Spectral finite element for vibration analysis of cracked viscoelastic Euler-Bernoulli beam subjected to moving load

In this article, a spectral finite element (SFE) model is presented for vibration analysis of a cracked viscoelastic beam subjected to moving loads. The dynamic shape functions are derived from the exact solution of the governing wave equations and are utilized for frequency-domain representation of a moving load. It is considered with either constant velocity or acceleration; then, the force vector for each spectral element is evaluated. The cracked beam is modeled as two segments connected by a massless rotational spring; thus, the beam dynamic stiffness matrix is extracted in frequency domain by considering compatibility conditions at the crack position. The effects of change in velocity and acceleration of moving load, crack parameters, and viscoelastic material properties on the dynamic response of the SFE beam model are investigated. The accuracy of SFE results is compared with that of finite elements. The results show the ascendency of the SFE model, as compared to FEM, for reducing the number of elements and computational effort, but increasing numerical accuracy.