铰接桁架结构动力学问题研究

以铰接桁架结构为对象,采用谱元法研究铰对桁架结构动力学行为的影响,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,分别建立铰、杆和梁单元的动力学刚度矩阵,并加以整合得到整体结构的动力学刚度阵,进而建立整体结构的动力学方程。通过求解整体结构的动力学方程,获得结构的固有频率、频响曲线和时间响应历程曲线,并将谱元法的计算结果同有限元法的相应结果进行了比较。分析结果表明,谱元法在求解铰接桁架结构的动力学问题上具有较高的精确性,并且铰的存在对桁架结构动力学行为具有显著影响。

Study on the Dynamics Problems of Truss Structure with Joints

In this paper,the dynamics problems of truss structure with joints are researched by using the spectral element method(SEM),and effects of joints on the dynamics behavior of the truss structure are analyzed,thus expanding application fields of the SEM.The joint structure is considered as a spectral element in the frequency domain.The dynamics stiffness matrices of the joint,rod and beam elements are established respectively.The dynamics stiffness matrix of the whole structure is obtained by integrating the dynamics stiffness matrices of the joint,rod and beam elements,and the dynamics equation of the whole structure is further established.The natural frequencies,frequency response curves and time domain responses of the structure are obtained by the calculation of the dynamics equation of the whole structure.The results calculated by the SEM are compared with the corresponding results obtained by the finite element method.From the numerical results,it is seen that the dynamics problems of truss structure with joints can be accurately solved by the SEM,and the joints have obvious influence on the dynamics behaviors of the truss structure.