Non-linear forced vibration analysis of rectangular plates including the coupling between transverse and in-plane displacements

The objective of this work is to study the geometrically non-linear steady state periodic forced response of fully clamped rectangular plates (FCRP) with immovable in-plane conditions, taking into account the effect of the in-plane displacements. A complete formulation has been proposed first, reducing the equations of motion to a system of coupled non-linear algebraic equations, which are decoupled once the in-plane inertia is omitted. An averaging technique has then been developed, in order to simplify the first method and to develop an engineering complete theory. The forced response is given in the case of a concentrated harmonic excitation force with various intensities. The numerical results obtained here with the two formulations, using an explicit analytical solution, were compared with those obtained previously using a formulation in which the in-plane displacements have been neglected, showing an “over-stiff” effect.