辛对偶体系下薄壁圆柱壳强迫振动响应分析  

Forced vibration analysis of thin cylindrical shells in symplectic duality system

作　　者：李榆银 张亚辉[1] 秦朝红[2] 

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,辽宁大连116024 [2]北京强度环境研究所可靠性与环境工程技术重点实验室,北京100076

出　　处：《振动工程学报》2017年第2期185-193,共9页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(11172056);国家重点基础研究发展计划资助项目(2014CB046803)

摘　　要：在辛对偶体系下,采用波传播分析方法研究了薄壁圆柱壳在简谐外力作用下的强迫振动响应。首先,通过Hamilton函数将薄壁圆柱壳的振动问题导入辛对偶体系;然后,通过求解辛本征问题建立了具有共轭辛正交性质的波形矩阵,并将物理空间中的问题转换到波形空间中进行描述;最后,结合外力作用处和边界处的位移和内力协调关系,以及圆柱壳轴向的波传播关系,得到圆柱壳任意位置处的波幅表达式。与振型叠加法相比,此方法对高频振动问题具有更高的计算精度和效率。另外,此方法可方便地处理复杂边界条件。算例考虑了不同边界条件的情况,与振型叠加法或NASTRAN的结果进行比较,验证了此方法的有效性。A forced vibration analysis of a thin cylindrical shell subjected to harmonic external load is presented by using the wave propagation method and the symplectic duality system. Initially the vibration problem of a thin cylindrical shell is derived into the symplectic dual space with the application of the Hamiltonian function. A wave shape matrix with symplectic orthogonal relation is then calculated by solving a symplectic eigenproblem, following which the problem in physical domain is transformed into wave co-ordinates. Finally, the equations of the wave amplitudes of the thin cylindrical shell are formulated based on the analysis of free elastic wave propagation through the structure, and consist of applying the appropriate equilibrium and compatibility conditions at boundaries and where the external load applied. The presented method is more effective and accurate than the modal superposition method, offering particular advantages in the study of high-frequency response of the thin cylindrical shell. It is found that the present method can readily deal with cases for which there are complex boundary conditions. The accuracy and efficiency of the present method is investigated by application to a thin cylindrical shell with different boundary conditions, and a comparison is made with the modal superposition method or NASTRAN.

关 键 词：强迫振动 薄壁圆柱壳 辛对偶体系 波传播方法 

分 类 号：O326[理学—一般力学与力学基础]