In-plane Operating Deflection Shape Measurement of an Aluminum Plate Using a Three-dimensional Continuously Scanning Laser Doppler Vibrometer System

Background

In-plane vibration is significant to a structure and has been accurately solved by many numerical methods; however, there are still not enough studies on its experimental measurement.

Objective

This work aims to propose a non-contact and fast way to measure dense full-field in-plane vibration of a plate structure, which has high frequencies and low response magnitudes.

Methods

A novel three-dimensional (3D) continuously scanning laser Doppler vibrometer (CSLDV) system that contains three CSLDVs is developed to conduct full-field scanning of a plate with free boundary conditions under sinusoidal excitation to measure its 3D vibrations. Calibration among the three CSLDVs in the 3D CSLDV system based on the geometrical model of its scan mirrors is conducted to adjust their rotational angles to ensure that three laser spots can continuously and synchronously move along the same two-dimensional scan trajectory on the plate. The demodulation method is used to process the measured response to obtain in-plane operating deflection shapes (ODSs) of the plate.

Results

Four in-plane ODSs are obtained in the frequency range of 0–5000 Hz. Modal assurance criterion (MAC) values between in-plane ODSs from 3D CSLDV and step-wise scanning laser Doppler vibrometer (SLDV) measurements are larger than 95%. MAC values between ODSs from 3D CSLDV measurements and corresponding mode shapes from the finite element model of the plate are larger than 91%.

Conclusions

Results from 3D CSLDV measurements have good accuracy compared to those from SLDV measurements and numerical calculation, and the 3D CSLDV system can scan much more measurement points in much less time than the SLDV system.

     

EXPERIMENTAL INVESTIGATIONS ON DYNAMIC CHARACTERISTICS OF A MULTILAYER PIEZOELECTRIC STACK ACTUATOR

Multilayer piezoelectric stack actuators are widely used in many industrial applications and the investigation on the dynamic behavior of this element is needed. In this study, two optical interferometric techniques called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV) are used to experimentally investigate the vibration characteristics of a single-layer piezoelectric disc and a multilayer piezoelectric stack actuator. These two techniques are full-field measurement for AF-ESPI and point-wise displacement measurement for LDV. Because the clear fringe patterns obtained by the AF-ESPI method will be shown only at resonant frequencies, both the resonant frequencies and corresponding vibration mode shapes of the piezoelectric disc and the multilayer piezoelectric stack actuator are obtained simultaneously by the AF-ESPI method. Interferometric fringe patterns for both the in-plane and out-of-plane vibration mode shapes are demonstrated. In addition to the proposed two optical techniques, numerical computations based on a commercially available finite element package are presented for comparison with the experimental results. Good agreement between the measured data by experimental methods and the numerical results predicted by FEM is found in resonant frequencies and mode shapes for the single-layer piezoelectric disc. However, some discrepancies are observed for the results obtained by AF-ESPI and impedance analysis for the multilayer piezoelectric stack actuator. A detailed discussion is made to address important issues of this problem.     

Characterization of a Laser Extensometer for Split Hopkinson Pressure bar Experiments

This paper examines a laser extensometer to calculate the strain in a sample during split Hopkinson pressure bar (SHPB) experiments. This method offers a non-contact, direct method for measuring sample strain which does not rely on one-dimensional wave propagation assumptions. First a single bar experiment is used to compare the extensometer’s accuracy and frequency response against a laser vibrometer and an accelerometer. The extensometer showed a close match with the vibrometer up to a bandwidth of 10 kHz. With the performance validated, the extensometer is applied to a SHPB experiment with silicone samples. For low strains, the extensometer shows a good match to the strain determined by strain gauges on the bars. At higher strains, the radial expansion of the sample can interfere with the measurement beam from the extensometer and produce inaccurate results.     

Tikhonov's regularization approach in mode shape curvature analysis applied to damage detection

In this paper an on-going research effort aimed at detecting and localizing damage in plate-like structures by using mode shape curvature based damage detection algorithm is described. The proposed damage index uses exclusively mode shape curvature data from the damaged structure. This method was originally developed for beam-like structures. In this paper, the method is generalized to plate-like structures which are characterized by two-dimensional mode shape curvature. To calculate mode shape curvatures from the measured mode shapes, three approaches are proposed: the first one is the well-known central difference approximation, the other two are classical approaches based on Tikhonov's regularization technique with smoothing functional. The applicability and effectiveness of the proposed damage detection algorithms are demonstrated experimentally on an aluminium plate containing mill-cut damage. The validity of the method is assessed by comparing the identification results of the experimental test case to the results obtained from the simulated test case. The modal frequencies and the corresponding mode shapes of the aluminium plate are obtained via finite element models for numerical simulations and by using a scanning laser vibrometer (SLV) for the experimental study.     

