Full-field FRF estimation from noisy high-speed-camera data using a dynamic substructuring approach

This paper presents a comparative study between accelerometer and laser vibrometer measurements aimed at on-line qualitycontrol carried out on universal motors of washing machines, which exhibit defects localized mainly in the bearings. Thetest is designed so to study measurement problems of an on-line station. Bearing defects include faults in the cage, in therolling element and in the outer and inner ring. A set of no defective and defective motors were analyzed by means of theacceleration signal provided by the accelerometer, and the displacement and velocity signals given by a single point laser vibrometer. Advantages and disadvantages of both absolute and relative sensors and of contact and non-contact instrumentation will be exposed taking into account the applicability in real on line quality control measurements andbringing to evidence the related measurement problems due to the specific environmental conditions of assembly lines andsensor installation constraints.Keywords: Quality control, vibration measurements, laser vibrometer, accelerometer.

This paper presents the design, fabrication and tests of a micro-fabricated MEMS ‘Chladni’ plate resonator. The proposed MEMS resonator has a square plate geometry having a side length of 1400 µm and a height of 35 µm. Its geometry and electrode layout are designed to analyze and test as many modes as possible. The MEMS plate is fabricated using a silicon-on-insulator process with a 35 µm thick silicon layer on a glass substrate. Transverse vibration of the plate is investigated to obtain closed form natural frequencies and mode shapes, which are derived using the Rayleigh–Ritz energy method, with an electrostatic softening effect included. Closed form equations for the calculation of effective stiffness’, masses and natural frequencies of the two modes (mode (1,1) and mode (2,0)–(0,2)) are presented, with and without electrostatic softening. The analytical model is verified for those modes by finite-element simulations, frequency response tests in vacuum and laser Doppler vibrometer (LDV) experiments. The derived model deviates from the finite-element analysis by 3.35% for mode (1,1) and 6.15% for mode (2,0)–(0,2). For verification, the frequency responses of the plates are measured with both electrostatic excitation-detection at around 20 mTorr vacuum ambient and LDV at around 0.364 mTorr vacuum ambient. The resonance frequency and Q-factor of mode (1,1) are measured to be 104.2 kHz and 14 300, respectively. For mode (2,0)–(0,2), the measured resonance frequency and Q-factor are 156.68 kHz and 10 700, respectively. The presented LDV results also support both natural frequencies of interest and corresponding mode shapes of the plate structure.

In this paper, the design, modeling, and characterization of a display compatible pMUT platform are presented. A FEM model is built using COMSOL Multiphysics for evaluating the frequency response, mechanical performance, acoustic pressure, and driving efficiency of our pMUT device across all vibration modes of circular plates. In parallel with it, a first mode analytical model has been developed including electrical, mechanical, and acoustic domains to provide fast estimation for future design. A laser Doppler vibrometer is used to measure the frequency response, displacement, velocity as well as mode shapes of pMUTs with different designs in air. The measured resonance frequency of first mode range from 121.5kHz to 1.1MHz with radius from 500μm to 120μm and fits the prediction of FEM and analytical models. A standard reference microphone is used to measure the acoustic pressure of pMUT inside its frequency range (<125 kHz). The measured acoustic pressure on transverse axis of a 500μm radius pMUT also fits the values from analytical model on acoustic domain.

This paper presents a method to determine soil stiffness properties using measured structural modes of bridges. Normally, the identified mode shapes have to be smoothed. The mode shapes are approximated using functions describing the transverse vibration of distributed-parameter systems. Artificial coefficients are introduced into this solution in order to sum up the error contributions of displacements and its derivatives up to second order. Then, a pier-soil model based on normalized mechanical impedance functions is used. Applying this method along with more than one vertical mode shape leads to acceptable and more accurate results. The amplitudes of pier bottom vibrations are chosen as the suitable weights for the averaging procedure. For the Warth Bridge situated near Vienna, shear wave velocities and shear moduli at the pier foundations have been estimated. The results correspond quite well to the geological investigation.

