基于转换矩阵法的中间带弹性支撑剪切梁模态求解

Modal Analysis of Shearing Beam with Intermediate Flexible Constraints Base on Transfer Matrix Method

基于转换矩阵法,根据弹性支承点处的协调条件,推导得到跨度不同、各跨刚度不同、单位长度质量不同、中间带弹性支承、不同边界条件下剪切梁的特征方程,并验证了方法的正确性。基于数值算例,探讨了边界条件对剪切梁模态的影响,给出了剪切梁与欧拉梁的对比分析。

Based on the transfer matrix method, the characteristic equations of continuous shearing beam with diverse characteristics including the varied length of span, the varied stiffness of span, the varied mass of unit-length beam, flexible constraint mounted in the intermediate and different boundary conditions, were derived. The modal analysis results of shearing beams were compared to those of Euler beam. The discrepancies of the frequencies obtained from these two types of beams were discussed by considering different span-depth ratio and number of modes.