Impact modes in discrete vibrating systems with rigid barriers

A class of strongly non-linear vibrating systems composed of linear elastic structures under absolutely rigid constraints condition is considered. Imp act mode exact solutions an expressed through a saw-tooth time argument and , as a result, represented in a closed unit form. Based on this special rep resentation, sufficient conditions of existence and also non-existence for the impact modes are formulated and interpreted on the spectral axes. In pa rticular, 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 impac t mode solutions are located at the right of the linear spectrum and have n o upper boundary. (C) 2001 Elsevier Science Ltd. All rights reserved.