Flexural motions under moving loads of structurally prestressed non-uniform simply supported beam with non-classical boundary conditions for moving mass case

Abstract

This article is sequel to [18] except that a moving mass case is considered that is the inertial term was not neglected as in [5,6,7,8,9,13,14,18 ]. The dynamical problem is solved using Mindlin Goodman, Generalized Generalized Galakin's method (GGM), Struble’s asymptotic techniques, Laplace Integral transformations and then convolution theory as alluded to in [5,6,7,8,9,13,14,18]. Using numerical example, various plots of the deflections for beams are presented and discussed for different values of axial force N, foundation modulli K and at fixed rotatory Inertial (r) and also for fixed axial force N and foundation moduli K but at various rotatory inertial (r) for moving mass. However, both moving force and moving mass cases were compared and reported as well. Obviously, the results presented in this paper shows good agreement with what is obtainable when compared with that of existing literatures.

Keywords: Non-uniform Rayleigh Beam, Moving mass, Critical Speed, Time-Dependent and Resonance, rotatory inertia