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Primary resonance in forced vibrations of in-plane translating viscoelastic plates with 3:1 internal resonance

Tang, You-Qi ; Chen, Li-Qun

Nonlinear dynamics, 2012-07, Vol.69 (1-2), p.159-172 [Periódico revisado por pares]

Dordrecht: Springer Netherlands

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Título:
Primary resonance in forced vibrations of in-plane translating viscoelastic plates with 3:1 internal resonance
Autor: Tang, You-Qi ; Chen, Li-Qun
Assuntos: Automotive Engineering ; Boundary conditions ; Classical Mechanics ; Control ; Dynamical Systems ; Engineering ; Forced vibration ; Hamilton's principle ; Mathematical analysis ; Mathematical models ; Mechanical Engineering ; Method of multiple scales ; Multiscale analysis ; Nonlinear equations ; Nonlinearity ; Original Paper ; Partial differential equations ; Plates ; Steady state ; Translating ; Vibration ; Viscoelasticity ; Viscosity
É parte de: Nonlinear dynamics, 2012-07, Vol.69 (1-2), p.159-172
Notas: ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
Descrição: Nonlinear forced vibrations of in-plane translating viscoelastic plates subjected to plane stresses are analytically and numerically investigated on the steady-state responses in external and internal resonances. A nonlinear partial-differential equation with the associated boundary conditions governing the transverse motion is derived from the generalized Hamilton principle and the Kelvin relation. The method of multiple scales is directly applied to establish the solvability conditions in the primary resonance and the 3:1 internal resonance. The steady-state responses are predicted in two patterns: single-mode and two-mode solutions. The Routh–Hurvitz criterion is used to determine the stabilities of the steady-state responses. The effects of the in-plane translating speed, the viscosity coefficient, and the excitation amplitude on the steady-state responses are examined. The differential quadrature scheme is developed to solve the nonlinear governing equations numerically. The numerical calculations confirm the approximate analytical results regarding the single-mode solutions of the steady-state responses.
Editor: Dordrecht: Springer Netherlands
Idioma: Inglês

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Primary resonance in forced vibrations of in-plane translating viscoelastic plates with 3:1 internal resonance

Tang, You-Qi ; Chen, Li-Qun

Dordrecht: Springer Netherlands

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