Effects of SH waves in a functionally graded plate
TL;DR: In this article, a computational method is presented to investigate SH waves in functionally graded material (FGM) plates, in which the material properties are assumed as a quadratic function in the thickness direction, and a general solution for the equation of motion governing the QLE has been derived.
About: This article is published in Mechanics Research Communications.The article was published on 2002-09-01. It has received 73 citations till now. The article focuses on the topics: Functionally graded material & Bessel function.
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TL;DR: A review of the reported studies in the area of thermo-elastic and vibration analyses of functionally graded (FG) plates with an emphasis on the recent works published since 1998 is presented in this paper.
695 citations
Cites methods from "Effects of SH waves in a functional..."
...Further, Han and Liu [46] presented a computational method to investigate the simple harmonic waves in FG...
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TL;DR: In this paper, various higher-order shear deformation plate theories for wave propagation in functionally graded plates are developed, which have fewer number of unknowns and equations of motion than the first-order deformation theory, but accounts for the transverse shear deformations without requiring shear correction factors.
Abstract: In this work, various higher-order shear deformation plate theories for wave propagation in functionally graded plates are developed. Due to porosities, possibly occurring inside functionally graded materials (FGMs) during fabrication, it is therefore necessary to consider the wave propagation in plates having porosities in this study. The developed refined plate theories have fewer number of unknowns and equations of motion than the first-order shear deformation theory, but accounts for the transverse shear deformation effects without requiring shear correction factors. The rule of mixture is modified to describe and approximate material properties of the functionally graded plates with porosity phases. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton
337 citations
TL;DR: In this article, the analysis of functionally graded thick hollow cylinders under dynamic load is presented, where each subcylinder is considered as an isotropic layer and material properties in each layer are constant and functionally graded properties are resulted by suitable arrangement of layers in multilayer cylinder.
114 citations
TL;DR: In this article, the propagation behavior of transverse surface waves (love waves) in a piezoelectric half space of polarized ceramics carrying a functionally graded material layer is studied from the three-dimensional equations of linear piezolectricity, and the effect of gradient coefficients on the dispersive relations and phase velocities of Love wave propagation is discussed in detail.
80 citations
TL;DR: In this article, an efficient shear deformation theory is developed for wave propagation analysis of an infinite functionally graded plate in the presence of thermal environments, and the results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.
Abstract: An efficient shear deformation theory is developed for wave propagation analysis of an infinite functionally graded plate in the presence of thermal environments. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The thermal effects and temperature-dependent material properties are both taken into account. The temperature field is assumed to be a uniform distribution over the plate surface and varied in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton\'s principle and the physical neutral surface concept. There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The analytic dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions and temperature on wave propagation of functionally graded plate are discussed in detail. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded plate. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.
80 citations
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01 Jan 1970
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29 Oct 2002
Abstract: Annotation Foreward Some Remarks and Notation First Order Differential Equations Simplest Equations with Arbitrary Functions Integrable in a Closed Form Riccati Equations: g(y)y'x = f2(x)y2 + f1(x)y + f0(x) Abel Equations of the Second Kind Equations Containing Polynomial Functions of y Nonlinear Equations of the Form f(x,y)y'x = g(x,y) Containing Arbitrary Parameters Equations Not Solved for Derivative Equations of the Form F(x,y)y'x = G(x,y) Containing Arbitrary Functions Equations of the Form F(x,y,y'x) = 0 Not Solved for the Derivative and Containing Arbitrary Functions Second Order Differential Equations Linear Equations Autonomous Equations y"xx = F(y,y'x) Emden-Fowler Equation y"xx = Axnym Equations of the Form y"xx = A1xn1ym1 + A2xn2ym2 Generalized Emden-Fowler Equation y"xx = Axnym(y'x)l Equations of the Form y"xx = A1xn1ym1(y'x)l1 + A2xn2ym2(y'x)l2 Equations of the Form y"xx = f(x)g(y)h(y'x) Some Nonlinear Equations with Arbitrary Parameters Equations Containing Arbitrary Functions Third Order Differential Equations Linear Equations Equations of the Form y'"xxx = Axayss(y'x)g(y"xx)d Equations of the Form y'"xxx = f(y)g(y'x)h(y"xx) Some Nonlinear Equations with Arbitrary Parameters Nonlinear Equations Containing Arbitrary Functions Fourth Order Differential Equations Linear Equations Nonlinear Equations Higher Order Differential Equations Linear Equations Nonlinear Equations Supplement 1. Some Elementary Functions and Their Properties Trigonometric Functions Hyperbolic Functions Inverse Trigonometric Functions Inverse Hyperbolic Functions Some Conventional Symbols Supplement 2. Some Special Functions Gamma-Function Bessel Functions Jn and Yn Modified Bessel Functions In and Kn Degenerate Hypergeometric Functions Legendre Functions The Weierstrass Function References Index
1,550 citations
TL;DR: In this paper, a hybrid numerical method for wave propagation analysis in anisotropic laminated plates is extended for functionally gradient piezoelectric material (FGPM) plates.
Abstract: The hybrid numerical method, which has been proposed by the present authors for wave propagation analysis in anisotropic laminated plates, is extended for functionally gradient piezoelectric material (FGPM) plates. The properties of the plate changes continuously in the thickness direction. Characteristics of waves in the plates, and responses of the plates in the time and frequency domain are considered. A technique for calculating responses in the frequency domain is presented. Energy velocities, mode shapes of the waves in an FGPM plate, and the responses of the plate excited by mechanical loads and electrodes are computed. It is found that waves of lower modes in the FGPM plates for large wave numbers appear as surface waves and that a strong surface wave is excited on the softer surface of the FGPM plate. These surface waves can be expected to be used in surface acoustic wave devices.
148 citations
TL;DR: In this paper, a method was presented to investigate elastic waves in functionally gradient material (FGM) plates excited by plane pressure wavelets, where the FGM plate was first divided into linearly inhomogeneous elements (LIEs) and a general solution for the equation of motion governing the LIE was derived.
Abstract: A method is presented to investigate elastic waves in functionally gradient material (FGM) plates excited by plane pressure wavelets The FGM plate was first divided into linearly inhomogeneous elements (LIEs) A general solution for the equation of motion governing the LIE was derived The general solution was then used together with the boundary and continuity conditions to obtain the displacement and stress in the frequency domain for an arbitrary FGM plate The response of the plate to a pressure wavelet was obtained using Fourier transform techniques Results obtained by the present method are compared with an existing method using homogeneous layer elements Relationships between the surface displacement response and the material mechanical properties of FGM plates were also obtained These relationships may be used for the material characterization of FGM plates
108 citations
TL;DR: In this paper, the coulomb wavefunctions, originally constructed for real ϱ > 0, real η and integer λ ⪖ 0, are defined for ϱ, η, and λ all complex.
102 citations