An accurate series solution for the transverse vibration of orthotropic plates with general elastic boundary conditions

摘要

This paper describes an accurate method for calculating the natural frequencies of orthotropic plates with general elastic boundary supports. The displacement function is expressed as a 2-D Fourier cosine series supplemented with several terms in the form of 1-D series. The series expansions for all the relevant derivatives can be directly obtained through term-by-term differentiations of the series of the displacement. Thus, a classical solution can be derived by letting the series exactly satisfy the governing differential equation and all the boundary conditions at every field and boundary point, respectively. Several numerical examples are presented to demonstrate the excellent accuracy and convergence of the current solutions.