S.T. Quek

Detection of cracks in plates using piezo-actuated Lamb waves

In this paper, a comprehensive methodology for locating and determining the extent of linear cracks in homogeneous plates based on the time-of-flight analysis of Lamb wave propagation is proposed. Piezoelectric sensors and actuators (PZTs) placed on a square grid configuration are used to excite and receive direct and reflected waves. The actuation frequency, spacing of PZTs and length of the signal to analyze are first determined. The grid is used to sweep across the plate to identify the location of a crack, if there is one. Elliptical loci of possible crack positions are constructed based on the flight time of crack-reflected waves estimated using energy spectra from the Hilbert–Huang transform of the sensor signals. A detailed procedure for obtaining the ellipses is described, including the blind zones. After identifying the crack position, the crack orientation is determined by varying the positions of the PZTs and observing the strength of the energy peaks in the Hilbert spectra. This provides the basis for moving the PZTs to estimate the extent of the crack. Experimental results obtained using aluminum plates with through, half-through and concealed cracks showed that the proposed method is feasible and accurate.

Analysis of piezoelectric coupled circular plate

This paper deals with the vibration analysis of a circular plate surface bonded by two piezoelectric layers, based on the Kirchhoff plate model. The form of the electric potential field in the piezoelectric layer is assumed such that the Maxwell static electricity equation is satisfied. The validation of the theoretical model is done by comparing the resonant frequencies of the piezoelectric coupled circular plate obtained by the theoretical model and those obtained by finite-element analysis. The mode shape of the electric potential obtained from free vibration analysis is generally shown to be non-uniform in the radial direction in contrast to what is commonly assumed. The piezoelectric layer is shown to have an effect on the frequencies of the host structure. The proposed model for the analysis of a coupled piezoelectric circular plate provides a means to obtain the distribution of electric potential in the piezoelectric layer. The model provides design reference for piezoelectric material application, such as an ultrasonic motor.

Implementation of Karhunen -Loeve expansion for simulation using a wavelet-Galerkin scheme

Abstract The feasibility of implementing Karhunen–Loeve (K–L) expansion as a practical simulation tool hinges crucially on the ability to compute a large number of K–L terms accurately and cheaply. This study presents a simple wavelet-Galerkin approach to solve the Fredholm integral equation for K–L simulation. The proposed method has significant computational advantages over the conventional Galerkin method. Wavelet bases provide localized compact support, which lead to sparse representations of functions and integral operators. Existing efficient numerical scheme to obtain wavelet coefficients and inverse wavelet transforms can be taken advantage of solving the integral equation. The computational efficiency of the wavelet-Garlekin method is illustrated using two stationary covariance functions (exponential and squared exponential) and one non-stationary covariance function (Wiener–Levy). The ability of the wavelet-Galerkin approach to compute a large number of eigensolutions accurately and cheaply can be exploited to great advantage in implementing the K–L expansion for practical simulation.

Sensitivity analysis of crack detection in beams by wavelet technique

Abstract This paper examines the sensitivity of wavelet technique in the detection of cracks in beam structures. Specifically, the effects of different crack characteristics, boundary conditions, and wavelet functions employed are investigated. Crack characteristics studied include the length, orientation and width of slit. The two different boundary conditions considered are simply supported and fixed end support, and the two types of wavelets compared in this study are the Haar and Gabor wavelets. The results show that the wavelet transform is a useful tool in detection of cracks in beam structures. The dimension of the crack projected along the longitudinal direction can be deduced from the analysis. The method is sensitive to the curvature of the deflection profile and is a function of the support condition. For detection of discrete cracks, Haar wavelets exhibit superior performance.

Detecting anomalies in beams and plate based on the Hilbert-Huang transform of real signals

This paper illustrates the feasibility of the Hilbert–Huang transform (HHT) as a signal processing tool for locating an anomaly, in the form of a crack, delamination, stiffness loss or boundary in beams and plate, based on physically acquired propagating wave signals. The basis of detection hinges on simple wave propagation concepts using flight times, velocities and frequency changes. The basic concept of HHT is first presented where the empirical mode decomposition must be applied on the signal using a sifting process to obtain intrinsic mode functions before the Hilbert spectral analysis can be meaningfully performed. Some implementation issues are discussed, such as end effects and the criterion to terminate the sifting process, and an alternative criterion is proposed and implemented using MATLAB V6.1. Four examples are used to illustrate the suitability of the technique, namely an aluminum beam with a crack, a sandwiched aluminum beam with an internal delamination, a reinforced concrete (RC) slab with different degrees of damage and a plate with distorted input signal. The results indicate that HHT is able to represent a localized event well and is sensitive to slight distortion in the signal. Crack and delamination in homogeneous beams can be located accurately and damage in a RC slab can be identified if it has been previously loaded beyond first crack. However, the sensitivity of HHT is such that analysis with a distorted signal needs careful interpretation, as illustrated by the aluminum plate example.

