A perturbation method for evaluating nonlinear normal modes of a piecewise linear two-degrees-of-freedom system
The aim of this paper is to investigate the dynamics of systems expected to exhibit superabundant modes. An important example of piecewise smooth system is considered, as a beam with a breathing crack by taking advantage of related works presnt in literature. The Lindstedt-Poincaré method is applied under the hypothesis the discontinuity is small. Passive and active frequencies, modified by the same damage-dependent factor, contribute to the motion although they are incommensurable. Results of the stability analysis show that while the second mode is always stable, the first mode is unstable for some values of the damage parameter. Numerical results, obtained by a Poincaré map approach, confirm the perturbation results and also show the existence of superabundant normal modes which arise in the unstable interval of the first mode.
scientific article; zbMATH DE number 5603311