薄板振动分析的辛空间波传播方法  

A wave propagation method in symplectic space for vibration analysis of thin plates

作　　者：张亚辉[1] 马永彬 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,大连116023

出　　处：《振动与冲击》2014年第12期1-6,14,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金项目11172056;新世纪优秀人才支持计划项目NCET-10-0288;中央高校基本科研业务费专项基金DUT13ZD(G)04

摘　　要：基于弹性力学问题求解的辛方法,结合波传播理论,提出一个薄板结构稳态动力响应分析的新思路。首先,将薄板振动的控制方程导入辛对偶体系,应用分离变量法得到薄板波传播问题的本征值方程,求解得到本征值(波传播参数)与本征向量(波形);然后将物理空间求解体系转换到波空间,进而结合波传播以及波反射关系求解薄板结构的受迫振动问题。算例给出了矩形薄板在四边简支(SSSS)和一对边固支、另一对边简支(CCSS)两种边界条件下的输入点导纳以及动能和应变能;四边简支的结果与模态叠加法给出的解析解以及波有限元法的结果做了对比,对边固支-对边简支边界下的结果与有限元程序系统ABAQUS的参考解以及波有限元法结果做了对比,对比结果验证了该方法的精确性与有效性。A new approach was presented for steady vibration analysis of thin plates based on the symplectic method of elasticity problems and the theory of wave propagation.The vibration governing equations of thin plates were introduced into a symplectic duality system,the eigenvalue equations were formulated by applying the method of variable separation,the eigenvalues （wave propagation parameters） and eigenvectors （wave modes） were solved.The equations of motion in physical domain were then transformed into wave co-ordinates,the forced vibration responses of thin plates were solved by using the incident and reflection wave components.Taking a rectangular thin plate as an illustrative example,the numerical results of the input mobility,kinetic energy and strain energy of the plate under two combinations of simply supported （S） and clamped （C） boundary conditions,i.e.,CCSS and SSSS were computed.The accuracy and efficiency of the method were validated by comparing the above results with those of the analytic solutions of the mode superposition method,the wave finite element method and ABAQUS software,respectively.

关 键 词：辛对偶体系 波导 波有限元 波传播 

分 类 号：O326[理学—一般力学与力学基础]