Wave propagation analysis in inhomogeneous piezo-composite layer by the thin-layer method

Abstract

SUMMARYThe thin-layer method (TLM) is used to study the propagation of waves in inhomogeneous piezocomposite layered media caused by mechanical loading and electrical excitation. The element is formulated in the time-wavenumber domain, which drastically reduces the cost of computation compared to the finite element (FE) method. Fourier series are used for the spatial representation of the unknown variables. The material properties are allowed to vary in the depthwise direction only. Both linear and exponential variations of elastic and electrical properties are considered. Several numerical examples are presented, which bring out the characteristics of wave propagation in anisotropic and inhomogeneous layered media. The element is useful for modelling ultrasonic transducers (UT) and one such example is given to show the effect of electric actuation in a composite material and the difference in the responses elicited for various ply-angles. Further, an ultrasonic transducer composed of functionally graded piezoelectric materials (FGPM) is modelled and the effect of gradation on mechanical response is demonstrated. The effect of anisotropy and inhomogeneity is shown in the normal modes for both displacement and electric potential. The element is further utilized to estimate the piezoelectric properties from the measured response using non-linear optimization, a strategy that is referred to as the pulse propagation technique (PPT).

Perfectly matched layers in the thin layer method

“…Equations (8)(9)(10) indicate that the higher the horizontal range of interest is, the higher the value needed for  ,  , or both.…”

“…Since its inception in the early 1970's [27,28,41], the TLM has found widespread use in soil dynamics and soil-structure interaction [37,38], non-destructive evaluation methods, seismic source simulations, wave propagation in waveguides of complex cross-section, wave propagation in laminated, anisotropic materials [20], waves in piezoelectric materials [8], heat diffusion in layered composites [15], consolidation in poroelastic media, solid-fluid interaction [39], and in many more areas of application. Although the origin and early development of the TLM technique hark back to the early 1970's, the designation TLM became common only since the beginning of the 1990's.…”

Wave propagation in functionally graded piezoelectric spherically curved plates

“…Chakraborty et al [11] formulated a set of finite elements to analyze wave propagation through FGPM plates when subjected to mechanical, thermal loading or piezoelectric actuation, where the material properties are allowed to vary both in length and in thickness. Chakraborty et al [12] used spectral element method to characterize the wave propagation in FGPM plates by the thin-layer model, and modeled an ultrasonic transducer composed of FGPM. Li et al [13] and Liu and Wang [14] studied the propagation of Love waves in FGPM structures by the WKB method.…”

“…In the first kind of approach, the FGPM is divided into a large number of inhomogeneous thin layers [6,7,9,10], and then finite-element-type techniques were employed. The second is finite-element [11] or spectral-element [5,12] methods. In these models, the materials should be divided into many elements.…”

Wave characteristics in functionally graded piezoelectric hollow cylinders

“…Using spectral element method, Chakraborty et al [8] characterized the wave propagation in FGPM plates by the thin-layer model, and modeled an ultrasonic transducer composed of FGPM. Li et al [9] and Liu et al [10] studied the propagation of Love wave in FGPM structures by the WKB method.…”