有轴力的部分作用组合梁的动力分析

摘要

针对轴力作用下部分作用组合梁的振动,给出了基于状态空间列式的求解方法,并导出了自由振动频率方程.进一步利用辛内积的概念,针对工程中常见的边界条件证明了振动模态的正交性,进而采用模态叠加法进行了瞬态响应分析,得到了移动集中荷载作用下该组合梁的动力响应.最后,给出了数值算例,计算了屈曲荷载,讨论了轴力对固有振动频率的影响以及对移动集中荷载作用下的部分作用组合梁的瞬态响应的影响.%Based on the state space formulae, a method is presented to analyze the dynamic behavior of partial-interactive composite beam with axial force and the frequency equations for free vibration are derived. By virtue of the conception of the sym-pletic inner product, the orthogonality of mode shape was proved for the partial-interactive composite beam under common boundary conditions in engineering and the transient responses were then investigated using the mode superposition method. The dynamic behaviors of the composite beam subjected to a moving concentrated force were obtained. Finally, numerical examples were given in which buckling loads were calculated and the effect of axial force on natural frequencies and the transient responses of the partial-interactive composite beams under a moving concentrated force were also discussed in detail.