基于辛叠加方法的正交各向异性矩形悬臂薄板受迫振动解析解  

Analytical Forced Vibration Solutions of Orthotropic Cantilever Rectangular Thin Plates With the Symplectic Superposition Method

作　　者：王森林 李进宝 马红艳[1] 李锐 WANG Senlin;LI Jinbao;MA Hongyan;LI Rui(State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian,Liaoning 116024,P.R.China)

机构地区：[1]大连理工大学工程力学系工业装备结构分析优化与CAE软件全国重点实验室,辽宁大连116024

出　　处：《应用数学和力学》2024年第9期1117-1132,共16页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12372067,12022209,11972103)。

摘　　要：基于辛叠加方法研究了正交各向异性矩形悬臂薄板在谐载载荷作用下的受迫振动问题.首先从薄板受迫振动的基本方程出发,将问题导入到Hamilton体系,并将原问题拆分为若干子问题,然后在辛空间中利用分离变量和本征展开方法推导出子问题的解析解,最后通过叠加求解出悬臂薄板受迫振动的解析解.辛叠加方法的主要优点是经过逐步严格推导获得解析解,不需要对解的形式做任何假设,突破了传统半逆解法的限制.算例针对不同谐载载荷情况进行了数值计算,并将该文方法与有限元方法获得的结果进行比较,验证了该文方法的可靠性和精确性.The forced vibrations of orthotropic cantilever rectangular thin plates under harmonic loadings were investigated with the symplectic superposition method.The basic equations for the forced vibration of thin plates were introduced into the Hamiltonian system.The original problem was divided into some fundamental subproblems,and the analytical solutions of the subproblems were derived with the method of separation of variables and through eigenvector expansion in the symplectic space.The solution of the original problem was finally obtained by superposition.The main advantage of the symplectic superposition method is that the analyti-cal solution can be obtained by step-by-step rigorous derivation,without any assumptions on the form of the solution,which breaks through the limitations of traditional semi-inverse methods.The numerical results calcu-lated corresponding to different harmonic loads were compared with those obtained via the finite element meth-od to verify the reliability and accuracy of the proposed method.

关 键 词：辛叠加方法 正交各向异性薄板 解析解 受迫振动 

分 类 号：O302[理学—力学]