含裂纹悬臂梁的振动特性分析

摘要

用一无质量扭转弹簧来模拟裂纹所在截面，这样就可以将裂纹梁分为两段研究。基于两段完整的梁的振型表达式，推导出了裂纹梁的传递矩阵，进而给出悬臂裂纹梁的频率方程。用Matlab软件编程求解悬臂裂纹梁的频率方程，把所得结果与有限元结果进行对比分析，研究裂纹位置和裂纹深度对悬臂裂纹梁固有频率的影响，验证了推导方法的合理性。%Simulating the cracked section by a massless torsion spring, the cracked cantilever beam can be divided into two sub-beams. Based on the vibration modes of the two sub-beams, the transfer matrix of the cracked cantilever beam is obtained. Frequency equation of the cantilever beam is given and solved by Matlab. The results are compared with those of finite element method. The effect of crack location and crack depth on the natural frequency of the cantilever beam is analyzed. The rationality of this method is verified.