Double Hopf bifurcation of composite laminated piezoelectric plate subjected to external and internal excitations

doi:10.1007/s10483-017-2196-9

Abstract

Abstract:

The double Hopf bifurcation of a composite laminated piezoelectric plate with combined external and internal excitations is studied. Using a multiple scale method, the average equations are obtained in two coordinates. The bifurcation response equations of the composite laminated piezoelectric plate with the primary parameter resonance, i.e., 1:3 internal resonance, are achieved. Then, the bifurcation feature of bifurcation equations is considered using the singularity theory. A bifurcation diagram is obtained on the parameter plane. Different steady state solutions of the average equations are analyzed. By numerical simulation, periodic vibration and quasi-periodic vibration responses of the composite laminated piezoelectric plate are obtained.

Key words: normal cone, increasing operator, positive solution for integral equation, double Hopf bifurcation, composite laminated piezoelectric plate, periodic solution, quasi-periodic solution

2010 MSC Number:

O193

Yan ZHOU, Wei ZHANG. Double Hopf bifurcation of composite laminated piezoelectric plate subjected to external and internal excitations. Applied Mathematics and Mechanics (English Edition), 2017, 38(5): 689-706.

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