An analysis of surface acoustic wave propagation in a plate of functionally graded materials with a layered model

Abstract

In a homogeneous plate, Rayleigh waves will have a symmetric and anti-symmetric mode regarding to the mid-plane with different phase velocities. If plate properties vary along the thickness, or the plate is of functionally graded material (FGM), the symmetry of modes and frequency behavior will be modified, thus producing different features for engineering applications such as amplifying or reducing the velocity and deformation. This kind of effect can also be easily realized by utilizing a layered structure with desired material properties that can produce these effects in terms of velocity and displacements, since Rayleigh waves in a solid with general material property grading schemes are difficult to analyze with known methods. Solutions from layered structures with exponential and polynomial property grading schemes are obtained from the layered model and comparisons with known analytical results are made to validate the method and examine possible applications of such structures in engineering.Rayleigh wave, surface acoustic wave, vibration, plate, layered structure, functionally graded material (FGM) Surface acoustic waves (SAW), also known as Rayleigh waves, exist in a semi-infinite solid with a free plane surface. Since its discovery by Rayleigh in 1885 [1] , surface acoustic waves have found wide engineering applications including piezoelectric surface acoustic wave resonators [2] . More general applications in foundations for vibration control and isolation caused by moving loads are also important because surface waves have been the destructive wave component due to its lower velocity (frequency) and energy concentration [3][4][5][6] . Although these applications are drastically different by nature, the common feature we can summarize is that both surface wave velocity and displacements are the major concerns for given structures. For SAW devices, which are widely

Interfacial delamination-induced unidirectional propagation of guided waves in multilayered media

“…To break the spatial inversion symmetry, a combined structure composed of a symmetric phononic crystal and an asymmetric structure was proposed [13,17,18]. It is known that the waves propagating in a finite thickness structure, called guided waves, have multi modes [19][20][21][22][23][24]. For example, there are three kinds of guided waves in an elastic layer, i.e., symmetric Lamb wave, antisymmetric Lamb wave, and SH wave, which can be transformed to each other by an asymmetric structure [25].…”

Study of the surface wave vibrations in a functionally graded material layered structure: a WKB method

“…The work done byWang et al [5] threw light on wave propagation through functionally graded materials; this problem is generally difficult to solve analytically, owing to the presence of variable coefficient differential equations as governing equations, except those with exponential variation in the thickness coordinate. Gao et al [6] suggested the technique of solving functionally graded material layer problems by dividing the initial layer into a number of homogeneous fine layers to facilitate the governing equations of each layer as differential equations with constant coefficients. By virtue of stress and displacements as continuities between the two layers, the problem can be elucidated and solved analytically with credible precision.…”

The Study of SH Wave Propagation Behavior in Functionally Graded Plates with Variant Material Components

“…Motivated by the application in piezoelectric material, nondestructive testing, shock absorption and isolation, etc, the theories of wave propagation in functionally graded materials have been widely explored. For the variant coefficients in wave equation of functionally graded materials cause much trouble to derive accurate analytical solution, hence, numerical methods must be applied, for example, homogeneous layer model [3], positive series method [4], Legendre polynomial approach [5], WKB method [6], Piano series method [7], finite element method [8], and so on.…”