一类浅垂度倾斜双梁系统动力特性研究

Dynamic characteristic research on the double-beam system with shallow sag and inclination

基于动刚度理论建立了倾斜双梁单元的动力平衡方程,给出了同时考虑双梁抗弯刚度差异、倾角、固定边界条件以及垂度等因素的系统横向动刚度阵的近似闭合解。以该闭合解为基础,分析了双梁系统横向动刚度阵的特征函数及动刚度系数在空间和频域上的分布规律。通过数值案例分析,研究了双梁系统的振动特性,进而建议了一种双梁系统模态频率贡献问题的快速判断方法。研究表明,在给定频率区间内,双梁系统的模态频率将同时受到每个单梁的影响,可以通过双梁横向动刚度阵的特征函数及动刚度系数在频域的分布规律进一步判断单梁对系统各阶频率的贡献程度。

Based on the theory of dynamic stiffness,the dynamic equilibrium equation of the inclined double-beam element is established.The approximate closed form solution of the transverse dynamic stiffness matrix of the system with simultaneously considering the bending stiffness difference of the double beam,inclination angle,fixed boundary condition and the sag effect are obtained.Based on this solution,the space and frequency domain distribution of the characteristic function and the dynamic stiffness coefficient of the transverse dynamic stiffness array are analyzed.Through a numerical case study,the vibration characteristics of the double-beam system are studied,and then a method for quickly determining the contribution of each single beam to the modal frequency of the system is proposed.The results show that the modal frequency of the double-beam system is affected by each single beam in a given frequency range.The contribution of each single beam to the system frequencies can be further determined by the distribution situationof the characteristic function of the transverse stiffness matrix and the dynamic stiffness coefficients in the frequency domain.