Multi-resonance analysis of a viscoelastically supported orthotropic plate with an inclined crack

Vibration behavior of an orthotropic cracked plate embedded in a nonlinear Winkler–Pasternak elastic foundation is studied in this paper. The plate’s imperfection is due to an inclined crack started on the surface and continued in the depth of the plate. Crack is located at the center of the plate and has an arbitrary angle of orientation with respect to its side edge. The harmonically excited plate is modeled based on the Kirchhoff’s plate theory. Galerkin’s procedure is applied to develop the time-dependent ordinary differential equations of the system, and multiple timescales method is used to obtain the solution. Two different phenomena, namely first primary resonance and the primary resonance with the 1:3 internal resonance, are investigated from the frequency responses of the system. The first four natural modes of vibration for the case of external forced vibration are studied, and for the combined primary and 1:3 internal resonances, the four-to-one internal resonances are considered. The effects of various parameters on these phenomena have been examined, and the results are discussed in detail.