NON-LINEAR FORCED VIBRATIONS OF PLATES BY AN ASYMPTOTIC–NUMERICAL METHOD

Non-linear forced vibrations of thin elastic plates have been investigated by an asymptotic–numerical method (ANM). Various types of harmonic excitation forces such as distributed and concentrated are considered. Using the harmonic balance method and Hamilton's principle, the equation of motion is converted into an operational formulation. Based on the finite element method a starting point corresponding to a non-linear solution associated to a given frequency and amplitude of excitation is computed. Applying perturbation techniques in the vicinity of this solution, the non-linear governing equation obtained is transformed into a sequence of linear problems having the same stiffness matrix. Employing one matrix inversion, a large number of terms of the perturbation series of the displacement and frequency can be easily computed with a small computation time. Iterations of this method lead to a powerful path-following technique. Comprehensive numerical tests for forced vibrations of plates subjected to time-harmonic lateral excitations are reported.