• Structural Engineering and Mechanics
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• v.61 no.1
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• pp.105-116
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• 2017

In this paper, the optimal extended homotopy analysis method (OEHAM) is introduced to deal with the damped Duffing resonator driven by a van der Pol oscillator, which can be described as a complex Multi-Degree-of-Freedom (MDOF) nonlinear coupling system. Ecumenically, the exact solutions of the MDOF nonlinear coupling systems are difficult to be obtained, thus the development of analytical approximation becomes an effective and meaningful approach to analyze these systems. Compared with traditional perturbation methods, HAM is more valid and available, and has been widely used for nonlinear problems in recent years. Hence, the method will be chosen to study the system in this article. In order to acquire more suitable solutions, we put forward HAM to the OEHAM. For the sake of verifying the accuracy of the above method, a series of comparisons are introduced between the results received by the OEHAM and the numerical integration method. The results in this article demonstrate that the OEHAM is an effective and robust technique for MDOF nonlinear coupling systems. Besides, the presented methods can also be broadly used for various strongly nonlinear MDOF dynamical systems.

• Journal of the Korean Ceramic Society
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• v.31 no.10
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• pp.1133-1140
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• 1994

Nonlinear resonance characteristics of transverse type-PZT ceramic resonator were investigated, and their nonlinear coefficients were calculated using the nonlinear theory proposed by Duffing. Resonance characteristics of sample showed nonlinearity by the thermal effects due to driving current. Nonlinear coefficients greatly affected by sample dimension, however comparing with respect to current density, it was almost constant. Nonlinear coefficients were not changed as driving current increased upto 40 mA/$\textrm{cm}^2$, when $\alpha$ and $\beta$ was 920 and -10.6, respectively, while nonlinear coefficients exponentially increased beyond the current density of 40 mA/$\textrm{cm}^2$. Nonlinear coefficients were slightly increased as temperature increased.