摘要
多源激励谱反演属于逆问题范畴,反演解在系统共振频率及低频段会出现振荡。文章以数值仿真与理论相结合的方法,开展了矩形板四种方案的虚拟实验来研究多源激励谱反演振荡问题。首先进行了板的模态分析和响应分析,数值解与理论解吻合良好,验证了方法的可行性。然后分别以直接法、截断奇异值分解法(TSVD)、Tikhonov 正则法对板的多源激励谱进行反演。结果表明:(1) 多源激励谱反演时,保证响应点数量大于激励点数量可有效抑制反演解在共振频率处的振荡;(2) 采用 TSVD 法、Tikhonov 正则法可有效抑制反演解的低频振荡。最后,用反演的激励谱重构接收点的响应谱,重构解与理想值吻合较好,验证了虚拟实验及方法的可信性。
Multiple excitations inversion belongs to backward problem, in which the solution always oscillates at the resonance frequencies of the system and low frequency range. In this paper, a virtual experiment with four schemes for a simply supported plate is conducted to research the inversion-oscillations of multiple excitations via computer simulation and theoretical methods. The modal and harmonic analysis of the plate is calculated, and the numerical solution agrees well with theoretical solution, which indicates the practicability of the method. The excitations are inversed by direct method, Truncated Singular Value Decomposition （TSVD） method, Tikhonov regularization method, respectively. Results show that： （1） In the process of excitations inversion, when the number of response points exceeds excitation points, the inversion-oscillation at resonance frequencies can be well depressed; （2） When adopting TSVD and Tikhonov regularization method, the inversion-oscillation at low frequency range can be well depressed. Finally, the inversed excitations are used to reconstruct the response spectrum of receiving point, and the reconstructed solution agrees well with its ideal value, which convinced the practicability of the simulation and method.
出处
《船舶力学》
EI
CSCD
北大核心
2013年第3期268-276,共9页
Journal of Ship Mechanics
关键词
多源激励
反演振荡
截断奇异值分解
Tikhonov
正则化
multiple excitations
inversion-oscillations
truncated singular value decomposition
Tikhonov regularization
