Subharmonic responses in harmonically excited rectangular plates with one-to-one internal resonance

DOI10.1016/S0960-0779(96)00157-9zbMath0962.74510OpenAlexW2086745847MaRDI QIDQ1807521

Yanyan Li

Publication date: 7 June 2001

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0960-0779(96)00157-9

zbMATH Keywords

Hopf bifurcationrectangular platemethod of averagingone-to-one resonancevon Kármán plate equationsone-to-one internal resonanceharmonic motionssubharmonic motionsnonlinear flexural vibrationslinear natural frequenciesperiod-doubling route to chaosuniform stretching

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Plates (74K20) Dynamical systems in solid mechanics (37N15) Chaotic behavior of solutions to dynamical problems in solid mechanics (74H65) Dynamical bifurcation of solutions to dynamical problems in solid mechanics (74H60)

Related Items (9)

Designing plates for minimum internal resonances ⋮ Chaotic and bifurcation dynamics of a simply-supported thermo-elastic circular plate with variable thickness in large deflection. ⋮ CHAOTIC VIBRATIONS OF CLOSED CYLINDRICAL SHELLS IN A TEMPERATURE FIELD ⋮ Nonlinear flexural vibration of a circular ring. A single mode approach ⋮ Single-mode control and chaos of cantilever beam under primary and principal parametric excitations ⋮ Vibration control of ultrasonic cutting via dynamic absorber ⋮ Chaotic [motion and bifurcation for a simply-supported thermo-mechanical coupling circular plate with variable thickness] ⋮ On methods for continuous systems with quadratic, cubic and quartic nonlinearities ⋮ Chaotic and bifurcation dynamics for a simply supported rectangular plate of the thermo-mechanical coupling in large deflection.

Uses Software

• AUTO
• AUTO-86

Cites Work

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• Subharmonic travelling waves in a geometrically nonlinear circular plate
• Singular Perturbations of Bifurcations

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