A dynamic stiffness analysis of damped tubes filled with granular materials

✍ Scribed by J.M. Bourinet; D. Le Houédec

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 232 KB
• Volume: 73
• Category: Article
• ISSN: 0045-7949
• DOI: 10.1016/s0045-7949(98)00272-7

✦ Synopsis

A non-conservative dynamic stiness method is applied to damped ¯exural vibrations of a uniform rectangular tube ®lled 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 materializes as the granular material damping eect. 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 stiness 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 the apparent simplicity of the granular material behaviour model, results are encouraging.