On non-stationary response of cracked thin rectangular plates acted upon by a moving random force

This paper is aimed to examine the dynamics of cracked thin rectangular plates subjected to a moving non-stationary random load. A random load is considered with a constant mean value, a constant moving velocity, and five different covariance patterns namely the white noise, constant, exponential, cosine wave, and exponential cosine covariance. Accordingly, an intact plate’s orthogonal polynomials in combination with the well-known corner functions are employed to explore the mechanical behavior of the cracked plate. As the non-dimensional deflection values, the functions of the squared mean values are obtained for the damped and undamped cracked plates at different points. Then an inclusive parametric study is performed to explore effects of the inclined crack angles and the crack lengths on the non-dimensional functions of squared mean values at middle point of the undamped and damped cracked plates. Based on the obtained results, there are non-monotonous nonlinear relations between increasing the incline crack angles as well as the crack lengths and the non-dimensional functions of squared mean values. Furthermore, it is found that in the exponential covariance cases, the effects of increasing crack angles and lengths on the non-dimensional squared mean values are profounder than the other four patterned covariance cases.