摘要
研究含常开裂纹矩形截面梁的自由振动问题。通过一计及裂纹对梁局部柔度影响的无质量扭簧模拟裂纹所在截面,建立起与含裂纹梁等效的力学模型;基于完整梁自由振动方程的基本解,推导出含裂纹梁的传递矩阵;以简支梁和悬臂梁为例,结合具体的边界条件,导出它们相应的频率方程。基于泰勒展开,给出求解该频率方程的一种迭代算法,能够简便地计算含裂纹梁的固有频率。
The free vibration problems of slender prismatic beam with a single opening crack are studied. An equivalent mechanics model of the cracked beam is established through modelling the cracked section by a massless rotational spring taking into account the effects of the crack on the local flexibility. Based on the fundamental solutions of the free vibration equation of intact beam,the transfer matrix of the cracked beam is obtained. The frequency equations of the simply supported beam and cantilever beam are given. An iteration procedure for solving the derived frequency equations is presented. The method proposed in this paper is efficient in calculating the natural frequencies of the cracked beams.
出处
《噪声与振动控制》
CSCD
北大核心
2008年第4期31-34,共4页
Noise and Vibration Control
关键词
振动与波
梁
裂纹
固有频率
vibration and wave
beam
crack
natural frequency
