DYNAMICAL ANALYSIS OF FINITE PRESTRESSED BERNOULLI-EULER BEAMS WITH GENERAL BOUNDARY CONDITIONS UNDERTRAVRLLING DISTRIBUTED LOADS

Abstract

This thesis presents the problems of dynamical analysis of finite prestressed Bernoulli-Euler beams with general boundary conditions under traveling distributed masses. The responses. of the elastic structures to moving distributed forces are special cases of such dynamical problems. The governing equation of this problem is a fourth order partial differential equation. The solution technique is based on generalized integral transforms, the use of the properties of Heaviside function H(x - ct) as the generalized derivative of the Dirac delta function 5(x - ct) in the distributed sense and a modification of the asymptotic method of Struble. By the use of this technique, one is able to obtain closed form' solutions for all variants of classical end conditions for this class of problems. The closed form solutions are analyzed and numerical analyses in plotted curves are presented. The results show that as the 'prestress value N and foundation modulli K increases, the response amplitude of the' dynamical system decreases. However, higher values of N and K are required for a more noticeable effect in the case of other boundary conditions than those of simply supported boundary condition. It is also found that for all the illustrative examples, the moving force solution is not an upper bound for the accurate solution of the moving masses problem of a uniform Bernoulli-Euler beam under the action of a uniform distributed load. This important result also agrees with similar problems that considered the moving load as a lump mass. Finally, in all the illustrative examples considered, for the same natural frequency, the critical speed for the moving mass problem is smaller than that of the moving force problem. Hence resonance is reached earlier in moving mass problem.