Keywords: free vibration, forced vibration, composite rectangular plates, first order shear deformation, Galerkin method, multiple time scales, closed–form expression, nonlinear frequency, steady–state motion, primary resonance, secondary resonance, frequency response equations, backbone curve, fibre–metal laminate, transverse pressure
Non–linear vibration response of laminated fibre–reinforced rectangular plates
This paper investigates the non–linear free and forced vibration response of immovable simply–supported composite rectangular plates. The plates are symmetric and are subjected to a transverse pressure which is harmonic in time. A novel procedure is implemented to obtain the non–linear ordinary differential equation by using first order shear deformation theory and Galerkin method. The multiple time scales perturbation method is utilised to obtain an analytical closed–form expression for the non–linear frequency and frequency response equation of the studied plates. After validation of present study with available literature, the non–linear free and forced vibrations of a fibre–metal laminated plate, named Glare 3, have been investigated. Also, the effects of some system parameters on the non–linear frequency have been studied.