DAMPING EFFECTS ON TRANSVERSE MOTIONS OF BERNOULLI – EULER BEAMS UNDER THE ACTION OF MOVING UNIFORMLY DISTRIBUTED MASSES

Abstract

This thesis studies the dynamics effects on the transverse motions of uniform Bernoulli-Euler Beams under the action of moving uniformly distributed masses. The governing equation is a fifth order non-homogeneous partial differential equation with Variable and singular coefficients. The solution technique is based on the generalized integral Transform, the expansion of the heaviside function in series form and the modification of Struble’s asymptotic method. By the use of this technique, one is able to obtain close form Solutions for all variants of classical end conditions for the dynamical problem. The closed form solutions are analysed and numerical analyses in plotted curves are presented. The results show that as the damping due to transverse displacement Cs increases, the response amplitudes of the damped Bernoulli-Euler beam decreases for both cases of moving distributed force and moving distributed mass problems for all variants of boundary conditions. The same behaviour characterizes the damping due to strain velocity C. However, Damping due to resistance to transverse displacement Cs has a more pronounced effect in reducing the response amplitudes of the damped beam than the damping due to resistance to strain velocity C. The effects of other structural parameters such as axial force N, foundation Stiffness K and inertia on the displacement response of the damped Bernoulli-Euler under the actions of distributed masses are presented. Finally, in all the illustrative examples considered, for the same natural frequency of a damped Bernoulli –Euler beam, resonance is reached earlier in moving distributed mass system than in moving distributed force system. Hence the need to always consider the inertia term of the moving distributed loads in this class of dynamical problems cannot be overemphasized.