The calculation of strongly nonlinear systems close to vibration impact systems

DOI10.1016/0021-8928(85)90073-5zbMath0614.70019OpenAlexW2055203486MaRDI QIDQ1819961

Valery N. Pilipchuk

Publication date: 1985

Published in: Journal of Applied Mathematics and Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8928(85)90073-5

zbMATH Keywords

periodic solutionsapproximate solutionnonlinear dynamic systemsaveraging methodsfinite number of degrees of freedomequivalent vibration impact systemperiodic piecewise smooth functionsquasiharmonic (quasilinear) analysis

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Free motions in linear vibration theory (70J30) Dynamical systems and ergodic theory (37-XX)

Related Items (7)

Study of a class of subharmonic motions using a non-smooth temporal transformation (NSTT) ⋮ Energy transfers in a system of two coupled oscillators with essential nonlinearity: 1:1 resonance manifold and transient bridging orbits ⋮ Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment ⋮ Periodic orbits, damped transitions and targeted energy transfers in oscillators with vibro-impact attachments ⋮ Non-smooth Spatial and Temporal Substitutions in Impact Dynamics ⋮ Periodic orbits of a conservative 2-DOF vibro-impact system by piecewise continuation: bifurcations and fractals ⋮ Asymptotic solutions for non-linear systems with high degrees of non- linearity

Cites Work

• Unnamed Item
• On periodic solutions close to rectilinear normal vibration modes
• On the existence of normal mode vibrations in nonlinear systems

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