Bifurcations of Nonlinear Normal Modes of Linear Oscillator with Strongly Nonlinear Damped Attachment

By Oleg V. Gendelman. 2004

169 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Civil and Structural Engineering, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/a16333fffd399177f0a051be5b357ad322706556

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Attractors of harmonically forced linear oscillator with attached nonlinear energy sink I: Description of response regimes (2007, methodology): “It should be mentioned, that similar “illegal” procedures were successfully used in papers [2, 6, 7 , 11] and many others.”
Targeted Energy Transfer Under Harmonic Forcing With a Vibro-Impact Nonlinear Energy Sink: Analytical and Experimental Developments (2015, background): “Introduction of a suitable asymptotic procedure based on the invariant manifold approach [6] has shown that in addition to periodic regimes, system with NES can exhibit beating response, referred as strongly modulated response (SMR) [7].”
Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. II: Optimization of a nonlinear vibration absorber (2007, result): “nonlinearity. In other recent works [8, 9 ], it has been shown analytically and numerically that properly designed strongly nonlinear attachments may passively absorb vibration energy from transiently loaded linear subsystems by acting like nonlinear energy sinks (NESs).”
Theoretical and Experimental Study of Multimodal Targeted Energy Transfer in a System of Coupled Oscillators (2006, methodology): “The damped nonlinear normal modes (NNMs) of the system were investigated using the invariant manifold approach in [23].”
Nonlinear normal modes, Part I: A useful framework for the structural dynamicist (2009, methodology): “The multiple scales method One perturbation method that has received considerable attention for the NNM computation is the method of multiple scales [31,51,58,60,61,77,78].”
Targeted energy transfer with parallel nonlinear energy sinks. Part I: Design theory and numerical results (2011, background): “The bifurcation which leads to the energy pumping, due to multiplicity of solutions, only occurs for small values of damping of absorbers [ 6 ].”