Vibration of Flexible Structures Under Nonlinear Boundary Conditions
Vibration of Flexible Structures Under Nonlinear Boundary Conditions
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DOI：
10.1115/1.4037883
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发表时间：
2017-11
期刊：
影响因子：
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通讯作者：
Xiao-Ye Mao;H. Ding;Liqun Chen
中科院分区：
文献类型：
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作者：
Xiao-Ye Mao;H. Ding;Liqun Chen
首次研究了一般支承条件下柔性结构的非线性响应。首先提出了一种分析方法。此外，通常采用的静态分析的仿真技术开发的确认。一般情况下，常规摄动法可以分析具有线性边界条件的柔性结构的动力学问题。由于考虑了非线性边界，因此对于难以得到的模态振型，边界不起作用，而模态振型是分析的关键。为了克服这一点，非线性边界条件重新标度和模态修正的技术。因此，不同时间尺度的控制方程可以根据相应的重标边界条件进行精确分析。柔性结构上任意一点的总响应将由解析方法得到的谐响应组成。此外，微分求积单元法（DQEM），一个数值模拟技术，可以满足严格的边界条件，以验证分析结果。比较表明，这两种方法之间的合理协议。实际上，非线性边界解析法的精度可以从理论上得到解释。在此基础上，对边界非线性进行了详细的分析讨论，发现边界非线性在响应中起着重要的作用。由于非线性因素在柔性结构的振动与控制中所起的重要作用，本文将展开具有非线性约束的柔性结构的振动分析与数值研究。
The nonlinear response of a flexible structure, subjected to generally supported conditions with nonlinearities, is investigated for the first time. An analytical procedure is proposed first. Moreover, a simulation technique usually employed in static analysis is developed for confirmation. Generally, ordinary perturbation methods could analyze dynamics of flexible structures with linear boundary conditions. As nonlinear boundaries are taken into account, they are out of operation for the modal shape that is hardly to be obtained, which is the key to the analysis. In order to overcome this, nonlinear boundary conditions are rescaled and the technique of modal revision is employed. Consequently, each governing equation with different time-scales could be analyzed exactly according to corresponding rescaled boundary conditions. The total response of any point at the flexible structure will be composed by harmonic responses yielded by the analytical method. Furthermore, the differential quadrature element method (DQEM), a numerical simulation technique could satisfy boundary conditions strictly, is introduced to certify analytical results. The comparison shows a reasonable agreement between these two methods. In fact, the accuracy of the analytical method for nonlinear boundaries could be explained in theory. Based on the certification, boundary nonlinearities are discussed in detail analytically and found to play an important role in responses. Because of the important role played by the nonlinear factors in the vibration and control of the flexible structure, this paper will open the vibration analysis and numerical study of the flexible structure with nonlinear constraints.