A perturbation method for evaluating nonlinear normal modes of a piecewise linear two-degrees-of-freedom system

作者：Vestroni Fabrizio; Luongo Angelo; Paolone Achille^*

来源：Nonlinear Dynamics, 2008, 54(4): 379-393.

DOI：10.1007/s11071-008-9337-3

• Nonlinear normal modes
• Piecewise-linear systems
• Perturbation methods
• Damaged systems
• Cracked beams

The classical Lindstedt-Poincare method is adapted to analyze the nonlinear normal modes of a piecewise linear system. A simple two degrees-of-freedom, representing a beam with a breathing crack is considered. The fundamental branches of the two modes and their stability are drawn by varying the severity of the crack, i.e., the level of nonlinearity. Results furnished by the asymptotic method give insight into the mechanical behavior of the system and agree well with numerical results; the existence of superabundant modes is proven. The unstable regions and the bifurcated branches are followed by a numerical procedure based on the Poincare map.

• 出版日期2008-12