含多条裂纹变截面简支梁的自由振动

Free vibration of a variable cross-section simple supported beam with multi-crack

基于传递矩阵方法,提出了一种求解含多条裂纹变截面简支梁固有频率的新方法。针对一类可推导振型函数的变截面梁结构,采用无质量弯曲弹簧来等效梁结构上的横向裂纹,推导出含变截面参数和裂纹几何参数的整段变截面梁传递矩阵;根据简支梁的边界条件,得到含裂纹变截面简支梁的特征传递矩阵,研究变截面参数、裂纹条数和裂纹几何参数对变截面简支梁固有频率的影响。结果表明:裂纹对变截面梁模态的影响非常大,会显著降低变截面简支梁的各阶固有频率。

Based on the transfer matrix method,a new method was proposed to solve natural frequencies of a variable cross-section beam with multi-crack.Aiming at a kind of variable cross-section beams with their vibration modal shape functions being able to be deduced,some bending springs without mass were used to be equivalent transverse cracks,the transfer matrix for a typical segment of a beam with variable cross-section parameters and crack geometric parameters was derived.Then,according to boundary conditions of simply supported beam,the characteristic transfer matrix of the whole variable cross-section simply supported beam with multi-crack was derived to study effects of variable cross-section parameters,crack number and crack geometric parameters on natural frequencies of the beam.Results indicated that effects of cracks on vibration modes of the variable cross-section beam are very large,they can significantly reduce each order natural frequency of the variable cross-section simply supported beam.