Localized Parametric Vibrations of Laminated Cylindrical Shell Under Non-uniform Axial Load Periodically Varying with Time.

Based on the equivalent single layer model for laminated shells, parametric vibrations of thin laminated non-circular cylindrical shells under non-uniform axial load periodically varying with time are studied. As the governing equations, the non-linear coupled differential equations written in terms of the displacement and stress functions accounting for transverse shears are used. It is assumed that the effective (reduced)shear modulus for an entire laminated package is much less than the reduced Young's modulus. Using the asymptotic method of Tovstik in combination with the multiple scales method with respect to time, solutions of the governing equations are constructed in the form of functions which are exponentially decay far from some generatrix and growing with time in the case of parametric resonance. The system of two differential equations with periodic in time coefficients and accounting for shears is derived to determine the amplitude of parametric vibrations. The main regions of parametric instability taking into account transverse shears were found. An example of parametric vibrations of a sandwich cylinder with the magnetorheological core affected by a magnetic field is considered.