Free Vibration of a Large-Amplitude Deflected Plate—Reexamination by the Dynamical Systems Theory

[+] Author and Article Information
J. Lee

Flight Dynamics Laboratory, Wright-Patterson AFB, OH 45433

J. Appl. Mech 53(3), 633-640 (Sep 01, 1986) (8 pages) doi:10.1115/1.3171823 History: Received March 18, 1985; Revised December 01, 1985; Online July 21, 2009


For a simply supported large-amplitude deflected plate, Fourier expansion of displacement reduces the nonlinear plate equation to a system of infinitely coupled modal equations. To close off this system, we have suppressed all but the four lowest-order symmetric modes. In the absence of damping and forcing, the four-mode truncation can be recasted into a Hamiltonian of 4 DOF. Hence, the free vibration of nonlinear plate can be investigated by the standard technique of Hamiltonian systems. It has been found that subsystems of 2 DOF are practically stable in that the invariant tori remain on a smooth surface up to total energy of 1000, at which modal displacements can be 40 times the plate thickness. On the other hand, the trajectory of 4 DOF system develops chaos at a much lower energy value of 76, corresponding to modal displacements twice the plate thickness. This has been evidenced by many spikes in the power spectral density of displacement time-series and an erratic pattern that modal energy components cut through an energy sphere.

Copyright © 1986 by ASME
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