含呼吸式斜裂纹梁的非线性振动分析

Non-linear vibration analysis of a beam with a breathing oblique crack

考虑振动环境中斜裂纹的呼吸行为,文中提出一种理论方法开展含呼吸式斜裂纹梁的模态和非线性振动分析.在双线性弹簧模型的基础上,建立含呼吸式斜裂纹梁的理论模型.根据虚功原理,将斜裂纹转化为梁结构的局部柔度.通过Galerkin方法,将含呼吸式斜裂纹梁的弯曲振动微分方程简化为多个单自由度系统.在方波激励作用下,采用精细积分方法的衍生格式——精细库塔法,研究裂纹倾角和裂纹尺寸对含呼吸式斜裂纹梁非线性振动响应的影响.算例表明:斜裂纹倾角是影响梁结构模态的一个重要因素,呼吸行为使得梁结构振动响应呈现非线性.含呼吸式斜裂纹梁理论模型实现斜裂纹倾角和呼吸行为的引入,与工程实际更为接近.

Considering the breathing behavior of the oblique crack in vibrating environment,a theoretical method is proposed to conduct the modal and non-linear vibration analysis of a beam with a breathing oblique crack in this paper.Based on the bilinear spring model,the theoretical model of a beam with a breathing oblique crack is established.According to the principle of virtual work,the oblique crack is transformed into the local flexibility of the beam.The vibrational differential equation of the oblique cracked beam is simplified to several single degree of freedom systems by the Galerkin method.Under square wave excitation,the influence of crack inclination and sizes is investigated by the precise Kutta method,which is one of the derivative scheme of the precise integration method.Numerical example shows:the inclined angle of the oblique crack is an important factor of the beam modal,and the breathing behavior of the oblique crack makes the vibration response of the beam non-linear.The theoretical model of the beam with a breathing oblique crack realizes the introduction of oblique crack inclination and breathing behavior,which is closer to the engineering practice.