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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 39
Edited by: B.H.V. Topping
Paper VI.2

Damping of Tubes Filled with Granular Materials: A Non-Conservative Dynamic Stiffness Analysis

J.M. Bourinet and D. Le Houedec

Laboratory of Mechanics and Materials, Ecole Centrale de Nantes, Nantes, France

Full Bibliographic Reference for this paper
J.M. Bourinet, D. Le Houedec, "Damping of Tubes Filled with Granular Materials: A Non-Conservative Dynamic Stiffness Analysis", in B.H.V. Topping, (Editor), "Advances in Finite Element Technology", Civil-Comp Press, Edinburgh, UK, pp 289-299, 1996. doi:10.4203/ccp.39.6.2
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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