Conditions for finiteness of the number of instability zones in the problem of normal vibrations of nonlinear systems

DOI10.1016/0021-8928(84)90020-0zbMath0575.70021OpenAlexW1981653738MaRDI QIDQ1064093

B. George

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(84)90020-0

zbMATH Keywords

eigenvalueseigenfunctionsfirst approximationinstability zonesnormal vibrationszone boundaries

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Modal analysis in linear vibration theory (70J10)

Cites Work

• Stability and branching of normal oscillation forms of nonlinear systems
• An example of elliptic stability with large parameters: Lamé’s equation and the Arnold-Moser-Rüssmann criterion
• Survey of works on conditions of stability of the trivial solution of a system of linear differential equations with periodic coefficients
• Normal modes, uncoupling, and stability for a class of nonlinear oscillators
• An Application of the Poincare´ Map to the Stability of Nonlinear Normal Modes