生物芯片压电微流体泵液-固耦合系统模态分析

对压电微流体泵粘性流体周期流动进行厚度积分平均近似,得到包含粘性的,非线性浅水波动方程,并采用有限元法得到微泵液体压强矩阵方程．液体压强矩阵方程和压电硅片振动有限元方程耦合,得到一个包含微泵进出口扩散管的液-固耦合系统振动方程．液-固耦合系统的模态分析结果表明,做泵液-固耦合系统的自然频率比不耦合的硅片振动自然频率低很多．随着微泵厚度的减少,液体附加质量和粘性阻尼对耦合系统自然频率的影响更加明显．同时发现,对应的压电片振型函数在液-固耦合前后没有明显变化,还给出硅片-阶模态的振幅-频率特征曲线,对薄型无阀压电微流体泵,浅水波模型合理地表达了微泵液体流动和压电硅片振动的相互作用,以及液体附加质量和粘性阻尼对微泵液-固耦合系统动力特征的影响。     

复合材料板冲击损伤检测的二维间隔平滑法

本文发展了一种基于振动的复合材料板的损伤检测方法,将原有的一维间隔平滑法(1D GSM,one dimensional gapped smoothing method)发展至二维(2D GSM),并进一步提出二维间隔平滑法的标准化损伤指标.与其他多数基于振动分析的损伤检测方法不同,该方法只需分析含有损伤结构的检测数据,无需结构健康时的数据或理论、计算结果作为对比信号,即可判定缺陷的存在,并能准确定位.针对由冲击造成的准各向同性碳纤维增强复合材料板中的层裂损伤,本文采用压电片阵列组合激励的方式,得到了复合材料板多频率扭转振型的同时激励,可实现快速、高效的损伤检测.通过扫描式激光测振仪测得结构在不同固定频率下的结构响应ODS(operational deflection shapes),利用提出的二维间隔平滑法,分析得出损伤指标.实验结果表明,二维间隔平滑法可以准确地检测碳纤维增强复合材料板的冲击损伤,并具有较好的精度.     

Experimental determination of bending strain power spectra from vibration measurements

Experimental results are presented of the power spectral density of the random bending strain on the surface of a beam obtained using a scanning laser vibrometer. The strain spectra were obtained by processing vibration data measured at discrete locations along the beam's length. The beam was driven by a stationary broad-band random force. The experimental setup is described along with the data analysis procedure. The results presented here indicate that the method is practical and can lead to reliable estimates.     

LIQUID-SOLID COUPLED SYSTEM OF MICROPUMP

This paper employs the integral-averaged method of thickness to approximate the periodical flows in a piezoelectric micropump, with a shallow water equation including nonlinearity and viscous damp presented to characterize the flows in micropump. The finite element method is used to obtain a matrix equation of fluid pressure. The fluid pressure equation is combined with the vibration equation of a silicon diaphragm to construct a liquid-solid coupled equation for reflecting the interaction between solid diaphragm and fluid motion in a micropump. Numerical results of a mode analysis of the coupled system indicate that the natural frequencies of the coupled system are much lower than those of the non-coupled system. The influence of additional mass and viscous damp of fluid on the natural frequencies of the coupled system is more significant as the pump thickness is small. It is found that the vibration shape functions of silicon diaphragm of the coupled system are almost the same as those of the non-coupled system. This paper also gives the first-order amplitude-frequency relationship of the silicon diaphragm, which is necessary for the flow-rate-frequency analysis of a micropump.     

Identification of Bending Modes of Vibration in Rails by a Laser Doppler Vibrometer on a Moving Platform

Experimental Techniques - This paper introduces a method to identify the bending modes of vibration of railway tracks by using a laser Doppler vibrometer (LDV) mounted on a moving platform. Two...     

Development of a Closed-Loop High-Cycle Resonant Fatigue Testing System

In this paper, a vibration-based testing methodology to assess fatigue behavior of a metallic structure is presented. To minimize the testing duration, the test setup is designed for a base-excited multiple-specimen arrangement driven in a high-frequency resonant mode, which allows completion of fatigue testing in an accelerated period. The shaker operates in closed-loop control with dynamic specimen response feedback provided by a scanning laser vibrometer. A test coordinator function is developed to synchronize the shaker controller and the laser vibrometer and complete the closed-loop scheme: the test coordinator monitors structural health of the test specimens throughout the test period, recognizes change in specimen dynamic behavior due to fatigue crack initiation, terminates test progression, and acquires test data in an orderly manner. The test methodology is demonstrated with cantilever specimens that are clasped on the shaker armature with specially-designed clamp fixtures. Experimental stress evaluation is carried out to verify the specimen stress predictions. A successful application of the experimental methodology is demonstrated by validation tests with Al 6061-T6 aluminum specimens subjected to fully-reversed bending stress.     

