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closed-form solutions for free vibration of rectangular FGM thin plates resting on elastic foundation

Acta Mechanica Sinica 2016年第6期32卷 1088-1103页

作者： T. F. Xu Y. F. Xing Institute of Solid Mechanics Beihang UniversityBeijing 100191 China China Academy of Launch Vehicle Technology R&D Center Beijing 100076 China

This article presents closed-form solutions for the frequency analysis of rectangular functionally graded material (FGM) thin plates subjected to initially in-plane loads and with an elastic foundation. Based on classical thin plate theory, the governing differential equations are derived using Hamilton's principle. A neutral surface is used to eliminate stretching-bending coupling in FGM plates on the basis of the assumption of constant Poisson's ratio. The resulting governing equation of FGM thin plates has the same form as homogeneous thin plates. The separation-of-variables method is adopted to obtain solutions for the free vibration problems of rectangular FGM thin plates with separable boundary conditions, including, for example, clamped plates. The obtained normal modes and frequencies are in elegant closed forms, and present formulations and solutions are validated by comparing present results with those in the literature and finite element method results obtained by the authors. A parameter study reveals the effects of the power law index n and aspect ratio a/b on frequencies.

关键词： Functionally graded material Free vibration Rectangular plate close form solutions Neutral surface

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Abundant closed form wave solutions to some nonlinear evolution equations in mathematical physics

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Journal of Ocean Engineering and Science 2020年第3期5卷 269-278页

作者： M.Mamun Miah Aly R.Seadawy H.M.Shahadat Ali M.Ali Akbar Department of Mathematics Khulna University of Engineering&TechnologyBangladesh Mathematics Department Taibah UniversityAl-Madinah Al-MunawarahSaudi Arabia Department of Mathematics Beni-Suef UniversityEgypt Department of Applied Mathematics Noakhali Science and Technology UniversityBangladesh Department of Applied Mathematics University of RajshahiRajshahi 6205Bangladesh

The propagation of waves in dispersive media,liquid flow containing gas bubbles,fluid flow in elastic tubes,oceans and gravity waves in a smaller domain,spatio-temporal rescaling of the nonlinear wave motion are delineated by the compound Korteweg-de Vries(KdV)-Burgers equation,the(2+1)-dimensional Maccari system and the generalized shallow water wave equation.In this work,we effectively derive abundant closed form wave solutions of these equations by using the double(G′/G,1/G)-expansion method.The obtained solutions include singular kink shaped soliton solutions,periodic solution,singular periodic solution,single soliton and other solutions as well.We show that the double(G′/G,1/G)-expansion method is an efficient and powerful method to examine nonlinear evolution equations(NLEEs)in mathematical physics and scientific application.

关键词： close form solutions KdV-Burgers equation The(2+1)-dimensional Maccari system The generalized shallow water wave equation

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