Simulation of second-order processes using Karhunen–Loeve expansion

Abstract A unified and practical framework is developed for generating second-order stationary and non-stationary, Gaussian and non-Gaussian processes with a specified marginal distribution function and covariance function. It utilizes the Karhunen–Loeve expansion for simulation and an iterative mapping scheme to fit the target marginal distribution function. The proposed method has three main advantages: (a) processes with Gaussian-like marginal distribution can be generated almost directly without iteration, (b) distributions that deviate significantly from the Gaussian case can be handled efficiently and (c) non-stationary processes can be generated within the same unified framework. Four numerical examples are used to demonstrate the validity and convergence characteristics of the proposed algorithm. Based on these examples, it was shown that the proposed algorithm is more robust and general than the commonly used spectral representation method.

Love waves in piezoelectric coupled solid media

The propagation of Love waves in a piezoelectric lamina bonded onto a semi-infinite solid medium is investigated in this paper. The dispersive characteristics and the mode shapes of the deflection and the electric potential in the thickness direction of the piezoelectric layer are theoretically derived. Numerical simulations show that the phase velocities initiate at the shear wave velocity of the host medium and tend towards the Bleustein-Gulyayev surface wave velocity for the piezoelectric layer at high wavenumbers for the first mode. The first two mode shapes of the electric potential correspond to a half-cosine and a full-cycle sinusoidal distribution, respectively, and become distorted as the wavenumber increases. These findings are significant in the application of inter-digital transducers for surface wave excitation in structural health monitoring.

Flexural vibration analysis of sandwich beam coupled with piezoelectric actuator

This paper provides a basic mechanics model for the flexural analysis of a sandwich beam coupled with a piezoelectric layer. The Euler beam model for a long and thin beam structure is employed, together with the electric potential satisfying the surface free charge condition for free vibration analysis. The distribution of the piezoelectric potential is obtained by including the Maxwell equation in the formulation. Based on the results of vibration analysis, it is shown that the dynamic characteristic of the entire structure is related to the position of the piezoelectric layer. More importantly, the mode shape distribution of the electric potential in the piezoelectric layer in the longitudinal direction is related to the transverse displacement, or more accurately the curvature, of the sandwich beam, and the latter is dependent on the boundary conditions. Hence, the commonly adopted assumption of uniform electric potential in the longitudinal direction needs to be carefully re-examined. The distribution of electric potential obtained serves as a guide for selecting the trial function for the mode shapes of the electric potential required in numerical methods, such as FE modelling, for coupled piezoelectric structures.

Practical issues in the detection of damage in beams using wavelets

Wavelet transform of dynamic response data, experimentally acquired using a piezoelectric sensor, is presented as a local non-destructive evaluation technique for locating damage in a beam. The higher consistency and accuracy of the results based on data from a piezoelectric sensor over a conventional strain gauge are demonstrated. The allowable range of wavelet scale to process the data is shown to be dependent on the sampling rate, filter frequency and length of signal, where edge effects due to transformation must also be considered in the latter. By estimating the wave arrival times based on theoretical flexural wave velocity, the approximate wavelet scale to process the data can be determined. Further processing of the signal at a finer wavelet scale is necessary to improve the accuracy. Based on experimental data, the method is shown to be robust with respect to boundary and damage conditions as well as impact position.

Analytical solution for free vibration of piezoelectric coupled moderately thick circular plates

Abstract An analytical model for free vibration analysis of piezoelectric coupled moderately thick circular plate is presented based on Mindlins plate theory for the cases where electrodes on the piezoelectric layers are shortly connected. The distribution of electric potential along the thickness direction is simulated by a sinusoidal function. The differential equations of motion are solved analytically for two boundary conditions of the plate: clamped edge and simply supported edge. The detailed mathematical derivations are presented. Numerical investigations are performed for plates with two surface-bonded piezoelectric layers for various diameter–thickness ratios and the results are verified by those obtained from three-dimensional finite element analyses (ABAQUS 6.1).