The application of interferometric techniques to the nondestructive inspection of fiber-reinforced materials

A method for increasing the sensitivity of dynamic materials evaluation (DME) to localized damage in fiber-reinforced composites was examined. To obtain this improved sensitivity, different aspects of DME were examined. These included an increase in the frequency used to evaluate the dynamic properties, utilization of mode-shape information and different procedures for evaluating the experimental data.The extent of the internal damage was determined using measured changes in the dynamic properties of the system (loss factor, dynamic stiffness and mode shape). To obtain the response information at higher frequencies a modalanalysis system was built around the performance characteristics of a laser doppler vibrometer (LDV) and an electronic speckle pattern interferometer (ESPI). These two devices provided complementary information for the determination of the dynamic characteristics of each vibration mode. With this system, damage-induced changes in the dynamic characteristics of composite materials were measured at frequencies up to 10 kHz.The results of this study showed the following. (1) Torsion modes provide the most sensitivity to localized internal damage. (2) The evaluation of higher frequency NDI data requires the ability to correlate the measured loss factor and resonant frequencies with the actual mode shape. (3) The data obtained over the frequency range of the test could be reduced to a series of slopes that provide a sensitive indication of the material condition. (4) The sensitivity of the dynamic method to localized damage is limited by the measurement of the loss factor.     

Simultaneous determination of position and mass of a particle by the vibration of a diaphragm-based nanomechanical resonator

We present a theoretical analysis of the vibration of a suspended circular diaphragm resonator with a particle at an arbitrary location when considering the effects of plate stiffness and membrane tension in the diaphragm. The analytical expression relating position and mass of a particle attached on a stretched diaphragm with varying residual stress to the resulting shifts in diaphragm resonant frequency is derived. It has been shown that the particle position and mass for the diaphragm configuration can be unambiguously resolved by combining resonant frequencies of the first three consecutive symmetric vibration modes. This finding is verified numerically in finite element modeling using a freestanding circular diaphragm with and without an added particle, and it proves that the method resolves the particle position and mass with high accuracy.     

Investigations on vibration characteristics of two-layered piezoceramic disks

This paper investigates the transverse and planar vibration characteristics of two-layered piezoceramic disks for traction-free boundary conditions by theoretical analysis, finite element numerical calculation, and experimental measurements. Amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), laser Doppler vibrometer (LDV), and impedance analysis were used to perform measurements and verify the theoretical solutions for extensional, tangential, and transverse vibrations. The poling direction of piezoelectric elements determines whether they are denoted as either of series- or parallel-type. This study observed that the resonant frequencies and mode shapes of the series- and parallel-type piezoceramic disks present different dynamic characteristics in resonance. Planar and transverse vibrations are coupled in series-type piezoceramic disks and uncoupled in those of parallel-type. Good agreements of dynamic characteristics determined by theoretical analysis, experimental measurements, and numerical calculation are presented for series- and parallel-type piezoceramic disks.     

Investigation of Damage in Composites Using Nondestructive Nonlinear Acoustic Spectroscopy

The presented experimental work describes the nondestructive damage examination of polymer-matrix composites using acoustic methods under the consideration of nonlinear effects. The aim is to analyze these nonlinear effects in order to provide a quantification of the nonlinear acoustic transmission which is related to the damage state and its severity in the composite material. The first objective was to study the effectiveness of the distortion evaluation method and its related parameter: the “Total Difference Frequency Distortion” (TDFD) parameter. The TDFD was utilized as a new damage indicator to quantify the progressive damage state in composite materials. The TDFD method had initially been proposed to characterize the distortion of audio amplifiers. A custom-made setup was developed that imposes acoustic signals to the structure. The samples’ vibrations were afterwards analyzed by a laser vibrometer and further spectrum evaluations. The developed method was applied to two composite materials, both reinforced with taffeta woven glass-fibers, but having different thermoset polymer matrix, i.e. vinylester and epoxy. The damage was introduced in the specimen by tensile tests with a stepwise increase of the tension loading. It was observed that damage influences the intensity of nonlinear intermodulation after having introduced two harmonic and constant signals of different and randomly chosen frequencies in the specimen. The nonlinear intermodulation was then quantified by computing the TDFD parameter. In the specific case of epoxy based composites, high frequency peaks were noted for the high tensile loading levels only. The TDFD parameter was then modified in order to take into account this effect. For both studied composites, the modified TDFD parameter increases with the damage accumulation caused by the applied stepwise tensile loading.     

