Further Reduction of Normal Forms for High Dimensional Nonlinear Systems and Application to a Composite Laminated Piezoelectric Plate

Abstract:

Normal form theory is robust and useful for direct bifurcation and stability analysis of nonlinear differential equations in real engineering problems. This paper develops a new computation method for obtaining a significant refinement of the normal forms for high dimensional nonlinear systems. In the theoretical model for the nonlinear oscillation of a composite laminated piezoelectric plate, the computation method is applied to compute the coefficients of the normal forms for the case of one double zero and a pair of pure imaginary eigenvalues. The algorithm is implemented in Maple V and the normal forms of the averaged equations and their coefficients for nonlinear oscillations of the composite laminated piezoelectric plate under combined parametric and transverse excitations are calculated.

• Periodical: Applied Mechanics and Materials (Volumes 291-294)
• Pages: 2662-2665
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.291-294.2662
• Online since: February 2013
• Authors: Shu Ping Chen, Wei Zhang
• Keywords: Composite Laminated Piezoelectric Plate, Nonlinear Oscillations, Nonlinear Transformation, Normal Form

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