Abstract
For the first time, the double half-Sinusoidal series is adopted as integral kernel to construct integral transform pair for new precise vibration analysis of orthotropic rectangular thin plates, supported with two adjacent edges rotationally-restrained and the other edges are free. Impose the defined single/double transforms on both the vibration governing partial differential equation (PDE) and some of the boundaries investigated, which gives the Fourier coefficient for the deflection expressed by some specific unknown constants. Utilizing the inverse formular to satify the remaining boundaries leads to a set of linear algebraic simultaneous equations, which yields the solutions of the natural frequency parameter and the associated mode shapes. Moreover, plates under classical boundary conditions also can be investigated via changing the rotating fixed coefficients introduced. Finally, more than 500 comprehensive analytical solutions were well validated by numerical results presented by finite element method (FEM), which can be treated as new reference results for further studies. Since its straightforward and rational solution procedure, the presented approach is promising to be further extended to solve more complicated boundary value problems (BVPs) of plates.
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