A solução fundamental na obtenção das frequências naturais e autofunções de um sistema de viga dupla Euler-Bernoulli com camada elástica e força axial

Abstract

In this work we approach a double Euler-Bernoulli beam system with axial force coupled by an elastic layer. We performed a matrix formulation for the system of equations and for the boundary conditions, which allows relating the double beam system with the single EulerBernoulli beam with axial force. Through modal analysis and using the matrix fundamental solution we write the solution of the modal equation, we determine the characteristic equation, the natural frequencies and the vibration modes. In addition to the classical boundary conditions, we consider the case of a double beam system with axial force and a restrained end. In order to make comparisons, we obtain the natural frequencies and graphically represent the vibration modes of single Euler-Bernoulli beams with axial force, and we compared the natural frequencies for various values of elastic layer and axial force.