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Accurate free vibration solutions of orthotropic rectangular thin plates by straightforward finite integral transform method

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Abstract

This paper aims to obtain the analytical free vibration solution of an orthotropic rectangular thin plate using the finite integral transformation. Due to the mathematical difficulty of complex boundary value problems, it is very hard to solve the title problem with common analytical methods. By imposing the integral transformation, the high-order partial differential equation with specified boundary conditions is converted into linear algebraic equation and the exact solutions with high precision and fast convergence are obtained elegantly. The main advantage of the proposed method is that it is simple and general, and it does not need to pre-determine the deflection function, which makes the solution procedure more reasonable. The method has a wide range of applications and can deal with other elastic plate problems, such as buckling and bending. The present results are validated by comparison with the existing analytical solutions that showed satisfactory agreement. The new analytical solution obtained can be used as a benchmark for validating other numerical and approximate methods.

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Correspondence to Salamat Ullah.

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Zhang, J., Ullah, S. & Zhong, Y. Accurate free vibration solutions of orthotropic rectangular thin plates by straightforward finite integral transform method. Arch Appl Mech 90, 353–368 (2020). https://doi.org/10.1007/s00419-019-01613-1

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Keywords

  • Free vibration
  • Finite integral transform
  • Analytical solution
  • Orthotropic rectangular thin plate