In this note, a closed-form solution of periodic motions in a periodically forced oscillator with quadratic nonlinearity is presented without any small parameters. The perturbation method is based on one harmonic term plus perturbation modification, and the traditional harmonic balance is to arbitrarily select harmonic terms with constant coefficients. If harmonic terms are not enough included in the approximate solution, such a solution is not an appropriate, analytical solution for periodic motions, and some analytical solutions cannot be caught.
Analytical Solutions for Stable and Unstable Period-1 Motions in a Periodically Forced Oscillator With Quadratic Nonlinearity
Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received June 13, 2012; final manuscript received January 14, 2013; published online April 24, 2013. Assoc. Editor: Philip Bayly.
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Luo, A. C. J., and Yu, B. (April 24, 2013). "Analytical Solutions for Stable and Unstable Period-1 Motions in a Periodically Forced Oscillator With Quadratic Nonlinearity." ASME. J. Vib. Acoust. June 2013; 135(3): 034503. https://doi.org/10.1115/1.4023834
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