含裂纹Timoshenko梁自由振动分析

提出了基于传递矩阵法的含裂纹Timoshenko梁自由振动分析方法。将含裂纹Timoshenko梁结构划分为裂纹、左段完整梁、右段完整梁三部分,梁内裂纹等效为无质量的扭转弹簧,分别推导出各部分的传递矩阵以及含裂纹Timoshenko梁的总体传递矩阵,根据具体的边界条件将总体传递矩阵简化成2×2的矩阵,并得到相应的解析频率方程,求解方程即可得到裂纹梁的各阶固有频率。通过数值算例验证了文中方法的有效性并得到相应结论。

Analysis of cracked Timoshenko beam under free vibration

A transfer matrix method for free vibration analysis of Timoshenko beam with crack is proposed. The cracked Timoshenko beam is divided into three parts, the crack part,left undamaged part and the right undamaged part. The crack is simulated by a massless torsional spring, and the transfer matrix of each part of the beam and the global transfer matrix are obtained. According to the boundary condition, the global transfer matrix can be simplified to a 2×2 matrix, and the frequency equation of vibration is obtained analytically, and the natural frequencies can be got by solving the frequency equation. The validity of the method proposed in this paper is verified by several numerical examples,and some useful conclusions are obtained from the numerical examples.