Vibration Cosine Solutions of Free Orthotropic Rectangular Plates on the Elastic Half-Space
In this paper, the analytic solutions of steady vibration of free orthotropic rectangular plate loaded with vertical steady loading on the elastic half-space was given by combining the general solution of double trigonometrically cosine series with supplementary terms with dynamic integral representations for displacements of the elastic half-space loaded with arbitrary vertical steady loading. This solution not only is four-order derivative, but also has less undetermined coefficients. It can be used to solve the problems of bending and steady vibration of orthotropic rectangular plates on the elastic half-space without be classified and be superimposed. This causes this kind of things, bending and steady vibration of orthotropic rectangular plates with four free edges on the elastic half-space, unionization, simplification and systematization. When the material is isotropic, the solutions are turned into analytic solutions of steady vibration of free rectangular plate on the elastic half-space. At last some computational examples are presented and the results are coincided with those in literatures. Then the method in this paper will be of important practical applications.
Yungang Li, Pengcheng Wang, Liqun Ai, Xiaoming Sang and Jinglong Bu
C. L. Wang et al., "Vibration Cosine Solutions of Free Orthotropic Rectangular Plates on the Elastic Half-Space", Advanced Materials Research, Vols. 291-294, pp. 2094-2097, 2011