The impact induced 3:1 internal resonance in nonlinear doubly curved shallow panels with rectangular platform

Geometrically non-linear vibrations of doubly curved shallow panels with rectangular platform under the low-velocity impact by an elastic sphere are investigated. It is assumed that the target is simply supported and partial differential equations are obtained in terms of its transverse displacement and Airy’s stress function. The local bearing of the target and impactor’s materials is neglected with respect to the shell deflection in the contact region. The equations of motion are reduced to a set of infinite nonlinear ordinary differential equations of the second order in time and with cubic and quadratic nonlinearities in terms of the generalized displacements. The internal resonance three-to-one induced during the process of impact is investigated by the method of multiple time scales. The time dependence of the contact force is determined. © 2015, World Scientific and Engineering Academy and Society. All Rights Reserved.