TRANSVERSE MOTIONS OF ELASTIC STRUCTURES UNDER CONCENTRATED MASSES MOVING AT VARYING VELOCITIES

Abstract

The problem of the flexural vibrations of structural members namely uniform Rayleigh beams, non-uniform Rayleigh beams and isotropic rectangular plates under the actions of concentrated loads traveling at varying velocities is studied in this thesis. The governing equations of motions in all the cases are fourth-order partial di flerential equations with variable and singular coefficients. The main objective of this study is to obtain closed form solutions to this class of problem for all pertinent boundary conditions. In order to obtain a closed form solution to these dynamical problems the property or the Dirac delta function as an even function was used to express it in series form and an approach due to the generalized finite integral transform was employed in the case or uni form Rayleigh beam to obtain a sequence of coupled second order ordinary differential equations. Unlike in the case of uniform Rayleigh beam, the non-uniform Rayleigh beam is resistant to the generalized integral transform technique. Thus, a modification of the generalized Galerkin's method was resorted to in order to reduce the fourth order partial differential equation governing the motion of the non-uniform beam to a sequence of coupled second order ordinary differential equations. In the case of two-dimensional plate problems, the two-dimensional analogue of the generalized finite integral transform mentioned above was used to transform the governing equation of motion to a sequence of coupled second order ordinary differential equations. The modified asymptotic method of Struble was then used to simplify these equations, while variation of parameters technique was employed in conjunction with Fresnel sine and Fresnel cosine