DYNAMIC ANALYSIS OF CONTINUOUS BEAMS WITH SINGULARITIES IN MASS AND STIFFNESS DISTRIBUTION

摘要

A linear elastic continuous system with singularities in its mass and stiffness distribution and subjected to general dynamic load is considered in this paper. Despite the singularities a closed form solution to the response problem is attempted. The free vibration characteristics of such system are determined. Simple closed form mathematical expressions for the vibrational modes are obtained using Galerkin's approach. Then the work is extended to the dynamic response problem and an approximate closed form solution is obtained. The Green's function for the response problem is developed which makes the analysis applicable to any dynamic loading two numerical examples are presented to show the accuracy and the applicability of the method.