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arXiv · 1811.09814

Natural response of non-smooth oscillators using homotopy analysis combined with Galerkin projections

Jeet Desai·Amol Marathe
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Abstract

We propose homotopy analysis method in combination with Galerkin projections to approximate the natural response of non-smooth oscillators with discontinuities of type Heaviside, signum, modulus etc. While constructing the homotopy, we think of convergence-control parameter as a function of the embedding parameter and call it a convergence-control function. Homotopy analysis provides an expression for the natural frequency of the oscillator that also includes free parameters arising from the convergence-control function. Generating extra equations using Galerkin projections and solving the same numerically gives the approximate natural response of the non-smooth oscillators. We also seek aperiodic natural response of a unilaterally constrained simple pendulum. The superiority of the approach is well-established over the method of harmonic balance, Lindstedt-Poincar\'e method and conventional homotopy analysis method.

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Jeet Desai, Amol Marathe. 2018-11-24. Natural response of non-smooth oscillators using homotopy analysis combined with Galerkin projections. https://arxiv.org/abs/1811.09814

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