Dynamic interaction of a semi-infinite linear chain of coupled oscillators with a strongly nonlinear end attachment

DOI10.1016/S0167-2789(02)00806-0zbMath1067.70020MaRDI QIDQ1860891

Alexander F. Vakakis, Andrey I. Musienko, Leonid I. Manevitch, Lawrence A. Bergman, Oleg V. Gendelman

Publication date: 4 March 2003

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

energy pumpinglocalized standing waves

Mathematics Subject Classification ID

Nonlinear resonances for nonlinear problems in mechanics (70K30) The dynamics of infinite particle systems (70F45)

Related Items (13)

Contribution to efficiency of irreversible passive energy pumping with a strong nonlinear attachment ⋮ Transient in a two-DOF nonlinear system ⋮ Suppression of vibrations in strongly nonhomogeneous 2DOF systems ⋮ New approach to beating phenomenon in coupled nonlinear oscillatory chains ⋮ Different dynamics of a periodic mass-in-mass nonlinear chain during a single mode excitation ⋮ Competitive energy transfer between a two degree-of-freedom dynamic system and an absorber with essential nonlinearity ⋮ Vibratory control of a linear system by addition of a chain of nonlinear oscillators ⋮ The almost-periodic solutions of the weakly coupled pendulum equations ⋮ Transient dynamics of a dispersive elastic wave guide weakly coupled to an essentially nonlinear end attachment ⋮ Design of Mechanical Energy Pumping Devices ⋮ Dynamical interaction of an elastic system and a vibro-impact absorber ⋮ New analytical approach to energy pumping problem in strongly nonhomogeneous 2dof systems ⋮ Targeted energy transfer in stochastically excited system with nonlinear energy sink

Cites Work

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• Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian
• Nonlinear surface modes in monoatomic and diatomic lattices
• Energy Pumping in Nonlinear Mechanical Oscillators: Part I—Dynamics of the Underlying Hamiltonian Systems
• Energy Pumping in Nonlinear Mechanical Oscillators: Part II—Resonance Capture
• Normal Modes for Non-Linear Vibratory Systems
• The description of localized normal modes in a chain of nonlinear coupled oscillators using complex variables
• Transition of energy to a nonlinear localized mode in a highly asymmetric system of two oscillators

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