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The solution structure of the Düffing oscillator’s transient response and general solution

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Abstract

A modification of homotopy analysis method (HAM) is developed in this paper. The solution structure of the Düffing oscillator’s free vibration at different damping levels is put forward based on this new modified HAM. Explicit expressions for the fundamental decaying rate and the fundamental frequency are derived. Numerical examples with different initial conditions are calculated to verify the proposed solution structures. The number of terms required to be considered in the modified HAM for yielding satisfactorily accurate solutions is analyzed. The structure of forced and damped Düffing oscillator’s general solution is also put forward and verified.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Rice University, Houston, TX, 77005, USA

    Keguan Zou & Satish Nagarajaiah

  2. Department of Mechanical Engineering, Rice University, Houston, TX, 77005, USA

    Satish Nagarajaiah

Authors
  1. Keguan Zou
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  2. Satish Nagarajaiah
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Correspondence to Keguan Zou.

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Zou, K., Nagarajaiah, S. The solution structure of the Düffing oscillator’s transient response and general solution. Nonlinear Dyn 81, 621–639 (2015). https://doi.org/10.1007/s11071-015-2015-3

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  • DOI: https://doi.org/10.1007/s11071-015-2015-3

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