The Modes of Non-Homogeneous Damped Beams
MI Friswell & AW Lees (University of Wales Swansea)
Journal of Sound and Vibration, Vol. 242, No. 2, April 2001, pp. 355-361
This short note is concerned with computing the eigenvalues and eigenfunctions of a continuous beam model with damping, using the separation of variables approach. The beam considered has different stiffness, damping and mass properties in each of two parts. Although applications are not considered in detail, one possible example is a thin beam partly submerged in a fluid. The fluid would add considerable damping and mass to the beam structure, and possibly some stiffness. Both the overdamped and the underdamped eigenvalues and associated eigenfunctions have been computed for two different sets of parameters. For high damping the lower underdamped modes seem to be local to the undamped part of the beam. The procedure given assumed the boundary conditions to be pinned. In the general case the spatial solution would require four unknown parameters for each beam section, and the boundary conditions equivalent to pinned-pinned could not be incorporated explicitly. The result would a search for a zero determinant of an 8x8 matrix rather than a 4x4.
This material has been published in the Journal of Sound and Vibration, Vol. 242, No. 2, April 2001, pp. 355-361, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Academic Press. This material may not be copied or reposted without explicit permission.
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Link to paper using doi:10.1006/jsvi.2000.3323
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