A dynamic stiffness analysis of damped tubes filled with granular materials

A non-conservative dynamic stiffness method is applied to damped flexural v ibrations of a uniform rectangular tube filled with granular material. An h ypothesis of internal resonance in the granular material is taken into acco unt by means of a frequency-dependent apparent mass which materializes as t he granular material damping effect. This apparent mass is injected into th e equations of motion of the tube assimilated to a Timoshenko beam. Equatio ns are then solved and the frequency-dependent dynamic stiffness matrix is established, A Newtonian procedure allied with a counting algorithm is used to obtain eigensolutions of the undamped empty tube. These solutions are t hen taken as initial approximations of a Rayleigh quotient iteration algori thm which provides damped eigensolutions. A general program has been develo ped under MATLAB environment. Despite the apparent simplicity of the granul ar material behaviour model, results are encouraging. (C) 1999 Civil-Comp L td and Elsevier Science Ltd. All rights reserved.