Near-field acoustic holography (NAH) provides a reconstruction of the normal particle velocity radiated by the source of interest on a nearby surface. Reconstructing structural admittance based on normal velocity establishes NAH as alternative to the conventional methods such as accelerometers or laser vibrometers. Measuring vibrating object using microphone array offers high-resolution measurements and with this the possibility to obtain spatially dense displacement field of the structure. Although useful, the method’s ill posed nature needs to be considered which introduces numerical noise to the reconstructed result. In this paper an alternative approach for improved estimation of FRFs from NAH is introduced by using dynamic substructuring methodology. Recently developed System Equivalent Model Mixing (SEMM) method is proposed that enables mixing of response models of the same structure into one hybrid model. In the hybrid formulation, each model contributes its own advantages to yield best combination of the two. NAH introduces a high spatial resolution to the hybrid model whereas discrete laser vibrometer measurements improve the accuracy of the reconstructed displacement field. Experimental validation of methodology is performed on a freely supported structure that is excited using electrodynamic shaker. Noisy acoustical environment introduces spurious peaks in FRFs acquired using NAH. The laser vibrometer measurement is not affected by a noisy environment, as only the structural response is measured. It is shown that hybrid model provides a more consistent FRFs of the structural response, especially with regard to the amplitude in the resonance regions.KeywordsNear-field acoustic holographyNoisy environmentFrequency-based substructuringSystem equivalent model mixingHybrid model

This paper presents a method to measure responses for a sinusoidally excited structure using a continuously scanning Laser Doppler Vibrometer (LDV). The LDV output signal is an amplitude-modulated vibration, whereby the excitation signal will be modulated by the response of the excited structure. Using an applicable demodulation the mode shape defined along a scan line can be derived by the envelope of the modulated vibration. By using an adaptable digital low-pass filter and parallel measuring of responses and mirror drive signal in the time domain the mode shape can be directly derived from the measured response. So the demodulation is a fast method to identify the mode shape from the measured response, because of its completion in the time domain. For that purpose the method is capable for using the responses online for normal mode tuning. Furthermore it is necessary for normal mode testing to measure complex responses to make an affirmation about the separation of real mode shapes. The method will match these requirements.

Piezoelectric plates can provide low-frequency transverse vibrational displacements and high-frequency planar vibrational displacements, which are usually uncoupled. However, piezoelectric shells can induce three-dimensional coupled vibrational displacements over a large frequency range. In this study, three-dimensional coupled vibrational characteristics of piezoelectric shells with free boundary conditions are investigated using three different experimental methods and finite element numerical modeling. For the experimental measurements, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) is used to obtain resonant frequencies and radial, lateral, and angular mode shapes. This optical technique utilizes a real-time, full-field, non-contact optical system that measures both the natural frequency and corresponding vibration mode shape simultaneously. The second experimental technique used, laser Doppler vibrometry (LDV), is a pointwise displacement measurement method that determines the resonant frequencies of the piezoelectric shell. An impedance analyzer is also used to determine the resonant frequencies of the piezoelectric shell. The experimental results of the resonant frequencies and mode shapes for the piezoelectric shell are verified with a numerical finite element model. Excellent agreement between the experimental and numerical results is found for the three-dimensional coupled vibrational characteristics of the piezoelectric shell. It is noted in this study that there is no coupled phenomenon at low frequencies over which radial modes dominate. However, three-dimensional coupled vibrational modes do occur at high resonant frequencies over which lateral or angular modes dominate.

Viscoelastic materials are used in vibration damping applications as they have the ability to dissipate energy, they are used in machine basis, bridges and many other applications. In this paper four plates with the same thickness but different material lamination are investigated for their modal properties. Namely,natural frequencies, mode shapes and damping loss factors. Experimental modal analysis is carried out using impact hammer for excitation and accelerometer for measurement. Data is processed using computer package to obtain frequency response function (FRF) for each plate and modal parameters are extracted from the plot. Results are compared to finite element model that was created using ANSYS package. It showed very well agreement between experimental and finite element. Damping effect on the shift in natural frequencies was obvious due to the viscoelastic material thickness in the laminated plates. It is concluded that the finite element analysis using ANSYS software is a powerful tool in predicting natural frequencies and mode shapes even in laminated plates with viscoelastic core, it is also confirmed the effect of damping increase due to the use of viscelastic cores on the plate natural modes and vibration behaviour.

