A series solution for the in-plane vibration analysis of orthotropic rectangular plates with elastically restrained edges

• A series solution of free in-plane vibration for orthotropic rectangular plates with elastically restrained edges is presented.
• Both two in-plane displacements are represented by a double Fourier cosine series and four supplementary functions.
• The computed results modal parameters agree well with those obtained from other analytical approach as well as Finite Element Analysis (FEA).
• This series solution can make accurate prediction for orthotropic rectangular plates with any classical boundary conditions as well as elastic edge supports.

In this paper, a series solution for the free in-plane vibration analysis of orthotropic rectangular plate with elastically restrained edges is obtained using an two-dimensional (2-D) improved Fourier series method. Both two in-plane displacements are represented by a double Fourier cosine series and four supplementary functions, in the form of the product of a polynomial function and a single cosine series expansion, introduced to remove the potential discontinuities associated with the original displacement functions along the edges when they are viewed as periodic functions defined over the entire x–y plane. All the unknown expansion coefficients are sought in a strong form by letting the solution accurately satisfy both the boundary conditions and the governing differential equations on a point-wise basis. Numerical examples are presented to demonstrate the reliability and effectiveness of the current solution through the comparison with those obtained from other analytical approach as well as Finite Element Analysis (FEA) by using NASTRAN.