Local and Global Nonlinear Dynamics of Harmonically Excited Rectangular Plates.
Abstract
Nonlinear flexural vibrations of rectangular plates with uniform stretching and transverse harmonic excitations are studied. The analysis results for the case when two distinct plate modes have nearly coincident natural frequencies, are based on the multi-mode approximation of von Karman plate equations. Local bifurcation analysis of the averaged equations, governing the time evolution of the response amplitudes of modes in internal resonance, shows that the plate motion can be either in the directly excited mode, or in a mixed-mode where both the interacting modes participate. The presence of Hopf bifurcation in the coupled-mode responses leads to amplitude modulated traveling waves as well as period doubling bifurcations to chaos. A global bifurcation analysis is also initiated which shows the existence of heteroclinic loops for an integrable limit of transformed and properly scaled averaged equations. Perturbation of these heteroclinic loops can lead to Smale horseshoes and chaotic behavior for the plates.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1993
- Accession Number
- ADP009088
Entities
People
- A. K. Bajaj
- P. Davies
- S. I. Chang
Organizations
- Purdue University