A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems
A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems
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DOI：
10.1016/j.ymssp.2016.10.017
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发表时间：
2017-03-15
影响因子：
8.4
通讯作者：
Banerjee, J. R.
中科院分区：
文献类型：
--
作者：
Liu, X.;Banerjee, J. R.
本文提出了一种基于平面应力和平面应变假设的平面弹性动力学问题模态分析的高效、高精度解析谱动刚度（SDS）方法。首先，应用两类一维修正傅里叶级数导出了精确满足控制微分方程的通解。然后，SDS矩阵的元素是制定象征性地使用通解。SDS矩阵的组装直接在一个类似的方式，有限元方法，证明了该方法的能力，以模拟复杂的结构。任意边界条件都可以用修正的傅里叶级数精确表示。然后使用Wittrick-Williams算法作为解决技术，其中解决了完全夹紧元件的模式计数问题（J（0））。该方法给出了高精度的解决方案，具有显着的计算效率，覆盖低，中，高频率范围。该方法适用于平面应力和平面应变问题与简单以及复杂的几何形状。本文中的所有理论结果都是准确的，直到引用的最后数字作为基准。
A highly efficient and accurate analytical spectral dynamic stiffness (SDS) method for modal analysis of plane elastodynamic problems based on both plane stress and plane strain assumptions is presented in this paper. First, the general solution satisfying the governing differential equation exactly is derived by applying two types of one-dimensional modified Fourier series. Then the SDS matrix for an element is formulated symbolically using the general solution. The SDS matrices are assembled directly in a similar way to that of the finite element method, demonstrating the method's capability to model complex structures. Any arbitrary boundary conditions are represented accurately in the form of the modified Fourier series. The Wittrick-Williams algorithm is then used as the solution technique where the mode count problem (J(0)) of a fully-clamped element is resolved. The proposed method gives highly accurate solutions with remarkable computational efficiency, covering low, medium and high frequency ranges. The method is applied to both plane stress and plane strain problems with simple as well as complex geometries. All results from the theory in this paper are accurate up to the last figures quoted to serve as benchmarks.