Uso da base dinâmica em um sistema de duas vigas acopladas

Abstract

This work researches on free and forced vibrations of a double beam coupled system. The system is regarded as two Euler-Bernoulli beams which are parallel, have the same length, are simply supported and are connected through a viscoelastic layer. Natural frequencies and their mode shapes, also called eigenfunctions, of the coupled system are obtained through a uniform beam methodology which uses the free dynamical basis to represent the solution of the the modal equation. This study uses modal analysis and block matrix formulation, while the dynamical basis used to represent the modal solution is obtained from the dynamical solution of a fourth order differential equation whose coefficients are just those of the original problem. The natural frequencies and mode shapes of the undamped system are determined for several values of beam parameters. For the damped case, damping ratios of each beam and also of the viscoelastic layer (which characterizes the coupling the system) are considered. The forced response is represented using matrix impulse response, which is the solution of an initial value problem with impulsive initial conditions.