On the moving loads problem in discontinuous homogeneous beams and layered beams with interlayer slip

This manuscript contains the main part of my research performed in this last triennium at the Department of Civil, Environmental, Aerospace and Materials Engineering, University of Palermo, and at the Department of Basic Sciences in Engineering Sciences (Unit of Applied Mechanics), University of Innsbruck, Austria. The research adheres to a common procedure of solving a scientistic problem. That is, introduction to the problem, selection of the mathematical and physical tools to model the problem, proposed solution, and numerical validation. The thesis proposes a novel modal superposition approach to the moving loads problem on discontinuous homogeneous beam and layered beam with interlayer slip, carrying an arbitrary number of translational supports, rotational joints and alternatively tuned mass dampers (TMDs). The beams are referred to as discontinuous for the discontinuities of response variables at the application points of supports/joints/TMDs. Supports and TMDs are taken as representative of external devices while the rotational joints may model rotational dampers or connections with flexibility and damping arising from imperfections or damage. Based on the theory of generalized functions to handle the discontinuities of response variables due to supports/joints/TMDs, exact beam modes are obtained regardless of the number of discontinuities. On using pertinent orthogonality condition for the de deflection modes, the dynamic response of the beam under moving loads is derived in time domain. All response variables are presented in a closed analytical form by using the relationship equations of the beam. Several numerical applications illustrate the efficiency of the proposed method.