M. Belubkyan, K. Ghazaryan, National Academy of Sciences, Yerevan, Armenia; P. Marzocca, Clarkson University, Potsdam, NY

Summary:

In this paper the study of the bending localized wave in a thin elastic orthotropic cantilever plate reinforced by a rigid rib is presented. Such waves are time–varying, spatially and non uniform bending perturbations that are localized in the proximity of free surface of an elastic plate and are decaying to zero very quickly outside this relatively narrow zone. The study of localized bending waves in an elastic isotropic semi-infinite plate has been presented by Konenkov [1], and it was further developed by Ambartsumyan and Belubekyan [2]. The plate is modeled as an orthotropic cantilever with one edge being free from mechanical stresses and reinforced with rigid rib, the opposite edge is fixed, while the other two edges of the plate are assumed to be simply supported. The rib is modeled as an elastic beam. The dynamic problem for the elastic bending waves is considered and the necessary and sufficient conditions for the existence of localized bending wave are derived. These conditions depend on elastic plate and rib properties. It is shown that the localized waves are dispersive ones. The inverse problem of determining the beam stiffness depending of plate localized bending vibration frequencies will be also considered. The effect of the localized bending waves, the implications of the proposed solution method are presented and pertinent conclusions are outlined. The present paper may provide some insight towards developing a procedure to detect a damage of a rib in more complex systems.