矩形简支薄板振动模态及灵敏度分析  

Research on Modal and Its Sensitivity of Rectangular Plate Supported Simply

作　　者：王秀颖 张军[1] 兆文忠[1] WANG Xiuying;ZHANG Jun;ZHAO Wenzhong(School of Traffic and Transportation Engineering,Dalian Jiaotong University,Dalian 116028,China)

机构地区：[1]大连交通大学交通工程学院,辽宁大连116028

出　　处：《大连交通大学学报》2018年第4期27-31,共5页Journal of Dalian Jiaotong University

基　　金：牵引动力国家重点实验室开放课题资助项目(TPL1402)

摘　　要：基于矩形简支薄板模态频率的理论解,推导了模态频率对薄板厚度灵敏度理论解,通过实例计算了矩形简支薄板前10阶模态频率及灵敏度,并计算分析了厚度增加单位值时模态频率灵敏度理论差分解;建立了矩形薄板的有限单元模型,用有限单元法计算了矩形简支薄板的模态频率和振型,分析比较了有限单元数量对模态计算精度的影响;基于有限单元法,用数值微分法计算了薄板模态频率对板厚度的灵敏度,并计算分析了基于有限单元法的模态频率灵敏度差分解.理论推导和计算结果表明,简支矩形薄板模态频率对板厚度灵敏度的理论解与厚度无关,数值微分模态频率灵敏度与理论解的误差最小,其精度高于理论差分解和有限元差分解,证明了数值微分法模态频率灵敏度的准确性和有效性.The modal frequency sensitivities of rectangle plate supported simply with respect to thicknesses are deduced based on the theoretical solutions of its modal frequency. The first 10 order modal frequencies and its sensitivities of a plate are computed as an example,while the theoretical difference solutions of modal frequency sensitivities are also computed when the thicknesses of 1 mm are increased. A finite element model of rectangle plate supported simply is set up,its modal frequencies and modal vectors are achieved by using of finite element method,and the effect of element number on precision is analyzed and compared. Based on finite element method,the sensitivities of the modal frequencies with respect to plate thicknesses using numerical differentiation method are achieved,and the sensitivities of modal frequencies using method of difference are also computed. The results show that the sensitivities of the plate modal frequencies with respect to the thicknesses have nothing to do with the plate thickness,the errors between the numerical differentiation solutions and theoretical solutions are the least,and the precision of the solutions using the numerical differentiation method are higher than the difference method. the accuracy and validity of numerical differentiation method are tested and verified by this research.

关 键 词：简支薄板 模态频率 灵敏度 有限元法 

分 类 号：O327[理学—一般力学与力学基础]