Autofunções e frequências de vibração do modelo Euler-Bernoulli para vigas não-clássicas

Abstract

This paper presents a methodology for determining eigenfunctions and frequencies of the Euler-Bernoulli model for elastic beams that can include damping and devices located at intermediate or end points of the beam. The eigenfunctions or vibration modes of the beam are obtained by using solution basis generated by the dynamic solution of a fourth-order differential equation, through a block matrix formulation of the boundary and compatibility conditions. The use of the dynamic basis has been often used to reduce the calculations in obtaining the modes and frequencies. Forced responses are obtained with the Galerkin method by modifying the classical modal analysis with the inclusion of new conditions of orthogonality between modes that are suitable for problems with viscous damping or non-classical boundary conditions.