含多条裂纹变截面简支梁的自由振动

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振动与冲击 ›› 2019, Vol. 38 ›› Issue (19) : 149-154.

论文

含多条裂纹变截面简支梁的自由振动

马一江1，李园园3，陈国平2，赵颖杰2

作者信息 +

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

MA Yijiang1, LI Yuanyuan3, CHEN Guoping2, ZHAO Yingjie2

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文章历史 +

摘要

基于传递矩阵方法，本文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。

Abstract

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.

关键词

变截面梁

/ 裂纹 / 固有频率 / 传递矩阵法

Key words

Variable cross-section beam / Cracks / Natural frequency / Transfer matrix method

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导出引用

马一江1，李园园3，陈国平2，赵颖杰2. 含多条裂纹变截面简支梁的自由振动[J]. 振动与冲击, 2019, 38(19): 149-154

MA Yijiang1, LI Yuanyuan3, CHEN Guoping2, ZHAO Yingjie2. Free vibration of a variable cross-section simple supported beam with multi-crack[J]. Journal of Vibration and Shock, 2019, 38(19): 149-154

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