WSEAS Transactions on Applied and Theoretical Mechanics
Print ISSN: 1991-8747, E-ISSN: 2224-3429
Volume 10, 2015
Phenomenological Analysis of the Additive Combinational Internal Resonance in Nonlinear Vibrations of Fractionally Damped Thin Plates
Authors: , ,
Abstract: The dynamic behaviour of a nonlinear plate embedded into a fractional derivative viscoelastic medium is studied by the method of multiple time scales under the conditions of the combinational internal resonances of additive-difference type using a newly developed approach resulting in uncoupling the linear parts of equations of motion of the plate. The influence of viscosity on the energy exchange mechanism between interacting nonlinear modes has been analyzed. The phenomenological analysis carried out for the combinational internal resonances of the additive type with the help of the phase portraits constructed for different magnitudes of the plate parameters reveals the great variety of vibrational motions: stationary vibrations, two-sided energy exchange between two subsystems under consideration, and one-sided energy interchange resulting in the complete one-sided energy transfer.
Search Articles
Keywords: Nonlinear elastic plate, Free nonlinear damped vibrations, Combinational internal resonances, Fractional derivative, Method of multiple time scales
Pages: 260-277
WSEAS Transactions on Applied and Theoretical Mechanics, ISSN / E-ISSN: 1991-8747 / 2224-3429, Volume 10, 2015, Art. #30