CAJ | 학술논문

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.
다원격려보반연속우역문제범주,반연해재계통공진빈솔급저빈단회출현진탕.문장이수치방진여이론상결합적방법,개전료구형판사충방안적허의실험래연구다원격려보반연진탕문제.수선진행료판적모태분석화향응분석,수치해여이론해문합량호,험증료방법적가행성.연후분별이직접법、절단기이치분해법(TSVD)、Tikhonov정칙법대판적다원격려보진행반연.결과표명:(1)다원격려보반연시,보증향응점수량대우격려점수량가유효억제반연해재공진빈솔처적진탕;(2)채용TSVD법、Tikhonov정칙법가유효억제반연해적저빈진탕.최후,용반연적격려보중구접수점적향응보,중구해여이상치문합교호,험증료허의실험급방법적가신성.
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 virtu-al experiment with four schemes for a simply supported plate is conducted to research the inver-sion-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 theo-retical solution, which indicates the practicability of the method. The excitations are inversed by di-rect 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 re-sponse 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 val-ue, which convinced the practicability of the simulation and method.