A non conservative dynamic stiffness method is applied to damped flexural vibrations of a uniform rectangular tube filled with granular material. An hypothesis of internal resonance in the granular material is taken into account by means of a frequency-dependent apparent mass which materialises granular material damping effect. This apparent mass is injected into the equations of motion of the tube assimilated to a Timoshenko beam. Equations 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 then taken as initial approximations of a Rayleigh quotient iteration algorithm which provides damped eigensolutions. A general program has been developed under Matlab environment. Despite of the apparent simplicity of the granular material behaviour model, results are encouraging.

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