Nonlinear forced vibration of damped plates by an Asymptotic Numerical Method

F. Boumediene, A. Miloudi, J. M. Cadou, L. Duigou, E. H. Boutyour a Laboratoire de Mécanique Avancée, Faculté de Génie Mécanique & Génie des Procédés, USTHB, BP 32, El Alia, 16111 Bab Ezzouar, Alger, Algérie. b Laboratoire d'Ingénierie des Matériaux de Bretagne, Université Européenne de Bretagne, Université de Bretagne Sud, Rue de Saint Maudé, BP 92116, 56321 Lorient cedex, France. c Département de Physique Appliquée, Faculté des Sciences et Techniques, Université Hassan I, BP 577, Settat, Maroc. Abstract This work deals with damped nonlinear forced vibrations of thin elastic rectangular plates subjected to harmonic excitation by an Asymptotic Numerical Method. Using the harmonic balance method and Hamilton’s principle, the governing equation is converted into a static formulation. A mixed formulation is used to transform the problem from cubic nonlinearity to quadratic one sequence. Displacement, stress and frequency are represented by power series with respect to a path parameter. Equating the like powers of this parameter, the nonlinear governing equation is transformed into a sequence of linear problems with the same stiffness matrix. Through a single matrix inversion, a considerable number of terms of the perturbation series can easily be computed with a limited computation time. The starting point, corresponding to a regular solution, is obtained by the Newton-Raphson method. In order to increase the step length, Padé approximants are used. Numerical tests are presented and compared with numerical results in the literature, for different boundary conditions, excitations and damping coefficients.