approach in different damage scenarios was discussed, as well as insights were drawn by putting the Machine Learning vibration-based damage detection approach into perspective with some of the simplest early-developed damage indicators.

One of the most challenging research areas in the field of structural dynamic and vibration is development of analytical solution for vibration and elasticity analyses of various structures. This paper focuses on developing a new semi-analytical solution to obtain lateral deflection of a wind turbine blade under external loadings. The proposed method maps a wind turbine blade to an Euler–Bernoulli beam with same conditions, in order to find vibration and dynamic responses of the blade by solving analytical vibration solutions of the Euler–Bernoulli beam. Piezoelectric patches are used in this research as actuator-sensor to excite the structures and sense the responses. The governing equations of the beam with piezoelectric patches are derived based on integration of the piezoelectric transducer vibration equations into the vibration equations of the Euler–Bernoulli beam structure. Finite Element model of the wind turbine blade with piezoelectric patches is developed. A unique transfer function matrix is derived by exciting the structures and achieving responses. The beam structure is projected to the blade by using the transfer function matrix under external forces. The results obtained from the mapping method are compared with the results achieved from the FE model of the blade. A satisfying agreement has been observed between the results. The results show that by increasing the distance from the base of the wind turbine blade structure, the accuracy of the method experiences a descending trend.

Structural dynamics can have a significant influence on the performance of robots. This has already been extensively shown for robot manipulators. In a previous work, we have also shown this for our biped walking robot Lola. Vibration issues caused by the mechanical structure of Lola are visible in the joint controllers and are limiting the performance of her walking and balancing controllers. We showed this by measuring the open-loop transfer functions of these controllers and linking the dynamics of the control plant to the structural dynamics of Lola by comparing the results to an Experimental Modal Analysis. The knowledge gained from this analysis influenced the redesign of Lola’s upper-body structure. In this work, we will show the benefits gained from the new mechanical design by performing and comparing the same tests as done in our previous work.

This chapter describes a novel and oven-controlled crystal oscillator (OCXO) high-precision synchronised wireless data acquisition system for modal testing of large structures. The system was used for the first time for a rare FRF-based modal testing of a full-scale multi-storey building in operation. National Instruments’ CompactRIO and LabVIEW were utilised to develop wireless multi-channel data loggers to resolve typical, and sometimes insurmountable, problems related to the logistics of long cables connecting sensors with data acquisition in ambient vibration testing (AVT) exercises on operational structures. Several OCXO-based data loggers were used to distribute sensors wirelessly across the structure, using a sub-microsecond sensor synchronisation procedure to measure simultaneously not only the structural vibration response but also the forcing function needed in FRF measurements. As part of the setup, a spectrum analyser (SA) was used to provide the shakers’ excitation signal and perform a point accelerance FRF measurement at a location close to the data acquisition centre and with minimum wired infrastructure. Two different data acquisition systems (OCXO- and SA-based) used independent time clocks.

To validate the OCXO-based FRF measurement in buildings, modal testing was carried out on a 15-tonne laboratory-based test floor and a full-scale seven-storey condominium building made of cross-laminated timber. The combination of distributed OXCO-based wireless and synchronised data loggers coupled with an SA-based force generation and FRF point mobility quality assurance measurement was successfully used to identify the sway modes’ dynamic properties of the structure.

Signal decomposition is an effective tool to assist the identification of modal information in time-domain signals. Two signal decomposition methods, including the empirical wavelet transform (EWT) and Fourier decomposition method (FDM), have been developed based on Fourier theory. However, the EWT can suffer from a mode mixing problem for signals with closely spaced modes, and decomposition results by FDM can suffer from an inconsistency problem. An accurate adaptive signal decomposition method, called the empirical Fourier decomposition (EFD), is proposed to solve the problems in this work. The proposed EFD combines the uses of an improved Fourier spectrum segmentation technique and an ideal filter bank. The segmentation technique can solve the inconsistency problem by predefining the number of modes in a signal to be decomposed, and filter functions in the ideal filter bank have no transition phases, which can solve the mode mixing problem. A numerical investigation is conducted to study the accuracy of the EFD. It is shown that the EFD can yield an accurate and consistent decomposition result for a signal with closely spaced modes, compared with decomposition results by the EWT, FDM, variational mode decomposition, and empirical mode decomposition.

Reducing vibrations in a 3D printer is crucial in improving the quality of printed prototypes. Ideally, the noise from the actuators in 3D printers should not hinder the print quality. However, isolating the printer surface from vibrations is challenging. Therefore, in this paper, a novel vibration-isolating frame is designed for building a novel 3D printer. Such a structure would absorb external vibrations and isolate the print-plate, thereby improving the print quality.

The proposed frame is a meta-structure that absorbs vibrations over a frequency bandwidth. The structure is built with assembling multiple identical unit cells. Each unit cell is an assembly of 1D beams of varying cross-sections. The current paper’s objective is to design a fame that produces in-plane and out-of-plane bandgaps. Finite element models iterate over multiple designs, which are validated in the lab through robust experimentation. The paper discusses the design methodology and the corresponding results.

Recent introduction of enhancements for the Simultaneous Frequency Domain (SFD) method of experimental modal analysis, specifically the exploitation of left-hand eigenvector data to validate modal orthogonality and estimate kinetic energy distributions, opens the opportunity for incorporation of nontraditional measured response variables. These variables include (1) strains and/or stresses for structures, and (2) dynamic pressures for fluids and gases (e.g., for launch vehicle system dynamics and vibroacoustics). Justification for the exploitation of the above-cited, measured variables stems from the following facts: (a) stresses and fluid pressures are theoretically proportional to accelerations, and (b) SFD estimates an effective dynamic system and permits identification of complex eigenvectors that occur in multiphysics applications. Validity of these expanded opportunities is demonstrated with two simple analytically simulated examples.

The purpose of this experiment was to observe the dynamic behavior of bi-stable composite plates with fixed-fixed boundary conditions. In particular, the team sought to observe the minimum energy required to induce snap-through of post-buckled carbon epoxy composites fixed inside an aluminum frame. Initially, students collected the time response of the plate using an impact hammer and laser vibrometer. From the frequency response, the natural frequencies of the plates were determined and compared to analytically predicted results based upon a model constructed using thin plate theory and classical laminate theory. Next, the dynamic responses of the plates were obtained by applying various loading conditions with the use of a shaker table. These tests yielded validating natural frequencies to impact testing and the resonant frequencies of post-buckled plates. The minimum loading conditions required to cause snap-through in a post-buckled plate were found and analyzed across various conditions. These results provide a basis for determining minimum energy requirements required to cause buckling behavior in composite plates for applications to the hypersonic environment.