高温下含多条裂纹简支钢梁的模态分析

Modal analysis of a simply supported steel beam with mutiple cracks under high temperature

基于传递矩阵方法,提出了一种在高温下对含多条裂纹简支钢梁进行模态分析的方法。在模态分析过程中,用无质量的扭转弹簧来等效横向裂纹,推导出每条裂纹产生的局部柔度;通过材料力学参数的变化引入温度模块,考虑温度变化在简支梁截面产生的轴向载荷的影响,推导出含温度参数、裂纹条数和裂纹几何参数的整条裂纹梁传递矩阵。根据简支梁的边界条件,求解出不同温度下含多条裂纹简支钢梁的固有频率。结果表明:简支梁横截面上的轴向温度载荷对固有频率的影响非常大,不能忽略不计;温度的升高会显著减小裂纹简支钢梁的各阶固有频率;随着裂纹相对深度的增大,裂纹简支钢梁第一阶固有频率和临界温度均逐渐降低。

Based on the transfer matrix method,an analytical method was proposed to conduct the modal analysis of a simply supported beam with multiple cracks under high temperature. In the modal analysis,transverse cracks were replaced by torsional springs without mass,and the local flexibility of each crack was derived. The temperature module was introduced by the change of the mechanical parameters of the structural material. Considering the axial load of the simply supported beam caused by the variation of temperature,the transfer matrix of the whole cracked beam including the temperature parameter and the number and geometric parameters of cracks was obtained. According to the boundary conditions,the natural frequencies of the simply supported steel beam with multiple cracks were calculated. The results indicate that the influence of the axial temperature load on the natural frequencies of the simply supported steel beam is rather great,and can not be ignored. The increase of the temperature can significantly decrease each order of natural frequencies of the cracked simply supported steel beam. The first order natural frequency and critical temperature of the cracked simply supported steel beam gradually decrease as the relative depth of cracks increases.