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。
Abstract
Based on the transfer matrix method, an analytical method is proposed to conduct the modal analysis of the simply supported beam with multiple cracks under high temperature. In the modal analysis process, transverse cracks are replaced with torsion springs without mass, and local flexibility of each crack is derived; The temperature module is introduced by the change of the mechanical parameters of the structural material, and considering the axial load of the simply supported beam caused by the variation of the temperature, the transfer matrix of the whole cracked beam with the temperature parameter, the number and geometric parameters of cracks is obtained. According to boundary conditions of the simply supported beam, natural frequencies of the simply supported steel beam with multiple cracks is calculated. Results indicate that the influence of the axial temperature load on natural frequencies of the simply supported steel beam is very large, and it can not be ignored; The increase of the temperature can significantly decrease each order natural frequency 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.
关键词
高温 /
温度载荷：多裂纹 /
简支钢梁 /
固有频率
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Key words
high temperature /
temperature load /
multiple cracks /
simply supported steel beam /
natural frequency
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