Chien-Ching Ma

The investigation of three-dimensional vibration for piezoelectric rectangular parallelepipeds using the AF-ESPI method

Electronic speckle pattern interferometry (ESPI) is a powerful tool for the full-field measurement of a deformed body. In this paper, a three-dimensional vibrating block that couples the out-of-plane and in-plane motions is investigated using the amplitude-fluctuation ESPI (AF-ESPI). This method demonstrates the advantages of combining high processing speed, such as in the subtraction method, with high fringe sensitivity, such as in the time-averaged method. The optical system for AF-ESPI is then employed to analyze the volume vibration of piezoelectric material for a rectangular parallelepiped configuration. Based on the fact that fringe patterns measured by the AF-ESPI method appear as a clear picture only at the resonant frequency, both the natural frequencies and the out-of-plane and in-plane vibration mode shapes are successfully obtained in this study. Finally, the impedance analysis as well as the finite element method (FEM) with three-dimensional model are also conducted to compare with the result obtained by AF-ESPI. It is shown that the numerical calculation and the experimental result agree fairly well for both the resonant frequency and the mode shape in three-dimensional configurations.

Vibration Characteristics for Piezoelectric Cylinders Using Amplitude-Fluctuation Electronic Speckle Pattern Interferometry

Electronicspecklepatterninterferometry (ESPI)isafull-e eld,noncontacttechniqueformeasuringthedeformation of a structure subjected to static loading or, especially, to dynamic vibration. Three-dimensional vibrations of piezoelectric materials with cylindrical surfaces are investigated using the amplitude-e uctuation ESPI (AF-ESPI) method. This method demonstrates the advantages of combining noise reduction, like the subtraction method, and high fringe sensitivity, like the time-averaged method. The optical system for AF-ESPI with two in-plane and one out-of-plane measurements is employed to study the volume vibration of a piezoelectric material for a thick circular disk, a ring, and a thin-walled tube. Because the clear fringe patterns measured by the AF-ESPI method will be shown only at resonant frequencies, both the resonant frequencies and the complete vibration mode shapes in three dimensions are obtained experimentally. Finally, impedance analysis and the e nite element method are also utilized, and the results are compared with the measurements obtained by AF-ESPI. It is shown that the numerical calculations and the experimental results agree fairly well for both the resonant frequencies and the mode shapes in three-dimensional cone gurations.

Theoretical analysis and experimental measurement for resonant vibration of piezoceramic circular plates

Based on the electroelastic theory for piezoelectric plates, the vibration characteristics of piezoceramic disks with free-boundary conditions are investigated in this work by theoretical analysis, numerical simulation, and experimental measurement. The resonance of thin piezoceramic disks is classified into three types of vibration modes: transverse, tangential, and radial extensional modes. All of these modes are investigated in detail. Two optical techniques, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), are used to validate the theoretical analysis. Because the clear fringe patterns are shown only at resonant frequencies, both the resonant frequencies and the corresponding mode shapes are obtained experimentally at the same time by the proposed AF-ESPI method. Good quality of the interferometric fringe patterns for both the transverse and extensional vibration mode shapes are demonstrated. The resonant frequencies of the piezoceramic disk also are measured by the conventional impedance analysis. Both theoretical and experimental results indicate that the transverse and tangential vibration modes cannot be measured by the impedance analysis, and only the resonant frequencies of extensional vibration modes can be obtained. Numerical calculations based on the finite element method also are performed, and the results are compared with the theoretical analysis and experimental measurements. It is shown that the finite element method (FEM) calculations and the experimental results agree fairly well for the resonant frequencies and mode shapes. The resonant frequencies and mode shapes predicted by theoretical analysis and calculated by finite element method are in good agreement, and the difference of resonant frequencies for both results with the thickness-to-diameter (h/D) ratios, ranging from 0.01 to 0.1, are presented.

Analytical investigations for heat conduction problems in anisotropic thin-layer media with embedded heat sources

Abstract This article develops the analytical rigorous solution of a fundamental problem of heat conduction in anisotropic media. The steady-state temperature and heat flux fields in a thin-layer medium with anisotropic properties subjected to concentrated embedded heat sources or prescribed temperature on the surface are analyzed. A linear coordinate transformation is used to transform anisotropic thin-layer problems into equivalent isotropic problems without complicating the geometry and boundary conditions of the problem. By using the Fourier transform and the series expansion technique, exact closed-form solutions of the specific problems are presented in series forms. The complete solutions of heat conduction problems for the thin-layer medium consist only of the simplest solutions for an infinite homogeneous medium with concentrated heat sources. The numerical results of the temperature and heat flux distributions are provided in full-field configurations.

Pointwise fiber Bragg grating displacement sensor system for dynamic measurements

A method for setting up a fiber Bragg grating (FBG) sensor which can measure the pointwise, out-of-plane or in-plane dynamic displacement is proposed. The proposed FBG sensor is reusable. A multiplexing demodulation system based on a single long-period fiber grating is used in this study. The experimental results of the steady-state motion for a multilayer piezoelectric actuator and the dynamic response of a cantilever beam subjected to impact loadings are presented. These results indicate that the proposed displacement sensor has the ability to measure the out-of-plane dynamic displacement with high sensitivity. Measurements for a piezoceramic plate excited by high frequency show that the proposed displacement sensor also has the ability to provide the in-plane dynamic displacement up to 20 kHz.