In this study the structural deployment dynamics of a rollable micro air vehicle wing are investigated. The wing is composed of a single layer of woven, carbon-fiber composite and behaves like a tape-spring, remaining stiff in one direction (lift) while rolling easily in the other for storage. A finite element model is developed and evaluated for its comparison to an experimental model. A vacuum chamber is used to eliminate fluid effects on the structural deployment dynamics, which are recorded using a high-speed video camera. Modal testing and finite element updating are used to estimate unknown composite material properties for the analysis. A laser vibrometer is used to record wing mode shapes, and they are found to agree well with fitted mode shapes and their frequencies from the updated Abaqus finite element model. A wing deployment is simulated in Abaqus and compared with experimental deployments, and the time history displacements matched well. The deployment is found to be sensitive to the wing mount as well as to material properties, particularly damping.

Application of modal analysis to the watermelon through finite element modeling for use in ripeness assessment

Structural damage detection based on wireless sensor networks can be affected significantlyby time synchronization errors among sensors. Precise time synchronization of sensor nodeshas been viewed as crucial for addressing this issue. However, precise time synchronizationover a long period of time is often impractical in large wireless sensor networks due to twoinherent challenges. First, time synchronization needs to be performed periodically,requiring frequent wireless communication among sensors at significant energy cost.Second, significant time synchronization errors may result from node failures which arelikely to occur during long-term deployment over civil infrastructures. In this paper, adamage detection approach is proposed that is robust against time synchronizationerrors in wireless sensor networks. The paper first examines the ways in whichtime synchronization errors distort identified mode shapes, and then proposes astrategy for reducing distortion in the identified mode shapes. Modified values forthese identified mode shapes are then used in conjunction with flexibility-baseddamage detection methods to localize damage. This alternative approach relaxesthe need for frequent sensor synchronization and can tolerate significant timesynchronization errors caused by node failures. The proposed approach is successfullydemonstrated through numerical simulations and experimental tests in a lab.

The dynamic characteristics of parallel-type and series-type piezoelectric bimorphs are analyzed in this study. The transverse (out-of-plane) and planar (in-plane) vibrations for piezoceramic bimorphs in normal and abnormal connections are investigated experimentally by 2 noncontact optical techniques and impedance analyzer. Electronic speckle pattern interferometry (ESPI) is the major experimental technique for measuring the resonant frequency and corresponding vibration mode shape. Out-of-plane and in-plane vibrations of piezoelectric bimorphs at resonance are obtained by a self-arranged ESPI optical setup. The laser Doppler vibrometer (LDV) is a point-wise measurement technique for out-of-plane displacement and is used to determine the out-of-plane resonant frequencies. The impedance analyzer is used to measure the resonant frequencies for in-plane motions. It is noted from the experimental results that the out-of-plane modes are the dominant motion for the normal connection and only symmetric vibration mode shapes can be excited. The in-plane motions are large enough to be measured using the ESPI method for normal connections. The in-plane resonant modes are observed for parallel-type piezoelectric bimorph in parallel connections; however, the in-plane mode shapes are similar to the out-of-plane mode shapes for the series-type piezoelectric bimorph in series connection. Hence, the particle motions of the piezoelectric bimorph at resonance are essentially 3-D for the normal connection. It is interesting to note that both symmetric and asymmetric out-of-plane vibration mode shapes can be excited with large applied voltage but no in-plane motion is observed for the abnormal connection. In addition to experimental methods, numerical computations based on the finite element method are used to verify the experimental results. Good agreements of the resonant frequencies and mode shapes are obtained for experimental and numerical results.

