Impact modes in discrete vibrating systems with rigid barriers

Valery Pilipchuk (1)

1 Wayne State University [Detroit]

A class of strongly non-linear vibrating systems composed of linear elastic structures under absolutely rigid constraints condition is considered. Impact mode exact solutions are expressed through a saw-tooth time argument and, as a result, represented in a closed unit form. Based on this special representation, su$cient conditions of existence and also non-existence for the impact modes are formulated and interpreted on the spectral axes. In particular, it was shown that impact modes exist when their basic frequencies are shifted into the right small neighborhood of any natural frequency of the linearized (no barriers) system. The frequencies of the localized impact mode solutions are located at the right of the linear spectrum and have no upper boundary.

Mots clés: Normal modes; Impact systems; Non-linear localization; Non-smooth transformations

Domaines: Sciences de l'ingénieur [physics]; Vibrations [physics.class-ph]

Valery Pilipchuk. Impact modes in discrete vibrating systems with rigid barriers. International Journal of Non-Linear Mechanics, 2001, 36 (6), pp.999-1012. ⟨10.1016/S0020-7462(00)00066-4⟩. ⟨hal-01295245⟩