Structural Dynamics Modelization of One-Dimensional Elements on Elastic Foundations under Fast Moving Load

Abstract

The structural dynamics analysis of one-dimensional elements (strings, beams) on continuous elastic support under high-velocity moving load is the main subject of the present doctoral dissertation. Two main types of mechanical systems have been considered, of a finite and of an infinite extension. Through ad hoc formulations and autonomous implementations, physical dynamic response characteristics of taut string/beam-foundation systems are revealed by virtue of analytical and numerical approaches, both in the linear and in the nonlinear regimes. First, two explicit closed-form analytical solutions relative to the static deflection of a finite Euler-Bernoulli elastic beam lying on aWinkler elastic foundation with space-dependent stiffness coefficient are derived. Then, a FEM implementation is developed to investigate the transient dynamic response of a simply-supported Euler-Bernoulli beam resting on spatially homogeneous Winkler nonlinear elastic foundations under the action of a transverse concentrated moving load, with a constant velocity and harmonic-varying magnitude in time. Regarding the analysis of infinite systems, the steady-state responses of a uniform infinite taut string and of a uniform infinite Euler-Bernoulli elastic beam, both resting on an elastic support and subjected to a concentrated transverse moving load, are numerically obtained by an original Discontinuous Least-Squares Finite Element Method (DLSFEM) and by effective Perfectly-Matched Layer (PML) implementations. In particular, concerning the steady-state response of the beam a wholly new, Perfectly Matched Layer (PML) for the underlying fourth-order differential problem is analytically formulated and implemented. In addition, a universal closed-form analytical solution is derived for the infinite beam moving load problem, apt to represent the response for all possible beam-foundation parameters. The present thesis demonstrates the reliability and effectiveness of all the derived analytical-numerical solutions, through extensive parametric analyses, carried out for interpreting the parametric variation of the mechanical response of the considered systems due to changes in their characteristic mechanical properties.