A solução fundamental no cálculo da resposta forçada de uma viga Euler-Bernoulli sobre fundação elástica e com condições de contorno não-clássicas

Abstract

In this work we consider an Euler-Bernoulli beam on elastic foundation. The solution to problems with and without external force was obtained through modal analysis and the fundamental solution was used to write the characteristic equations for some combinations of classical and non-classical boundary conditions, the free response and the forced response. We obtained orthogonality relations that allowed us to decouple the equations from motion and write the solutions. In the case of non-classical boundary conditions, the orthogonality relation obtained was written in terms of the devices attached to the end of the beam. We perform simulations for some cases of boundary conditions and vary the values of the mass and spring devices attached to the ends of the beam. We compare the natural frequencies and graph the vibration modes, the free response and the forced response.