An analytical method for the in-plane vibration analysis of rectangular plates with elastically restrained edges

In this investigation, the in-plane vibration problems are solved for plates with general elastically restrained boundary conditions. Under the current framework, all the classical homogeneous boundary condition for in-plane displacements can be easily simulated by simply setting the stiffnesses of the restraining springs to either infinite or zero. The vibration problems are solved using an improved Fourier series method in which the in-plane displacements are expressed as the superposition of 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. The use of these supplementary functions is to overcome the discontinuity problems which the original displacement functions will potentially encounter along the edges when they are viewed as a periodic function defined over the entire x–y plane. The excellent accuracy and convergence of the current solution are demonstrated through numerical examples. To the best of authors’ knowledge, this work represents the first time that an analytical solution has been obtained for the in-plane vibrations of a rectangular plate with elastically restrained edges.