Two-mode response of simply supported, rectangular laminated plates

Two-mode responses of thin rectangular laminated plates subjected to a harmonic excitation are studied by using the method of multiple scales (MMS). The plates are assumed to be simply supported along all edges, and internal resonances between two symmetric modes of vibration are analysed. In order to use MMS properly, we introduce new detuning parameters which indicate the relationship of natural frequencies of each mode. It is found analytically that two-mode responses can occur at each primary resonance. The accuracy of analytical results is confirmed in comparison with results of numerical integration of the equation of motion. Furthermore, it is detected that the two-mode response near the primary resonance of the second mode loses its stability via a Hopf bifurcation, giving rise to quasi-periodic response. (C) 1997 Elsevier Science Ltd.