期刊
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
卷 38, 期 5, 页码 689-706出版社
SHANGHAI UNIV
DOI: 10.1007/s10483-017-2196-9
关键词
double Hopf bifurcation; composite laminated piezoelectric plate; periodic solution; quasi-periodic solution
资金
- Project for Academic Human Resources Development in Institutions of Higher Learning under the jurisdiction of Beijing
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.
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