The Analysis Of Wave Propagation And Impact Response Of A Functionally Graded Material Plate

Functionally graded materials (FGMs) are a new generation of composite materials, microscopically inhomogeneous, which are usually composed of two or more materials whose volume fractions are changing smoothly and continuously along desired dimension(s). The continuous change in the compositions leads to a smoothing variation in mechanical property and eliminates jumps or abrupt changes in the stress and displacement distributions. FGMs are superior to the traditional composite materials, and have been widely applied in various fields such as aerospace, power generation industries, and energy conversion, biomedicine, etc. Investigations on the mechanical of FGM structures, especially, on wave propagation and response of functionally graded plates, are very meaningful in theory and valuable in application.The wave propagation and response of a functionally graded plate under impact load are investigated in this paper.Firstly, wave propagation and dynamic response of the rectangular FGM plates with completed clamped supports under impulse load are analyzed. Considering the effects of transverse shear deformation and rotary inertia, the governing equations of the wave propagation in the functionally graded plate with completed clamped supports are derived from Hamilton’s principle. A complete discussion of dispersion of the functionally graded plates with completed clamped supports is given. Analytical response solutions for the functionally graded plates with completed clamped supports under impulse load are obtained by using Laplace integral transform and the dispersion relation. The influence of volume fraction distributions on wave propagation and response of the FGM plates with completed clamped supports is analyzed. Secondly, wave propagation and transient response of an infinite functionally graded plate under a point impact load and an annular line impact load are investigated. The effective material properties of functionally graded materials (FGMs) for the plate are assumed to vary continuously through the plate thickness and be distributed according to a volume fraction power law along the plate thickness. The governing equations of wave propagation in the functionally graded plate are established. The analytic dispersion relation of the functionally graded plate is obtained and the discussion of dispersion for the functionally graded plate is given. Then, using the dispersion relation and integral transforms, exact integral response solutions of the functionally graded plate under a point impact load and an annular line impact load are obtained. The influence of volume fraction distributions on transient response of functionally graded plates is discussed in details. The convergence effect of wave propagation at the centre of the functionally graded plate under an annular impact load is studied and it is found that the deflection and circumferential stress at the centre of the functionally graded plate are much larger than the deflection and circumferential stress at other points of the plate. Thirdly, wave propagation and transient response of an infinite functionally graded plate under a point impact load in thermal environments are studied. The thermal effects and temperature-dependent material properties are taken into account. The governing equations of the wave propagation in the functionally graded plate are derived from Hamilton’s principle. The analytic dispersion relation of the functionally graded plate and exact integral solutions of the functionally graded plate under a point impact load in thermal environments are obtained. The influences of the volume fraction distributions and thermal environmental conditions on the wave propagation and transient response of functionally graded plates are discussed. Finally, the nonlinear wave propagation in a functionally graded beam is analyzed. The solitary wave solutions of displacement are obtained by solving the nonlinear differential equation of wave propagation using method of undetermined coefficient of displacement functions. Two cases of functionally graded materials, elastic modulus and mass density along the depth varying with exponentially and parabolic type, are analyzed by examples. The influence of the functionally graded materials and velocity of wave propagation on amplitude and width of solitary wave are discussed.