Experimental whole-field interferometry for transverse vibration of plates

Abstract Most of the work on vibration analysis of plates published in the literature are analytical and numerical and very few experimental results are available. Existing modal analysis techniques such as accelerometers and laser Doppler vibrometers are pointwise measurement techniques and are used in conjunction with spectrum analyzers and modal analysis software to characterize the vibration behaviour. In this study, a whole-field technique called amplitude-fluctuation electronic speckle pattern interferometry optical system is employed to investigate the vibration behaviour of square isotropic plates with different boundary conditions. This method is very convenient to investigate vibration objects because no contact is required compared to classical modal analysis using accelerometers. High-quality interferometric fringes for mode shapes are produced instantly by a video recording system. Based on the fact that clear fringe patterns will appear only at resonant frequencies, both resonant frequencies and corresponding mode shapes can be obtained experimentally using the present method. Two different types of boundary conditions are investigated in this study, namely free–free–free–free (FFFF, 27 modes) and clamped–clamped–clamped–clamped (CCCC, 12 modes). The numerical calculations by finite element method are also performed and the results are compared with the experimental measurements. Excellent agreements are obtained for both results of resonant frequencies and mode shapes.

Experimental measurement and numerical analysis on resonant characteristics of piezoelectric disks with partial electrode designs

Three experimental techniques are used in this study to access the influence of the electrode arrangement on the resonant characteristics of piezoceramic disks. These methods, including the amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), laser Doppler vibrometer-dynamic signal analyzer (LDV-DSA), and impedance analysis, are based on the measurement of full-field displacement, pointwise displacement, and electric impedance, respectively. In this study, one full electrode design and three nonsymmetrical partial electrode designs of piezoelectric disks are investigated. Because the clear fringe patterns measured by the AF-ESPI method will be shown only at resonant frequencies, both the resonant frequencies and the corresponding vibration mode shapes are successfully obtained at the same time for out-of-plane and in-plane motions. The second experimental method is the impedance analysis, which is used to measure the resonant and antiresonant frequencies. In addition to these experimental methods, LDV-DSA is used to determine the resonant frequencies of the vibration mode with out-of-plane motion. From the experimental results, the dependence of electrode design on the vibration frequencies and mode shapes is addressed. Numerical computations based on the finite element method are presented, and the results are compared with the experimental measurements. The effect of different designs of electrode is more significant in the in-plane modes than that in the out-of-plane modes.

Transient Analysis for Antiplane Crack Subjected to Dynamic Loadings

The problem considered here is the antiplane response of an elastic solid containing a half-plane crack subjected to suddenly applied concentrated point forces acting at a finite distance from the crack tip. A fundamental solution for the dynamic dislocation is obtained to construct the dynamic fracture problem containing a characteristic length. Attention is focused on the time-dependent full-field solutions of stresses and stress intensity factor. It is found that at the instant that the first shear wave reaches the crack tip, the stress intensity factor jumps from zero to the appropriate static value. The stresses will take on the appropriate static value instantaneously upon arrival of the shear wave diffracted from the crack tip, and this static value is thereafter maintained. The dynamic stress intensity factor of a kinked crack from this stationary semi-infinite crack after the arrival of shear wave is obtained in an explicit form as a function of the kinked crack velocity, the kink angle, and time. A perturbation method, using the kink angle as the perturbation parameter, is used. If the maximum energy release rate is accepted as the crack propagation criterion, then the crack will propagate straight ahead of the original crack when applying point load at the crack face.

Transient elastic waves propagating in a multi–layered medium subjected to in–plane dynamic loadings. I. Theory

The propagation of elastic transient waves in a multi–layered medium subjected to in–plane loadings is investigated in this study. One of the objectives of this study is to develop an effective analytical method for determining transient full–field solutions in the layered medium. A matrix method is developed by expanding the matrix solution obtained directly from the boundary–value problem in the integral transform domain into a power series of the phase–related reflection and transmission matrix which characterizes the multiple reflections and transmissions of all waves in every layer. The transient response of the multi–layered medium is decomposed into infinite wave groups in which the waves are either reflected by, or transmitted through, the interfaces. The connection between the proposed matrix method and the generalized ray method is established for the layered medium in the transform domain. The matrix representation of the solution enables us to calculate the transient response of the layered medium without tracing the ray path manually. The obtained analytical solution can easily be applied to numerical calculations. The double inverse transform is performed based on Cagniards method and the theoretical transient solution for a layered half–space subjected to an in–plane dynamic force will be presented in part II. An experimental set–up that simulates the plane stress condition for a layered half–space was established to obtain the dynamic displacement response. The experimental result agrees well with the theoretical solution. The proposed methodology in this study can be extended to solve more complicated problems such as waves propagating in three–dimensional space.

Experimental and numerical analysis of vibrating cracked plates at resonant frequencies

Owing to the advantages of noncontact and fullfield measurement, an optical system called the amplitude fluctuation electronic speckle pattern interferometry (AFESPI) method with an out-of-plane setup is employed to investigate the vibration of a cantilever square plate with a crack emanating from one edge. Based on the fact that clear fringe patterns will be shown by the AFESPI method only at resonant frequencies, both the resonant frequencies and the vibration mode shapes can be obtained experimentally at the same time. Three different crack locations will be discussed in detail in this study. One is parallel to the clamped edge, and the other two are perpendicular to the clamped edge. The numerical finite element calculations are compared with the experimental results, and good agreement is obtained for resonant frequencies and mode shapes. The influences of crack locations and lengths on the vibration behavior of the clamped cantilever plate are studied in terms of the dimensionless frequency parameter (λ2) versus crack length ratio (a/L). The authors find that if the crack face displacements are out of phase, a large value of stress intensity factor may be induced, and the cracked plate will be dangerous from the fracture mechanics point of view. However, there are some resonant frequencies for which the crack face displacements are completely in phase, causing a zero stress intensity factor, and the cracked plate will be safe.