Large amplitude oscillatory extension of soft polymeric networks

Using a filament stretching rheometer surrounded by a thermostatic chamber and equipped with a micrometric laser, it is possible to measure large amplitude oscillatory elongation (LAOE) on elastomeric based networks with no base flow as in the LAOE method for polymer melts. Poly(dimethylsiloxane)-based networks, considered as a model system for studying the development of soft elasticity, are mechanically characterised through reversed LAOE deformation, applying oscillatory measurements with several amplitudes and frequencies.     

谐振腔参数对激光陀螺性能影响的分析

谐振腔是构成激光陀螺的主体，其参数直接影响陀螺的性能，从激光陀螺基本误差理论出发，分析了谐振腔腔长、光阑、毛细孔孔径一致性、毛细孔与光轴相对关系等与陀螺误差的关系。利用激光陀螺的尺度定律 分析了两种典型腔长的激光陀螺，给出了分析结果。根据激光陀螺放电引起的陀螺误差关系及谐振腔振荡模式特性，研究了谐振腔放电毛细孔的加工误差及谐振腔光阑对激光陀螺的影响，给出了毛细孔、光 阑的设计准则，并根据高斯光束特性得出光阑背向散射系数的表达式。这对激光陀螺的设计具有重要的参考价值。     

Elasto-optic technique for measurement of elastic wave propagation in solids

The modulation of the optical path of the beam of a laser vibrometer in a specimen under acoustic excitation is measured at two planes, separated by a precisely known distance. The phase shift and the decrease in magnitude are used to calculate the phase velocity and attenuation, respectively. The method is demonstrated for a homogeneous specimen, and the results compare favorably with those obtained by a conventional ultrasonic technique. The method is then applied to measure specular and first diffraction-order reflection from a coplanar periodic array of particles in an elastic matrix and phase velocity spectra in a tetragonal periodic particulate composite. As expected, in a periodic composite the establishment of dispersive Floquet-type waves is observed throughout the entire periodic particulate composite.     

Frequency response of a synthetic jet cavity

A synthetic jet results from periodic oscillations of a diaphragm in a cavity. We present the results of a detailed experimental investigation wherein the effect of excitation frequency on the synthetic jet flow is studied for cavities of different depths and for orifices of different diameters. The exit velocity averaged over an excitation cycle indicates a lower and an upper bound on the frequency for the formation of a jet, and shows resonance at two frequencies. The resonant frequencies have been identified as being close to the diaphragm and the Helmholtz frequencies, with the former being more important in the present set of experiments. We discuss approaches to manipulate these frequencies from the point of view of cavity design. Interestingly, the input power is found to be at a minimum at the diaphragm frequency. Our measurements over a relatively large parameter domain suggest that the turbulence intensity in the near field is independent of the cavity depth and excitation frequency, but depends on the orifice diameter. These results are expected to be useful for designing synthetic jet cavity.     

Frequency analysis of turbulent compressible flows by laser vibrometry

The objective of this work was the application of laser vibrometry as a tool for non-intrusive measurement of frequency spectra in turbulent flows. A laser vibrometer system together with a signal analyser was used to obtain frequency spectra of density fluctuations across a turbulent free jet. Since laser vibrometry is based on interferometric techniques, the derived signals are path integrals along the measurement beam. Frequency spectra recorded in the rotational symmetric flow were then treated using Abel inversion in order to derive information on local density fluctuations. Results for two different flow conditions were compared to spectral data from a constant temperature anemometer and a pitot-mounted pressure sensor. Received: 21 February 2000/Accepted: 13 December 2000     

Surface Strain Measurements Using a 3D Scanning Laser Vibrometer

Three-dimensional scanning laser vibrometers enable extremely accurate non-contact measurement of the three-dimensional displacements on the surface of structures. This paper looks at the feasibility of using such a scanning laser vibrometer for the non-contact measurement of dynamic strain fields across the surface of a planar structure subjected to in-plane loading. Issues such as laser head alignment and choice of differentiation filter parameters are discussed. Finally, experimental results of two test specimens are presented which clearly demonstrate the significant potential of this new experimental technique as well as highlighting several limitations.