For a strongly non-linear multi-degree-of-freedom system, in general, one cannot consider one mode at a time as in linear modal analysis. In the absence of external excitation, the natural vibration often involves more than one mode at a time resulting in quasi-periodic or multi-periodic (toroidal)
THE MODES OF NON-HOMOGENEOUS DAMPED BEAMS
β Scribed by M.I. FRISWELL; A.W. LEES
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 215 KB
- Volume
- 242
- Category
- Article
- ISSN
- 0022-460X
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β¦ Synopsis
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 di!erent sti!ness, damping and mass properties in each of two parts. Pinned boundary conditions are assumed at each end, although other boundary conditions may be applied at the ends quite simply. Although applications are not considered in detail, one possible example is a thin beam partly submerged in a #uid. The #uid would add considerable damping and mass to the beam structure, and possibly some sti!ness. Yang and Zhang [1] calculated these added mass and damping coe$cients for parallel #at plates.
π SIMILAR VOLUMES
Non-linear modal analysis approach based on invariant manifold method proposed earlier by Shaw and Pierre (Journal of Sound and <ibration 164, 85}124) is utilized here to obtain the non-linear normal modes of a clamped}clamped beam for large amplitude displacements. The results obtained for the fund
Non-linear normal modes and the associated frequencies of a uniform beam with simply-supported or clamped conditions at both ends have been derived. Some restricted orthogonality conditions have been pointed out. The effects of the longitudinal inertia on the non-linear transverse motion are shown t