Uma formulação de elementos de contorno para análise de vibrações livres

Abstract

This work presents an alternative formulation for the boundary element analysis of free vibrations of elastic bodies in plane stress or plane strain. The main characteristic of this method is the transformation of the inertial domain integral into equivalent boundary integrals, by employing special interpolation functions to approximate the accelerations within the body. With this procedure the free vibration problem is reduced to a generalized algebraic eigenvalue problem, whose solution is carried out in a direct and simultaneous way. This is only possible due to the elastostatic fundamental solution which is used instead of the non-linear frequency dependent harmonic fundamental solution. The numerical implementation is carried out for plane stress or plane strain. The boundary geometry is represented by straight elements, being the tractions and boundary displacements aproximated by quadratic interpolation functions over each boundary element. Gaussian Quadrature is used to compute integrals over non-singular elements. As usual in Boundary Element analysis, rigid body motion considerations are employed to evaluate the contributions of the Cauchy principal value integrals. Four examples are analysed using a FORTRAN computer code, based on the above described, and the numerical solutions obtained are compared with Finite Elements results.