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| Abstract: |
| A three-dimensional state space method has been developed for the calculation of dynamic response of plates with two free edges and two simply supported edges. A complex damping model was introduced, then the exact solutions which satisfy all the governing equations and boundary conditions were obtained. In order to overcome the difficulty of satisfying all the stress conditions at free edges, the displacement functions of free edges were assumed. The boundary conditions were strictly satisfied when the convergence rate was good. The computing time was evidently less than that of finite element method. The comparison of the solution with those of finite element method show that there is an excellent agreement for displacements. When the imaginary parts of normal stress deviated, the finite element results showed existence of shear stresses at top and bottom surfaces, and the boundary conditions of FEM model were not strictly satisfied. |
| Key words: three-dimensional exact solution state space method free edge response |
| DOI：10.11916/j.issn.1005-9113.18044 |
| Clc Number:O326 |
| Fund: |
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| Descriptions in Chinese: |
| 具有两自由边壁板动力学响应的三维精确解 王乐，余慕春 （中国运载火箭技术研究院，北京100076） 创新点说明：本文提出一种计算具有两自由边和两简支边壁板有阻尼振动响应的三维精确解法。通过在本构方程中引入复阻尼模型，并假设自由边的位移函数，得到了满足所有控制方程和边界条件的精确解。通过与三维有限元结果的对比验证了三维精确解法的优越性。 研究目的： 从几何方程、本构方程和平衡方程出发，不引入任何关于位移或应力分布的假设，研究具有两自由边和两简支边壁板有阻尼振动响应的三维精确解法。 研究方法： 将控制方程写成状态空间形式，在本构方程中引入复阻尼模型，对自由边的位移进行假设，结合边界条件求解板的应力和位移分量。 研究结果： 获得了严格满足边界条件的位移和应力解，而且收敛速度快，计算时间明显小于有限元法。 结论： 本文提出的计算具有两自由边和两简支边壁板有阻尼振动响应的三维精确解法可提供严格满足边界条件的位移和应力解。通过与三维有限元计算结果的对比验证了本文方法的优越性。 关键词：三维，精确解，状态空间法，自由边界条件，响应 |
