轴力作用下带弹性支座的Timoshenko梁的动力优化

Dynamic optimization of Timoshenko beam with internal elastic support under axial force

考察了轴力作用下中间带支座的Timoshenko梁的动力优化问题,在指出传统回传矩阵法优越性的基础上提出了实数形式的回传矩阵列式,从而避免了回传矩阵法在复数域内的运算,方便了频率的求解,并在一定程度上提高了计算效率.同时利用该方法建立了频率方程,给出了算例,验证了该方法的计算精度及高频计算的稳定性,并且探讨了轴力、支座位置及支座刚度对梁动力性能的影响,确定了最佳支座位置和最小支座刚度.提出的实数形式回传矩阵列式不仅适用于任何一维结构形式,还可将其应用于连续梁、平面框架和空间框架等复杂结构的静动力分析.

A new reverberation-ray matrix method formulated completely in real form（RF-RMM） was presented to avoid computation in complex domain and facilitate the search of frequencies as well as improve the computational efficiency. A frequency equation was established and numerical examples were given to demonstrate the accuracy and numerical stability in high-frequency range of the proposed method. The effects of axial force, the location and stiffness of the internal elastic support on the dynamic performance were investigated, and the optimized location and the minimized stiffness were determined. Besides one-dimensional structure, the RF-RMM can also be applied to static/dynamic analysis of multi-span beams, planar frames and complex space framed structures.