Shahrood University of Technology Journal of Solid and Fluid Mechanics 2251-9475 5 1 2015 06 15 Dynamic Response of Curved Sandwich Beam with a Soft Flexible Core Subjected to Radial Low Velocity Impact Dynamic Response of Curved Sandwich Beam with a Soft Flexible Core Subjected to Radial Low Velocity Impact 1 11 417 10.22044/jsfm.2015.417 FA Hamze Salehipoor Isfahan University of Technology Rouhollah Hosseini Ph.D. student, Mechanical Engineering Department, University of Tehran Journal Article 2013 11 02 In this paper, an exact closed-form solution is presented for out-of-plane free vibration of thick homogeneous and isotropic multilayered rectangular plates with simply supported boundary conditions based on the linear three-dimensional elasticity theory. The solution procedure is on the basis of using of some proposed displacement fields. Proposed displacement fields satisfied simply supported boundary conditions on the edges of the plate. On the continuation of the solution, by replacing the proposed displacement fields into the three-dimensional elasticity equations of motion and simplifying the results some independent ordinary differential equations are obtained. The natural frequencies are extracted by satisfying the boundary conditions on the surfaces of the plate and surfaces between the layers. In order to establish the accuracy and stability of the proposed solution, several numerical results for one layered and two layered square and rectangular plates are presented and compared with corresponding results in the literatures and obtained results of 3-D finite element method. In this paper, an exact closed-form solution is presented for out-of-plane free vibration of thick homogeneous and isotropic multilayered rectangular plates with simply supported boundary conditions based on the linear three-dimensional elasticity theory. The solution procedure is on the basis of using of some proposed displacement fields. Proposed displacement fields satisfied simply supported boundary conditions on the edges of the plate. On the continuation of the solution, by replacing the proposed displacement fields into the three-dimensional elasticity equations of motion and simplifying the results some independent ordinary differential equations are obtained. The natural frequencies are extracted by satisfying the boundary conditions on the surfaces of the plate and surfaces between the layers. In order to establish the accuracy and stability of the proposed solution, several numerical results for one layered and two layered square and rectangular plates are presented and compared with corresponding results in the literatures and obtained results of 3-D finite element method. https://jsfm.shahroodut.ac.ir/article_417_3d46d98450c62f4b0e1d32a386e81fd9.pdf