谱元法研究杆系结构的动力学问题

发布时间：2018-04-05 22:34

本文选题：谱元法　切入点：刚架　出处：《哈尔滨工业大学》2011年硕士论文

【摘要】：有限元法,有限差分法和谱元法是当前被用来求解结构动力学问题的主要方法。其中谱元法因其采用与频率有关的插值函数、与有限元方法相结合、对复杂边界具有广泛的适应性以及具有谱方法的快速收敛性,具有重要的研究价值。谱元法由有限元法、动力学刚度法和谱分析方法的关键要素整合而来。精确的动力学刚度矩阵以由控制方程的波动解推导出的频域上精确的动力学形函数为基础,所以在理论上谱元法会得到精确的频域解。本文在总结了谱元法的优缺点之后,推导了杆单元和梁单元的动力学刚度矩阵,并计算了杆结构和梁结构的固有频率和时域响应。然后,论文将谱元法应用于杆系结构的动力学响应分析和计算中。杆系结构由于连接方式的不同被分为刚架结构和桁架结构。针对刚架结构组装了整体动力学刚度阵,给出了整体结构的运动方程,计算了结构的固有频率和时域响应,并与采用有限元方法得到的结果进行了对比。从结果中可以看出谱元法在数值模拟中的独特优势。分别以含理想铰的连接杆结构和桁架结构为对象,采用谱元法研究了铰结构对整体结构动力学行为的影响。论文将铰模拟为分段线性模型,并将谱元法推广应用到求解分段线性问题,拓展了谱元法的应用领域。在频域下将铰结构考虑为一个谱单元,将铰结构和其它结构的动力学刚度矩阵整合起来得到整体结构的动力学刚度阵,进而得到整体结构的运动方程,通过求解整体结构的动力学方程,获得结构的时间响应历程曲线,分析了含铰的连接杆结构和桁架结构动力学行为。
[Abstract]:Finite element method, finite difference method and spectral element method are the main methods used to solve structural dynamics problems.The spectral element method has extensive adaptability to complex boundary and fast convergence of spectral method because of its use of frequency-related interpolation function and finite element method.The spectral element method integrates the key elements of finite element method, dynamic stiffness method and spectral analysis method.The exact dynamic stiffness matrix is based on the exact dynamic form function in the frequency domain derived from the wave solution of the governing equation, so the spectral element method can obtain the exact frequency domain solution in theory.After summarizing the merits and demerits of the spectral element method, the dynamic stiffness matrix of the bar element and the beam element is derived, and the natural frequency and the time domain response of the rod structure and the beam structure are calculated.Then, the spectral element method is applied to the dynamic response analysis and calculation of the bar structure.The bar structure is divided into rigid frame structure and truss structure because of the different connection mode.The integral dynamic stiffness matrix is assembled for the rigid frame structure, the motion equation of the whole structure is given, the natural frequency and the time domain response of the structure are calculated, and the results obtained by the finite element method are compared with those obtained by the finite element method.From the results, we can see the unique advantages of spectral element method in numerical simulation.The influence of the hinge structure on the dynamic behavior of the whole structure is studied by using the spectral element method, taking the connecting bar structure and the truss structure with ideal hinges as the objects.In this paper, the hinge is simulated as a piecewise linear model, and the spectral element method is extended to solve the piecewise linear problem, which extends the application field of the spectral element method.Considering the hinge structure as a spectral element in frequency domain, the dynamic stiffness matrix of the whole structure is obtained by integrating the dynamic stiffness matrix of the hinge structure and other structures, and then the motion equation of the whole structure is obtained.By solving the dynamic equation of the whole structure, the time response history curve of the structure is obtained, and the dynamic behavior of the connecting bar structure and truss structure with hinge is analyzed.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：TH113

【引证文献】