The vibrations of rectangular orthotropic plates with massive inclusions

The problem of vibration of plates with different kinds of stiffeners and the concentrated mass is rather widely considered in science. In the articles of Chain Gin Boay a free vibration analysis of rectangular plates carrying a concentrated mass is analysed where the deflection of the plate is postulated by a multi-term trigonometric series function and the Ritz approach and Rayley-energy method is applied to rectangular plates with various edge support combinations of clamp and simple support conditions [8][9]. In the work of B.P.Shastry and G.Venkateswara Rao free vibration of plates with arbitrary oriented stiffeners are studied using high precision plate bending and stiffener elements for both simply supported and clamped boundary conditions [7]. In the work of Ding Zhou and Tianjian the vibratory characteristics of rectangular plates attached with continuously and uniformly distributed spring-mass in a rectangular region are studied and the Ritz-Galerkin method is used to derive the approximate solution when the spring-mass is distributed on part the plate by using the Chebyshev polynomial series to construct the admissible functions [6]. In the paper of N.Li and D.J.Gorman the problem of free vibration of simply supported rectangular plates with internal line support along diagonals is considered and here fore the solution is used the approach where the line supports are replaced by multi point support [5]. The exact approach for free vibration analysis of rectangular isotropic plates with line-concentrated mass and elastic line-support is presented in the paper of O.S.Li [4].