A new method for analytical solution of inplane free vibration of rectangular orthotropic plates based on the analysis of infinite systems

In this paper, a new method for in-plane free vibration analysis of rectangular orthotropic plate is presented. The cases for completely clamped and completely free plates are considered in detail. The boundary value problem is essentially reduced to infinite systems of linear algebraic equations. New mathematical theory and associated results are presented for investigating the asymptotic behavior of non-trivial solution of quasi-regular infinite system. By enhancing the theory, an effective and accurate algorithm for determining the natural frequencies and modes shapes vibrations is developed. The accuracy and computational efficiency of the method are demonstrated by examples.