Dynamic response of cracked Timoshenko beams on elastic foundations under moving harmonic loads

A thorough understanding of the dynamic behavior of one-dimensional structural members such as beams plays a crucial role in specialized disciplines including ocean, bridge and railway engineering. The vibratory response of an in-service beam-like component may deviate from that expected from the intact structure when defects are present. In this work, we present a semi-analytical approach to predict the forced response of a multi-cracked Timoshenko beam traversed by a moving harmonic load with constant speed. The beam is fully or partially supported by the viscoelastic foundation, where the normal stiffness and shear modulus of the subgrade are considered. The effects of transverse open cracks are modeled by massless rotational springs with a linear moment-rotation constitutive law to account for the local flexibility induced by the damage. Based on the transfer matrix method, the defective structure is treated as an assembly of sub-beams to derive the eigenvalue solution of the system. The time response is then obtained by utilizing identical generalized coordinates for lateral and rotational displacement components when applying the modal expansion technique. The use of general elastic end constraints allows us to recover all possible boundary conditions. Numerical examples are also provided to demonstrate the robustness and accuracy of the proposed method, and also to investigate the influence of important parameters on the dynamic behavior of the damaged structure.