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The Asymptotic Perturbation Method for Nonlinear Continuous Systems

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Abstract

We apply the asymptotic perturbation (AP) method to the study of the vibrations of Euler--Bernoulli beam resting on a nonlinear elastic foundation. An external periodic excitation is in primary resonance or in subharmonic resonance in the order of one-half with an nth mode frequency. The AP method uses two different procedures for the solutions: introducing an asymptotic temporal rescaling and balancing the harmonic terms with a simple iteration. We obtain amplitude and phase modulation equations and determine external force-response and frequency-response curves. The validity of the method is highlighted by comparing the approximate solutions with the results of the numerical integration and multiple-scale methods.

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Authors and Affiliations

  1. Technical Institute “G. Cardano”, Piazza della Resistenza 1, 00015, Monterotondo (Rome), Italy

    Attilio Maccari

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  1. Attilio Maccari
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Maccari, A. The Asymptotic Perturbation Method for Nonlinear Continuous Systems. Nonlinear Dynamics 19, 1–18 (1999). https://doi.org/10.1023/A:1008304701252

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