斜裂缝梁的振动特性分析

Analysis of vibration characteristics of beam with diagonal cracks

基于弹性力学平面应力理论,采用Chebyshev-Ritz法分析斜裂缝梁的振动特性。首先将斜裂缝梁划分成3个子域,再通过坐标变换将划分后的梯形子域等效转换为矩形子域,分别建立各子域的振动特征方程,根据各子域界面交界处的位移连续性得到整个梁的振动特征方程,利用Chebyshev-Ritz法求得具有高收敛性的解,通过实际算例与有限元分析结果、文献试验及理论结果进行对比,验证了该理论方法的精确性;通过参数分析研究了斜裂缝的倾斜角度和位置对结构振动特性的影响。研究结果表明,斜裂缝倾斜角度的增大将导致梁自振频率变大,振型的变化也更明显,斜裂缝位于跨中时对振型影响较大。

The vibration characteristics of beams with diagonal crack were analyzed using the Chebyshev-Ritz method based on the elastic mechanics plane stress theory in this paper.The beam with diagonal crack was divided into three subdomains at first,and then the trapezoidal subdomain was transformed into a rectangular subdomain by coordinate transformation,and the vibration characteristic equations of each subdomain were established,respectively,and the vibration characteristic equation of the whole beam was obtained according to the displacement continuity at the interface junction of each subdomain,and the solution with high convergence was obtained by using the Chebyshev-Ritz method.The accuracy of the theoretical method was verified by comparing with the finite element results and literature experimental and theoretical results.The influence of the inclined angle and position of the diagonal crack on the vibration characteristics of the structure was studied by the way of parametric analysis.Results show that the increase of the inclined angle of the diagonal crack will lead to a larger natural frequency of the beam and a more obvious change of the vibration mode,and the influence on the vibration mode is greater when the diagonal crack locates in the middle of the span.