In this paper, the large amplitude vibrations of clamped-clamped thin viscoelastic rectangular plates due to a concentrated transversal harmonic load are investigated both theoretically and experimentally. Clamped boundary condition on all edges and von Kármán nonlinear strain-displacement relationships are considered while rotary inertia, geometric imperfections, and shear deformation are neglected. In the theoretical study, the viscoelastic behaviour of the material is modelled using the Kelvin-Voigt model. In-plane loads applied during the assembly of the plate are taken into account and clamped boundary conditions are modelled using artificial rotational springs. The nonlinear ordinary differential equations for the considered Kelvin-Voigt model are obtained using the generalized energy approach. These equations contain quadratic and cubic nonlinear viscoelasticity terms in addition to quadratic and cubic stiffness terms. Non-dimensionalization of variables is carried out and each second order equation is converted into two first order equations. The resulting system of equations is solved using AUTO (software based on the arclength continuation method that allows bifurcation analysis), to get the frequency-response curves at various force levels. Moreover numerical time integration of equations was also performed using the fourth-order Runge-Kutta method to understand the time response of the structure. In the experimental study, two rubber plates with different material and thicknesses were considered; a silicone plate with 0.0015 m thickness and a neoprene plate with 0.003 m thickness. The plates were fixed on a heavy rectangular metal frame thereby ensuring the clamped boundary condition on all edges. Linear experimental modal analysis was carried out as a first step to estimate the mode shapes and natural frequencies. In the second step, the nonlinear vibration response of the plate around its first resonance was measured at various harmonic force levels. At each force level, the amplitude of the harmonic excitation was kept constant by LMS Data Acquisition System and Test.Lab Stepped Sine software module while slowly varying the frequency of excitation to get the frequency-response curves. Laser Doppler Vibrometry was used to measure the response from the plate as it eliminates the possible mass loading effect introduced by any contact type sensors. A maximum amplitude of more than three times the thickness of the plate was achieved. The nonlinear response curves showed a typical hardening type nonlinearity along with sudden jumps as expected for plates. Experimental frequency-response curves were compared with theoretical results and a good agreement was found. The influence of nonlinear viscoelastic damping terms was clearly noticed on the response curves of the plate. The retardation time, measured in seconds decreases with increasing excitation force and larger amplitude vibrations.

Accurate determination of modal parameters for disk-like structures submerged in heavy fluids is a topic of interest in many fields. For instance, some type of hydraulic turbomachinery can be modeled as disk structures due to the similarity in their mode shapes. Although in the recent years many studies have analyzed and correctly predicted the fluid added mass effect on the natural frequencies and mode shapes of these types of structures, it is particularly challenging to determine fluid damping and characterize its most influential effects. In this article, the influence of vibration amplitude on the fluid damping ratio of a submerged disk, when the disk gets close to a rigid wall, is analytically and experimentally studied. Particularly, the first diametrical modes of the disk have been analyzed at different vibration amplitudes and at very small distances away from a rigid surface. The disk is put in a resonant state by means of a piezoelectric patch generating a harmonic excitation and the response is measured by means of a Laser Doppler Vibrometer (LDV). The damping ratio is obtained directly from the vibrating free decay following a sudden stop of the excitation. It is shown that the fluid damping ratio values are related to the vibration amplitude: there is a trend of increasing damping ratio as the amplitude of the vibration increases. This effect is found to be much larger for small distances between the disk and the rigid surface.

3D scanning laser Doppler vibrometry (LDV) systems continue to gain popularity for use in experimental modal analysis as the systems become more widespread. LDV is, by its nature, limited to measurements with line-of-sight visibility. This work presents an application of 3D scanning LDV to a test article with un-instrumented internal features that were not accessible to the lasers. The internal features, while not directly measurable, were known to contribute strongly to the modal characteristics of the test article. Initially, a traditional roving hammer test was conducted and modal parameters were extracted. The limited degrees of freedom inherent to this test method proved to be inadequate to correctly identify key mode shapes. It was found that by increasing the measurement point density and including all three translational degrees of freedom at each point, the key modal characteristics of the full system were able to be inferred from purely external measurements. These characteristics were essential in updating the mechanical behavior and material properties of the corresponding finite element model. The response measurements required for system identification were only practically achievable using the 3D LDV system. Comparisons of key experimental results to those of the calibrated analytical model are demonstrated.