基于裂缝梁动力特性和自振频率的参数敏感性

基于Bernoulli-Euler理论,将开口裂缝梁视为变截面梁,利用模态摄动方法建立了一种求解带任意数量开口裂缝简支梁和连续梁动力特性的半解析分析方法。在等截面无损梁的模态子空间内将裂缝梁的变系数微分方程的求解转化为非线性代数方程组的求解;利用无损梁的自振频率和振型函数摄动求解裂缝梁的模态参数;通过矩形开口裂缝简支梁和两跨连续梁的动力试验验证了笔者方法的准确性;最后,利用开口裂缝梁动力特性的半解析解研究了简支梁和两跨连续梁的自振频率对裂缝尺寸和位置的敏感性。

Sensitivity of Natural Frequency and Dynamic Characteristics-of the Beam with Open Cracks to Crack Parameters

This paper examines a beam with open cracks, which is regarded as a non-uniform beam. Based on the Bernoulli-Euler beam theory, the semi-analytical solution of dynamic characteristics of a simply supported beam and continuous beam with an arbitrary number of open cracks was obtained using the modal perturbation method. In the modal subspace of the uniform beam, the variable coefficient differential vibration equation of the non-uniform beam was converted to nonlinear algebraic equations. The modal parameters of the cracked beam were solved using the natural frequency and vibration mode of the uniform beam. The dynamic test analysis of the simply supported beam and two-span continuous beam with rectangular open cracks indicated that the semi-analytical solution was highly precise. Finally, the sensitivity of the natural frequency to crack parameters was studied using the semi-analytical solution of dynamic characteristics of the beam with open cracks.