Exact dynamic stiffness elements based on one-dimensional higher-order theories for free vibration analysis of solid and thin-walled structures
Exact dynamic stiffness elements based on one-dimensional higher-order theories for free vibration analysis of solid and thin-walled structures
复制标题
DOI：
10.1016/j.jsv.2013.06.023
复制
发表时间：
2013-11
影响因子：
4.7
通讯作者：
A. Pagani;M. Boscolo;J. Banerjee;E. Carrera
中科院分区：
文献类型：
--
作者：
A. Pagani;M. Boscolo;J. Banerjee;E. Carrera
在本文中，一个精确的动态刚度公式使用一维（1D）高阶理论，随后被用来研究固体和薄壁结构的自由振动特性。高阶运动学领域的开发使用卡雷拉统一配方，它允许直接实施的任何阶理论，而不需要特设配方。经典的梁理论（欧拉-伯努利和Eulshenko）也被捕获的制剂作为退化的情况下。利用虚位移原理导出了控制微分方程和相应的自然边界条件。一个精确的动态刚度矩阵，然后开发有关的谐波变化的负载的振幅的响应。文中还给出了动力刚度矩阵的显式项。所得的动态刚度矩阵，特别是参考Wittrick-Williams算法进行固体和薄壁结构的自由振动分析。理论的准确性得到了文献和使用商业代码MSC/NASTRAN®的大量有限元解的证实。
In this paper, an exact dynamic stiffness formulation using one-dimensional (1D) higher-order theories is presented and subsequently used to investigate the free vibration characteristics of solid and thin-walled structures. Higher-order kinematic fields are developed using the Carrera Unified Formulation, which allows for straightforward implementation of any-order theory without the need for ad hoc formulations. Classical beam theories (Euler–Bernoulli and Timoshenko) are also captured from the formulation as degenerate cases. The Principle of Virtual Displacements is used to derive the governing differential equations and the associated natural boundary conditions. An exact dynamic stiffness matrix is then developed by relating the amplitudes of harmonically varying loads to those of the responses. The explicit terms of the dynamic stiffness matrices are also presented. The resulting dynamic stiffness matrix is used with particular reference to the Wittrick–Williams algorithm to carry out the free vibration analysis of solid and thin-walled structures. The accuracy of the theory is confirmed both by published literature and by extensive finite element solutions using the commercial code MSC/NASTRAN®.