Free vibration analysis of thin rectangular plates with two adjacent edges rotationally-restrained and the others free using finite Fourier integral transform method

For the first time, the finite Fourier integral transform approach is extended to analytically solve the free vibration problem of rectangular thin plates with two adjacent edges rotationally-restrained and others free. Based on the fundamental transform theory, the governing partial differential equations (PDEs) of the plate is converted to ordinary linear algebraic simultaneous equations without assuming trial function for deflection, which reduces the mathematical complexity caused by both the free corner and rotationally-restrained edges. By coupling with mathematical manipulation, the analytical solutions are elegantly achieved in a straightforward procedure. In addition, the vibration characteristics of plates under classical boundary conditions are also studied by choosing different rotating fixed coefficients. Finally, more than 400 comprehensive analytical solutions were well validated by finite element method (FEM) results, which can be served as reference data for further studies. The advantages of the present method are that it does not need to preselect the deformation function, and it has general applicability to various boundary conditions. The presented approach is promising to be further extended to solve the static and dynamic problems of moderately thick plates and thick plates.