Iterative Homotopy Harmonic Balance Approach for Determining the Periodic Solution of a Strongly Nonlinear Oscillator

<div>Comparison of the approximate solution with the exact solution; <svg height="7.35473pt" id="M142" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.0498162 -7.0048 38.3496 7.35473" width="38.3496pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M320 255C320 327 260 385 186 385S52 327 52 255S112 125 186 125S320 183 320 255Z" id="g117-74"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="371" vert-adv-y="371"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,12.087,0)"><path d="M320 255C320 327 260 385 186 385S52 327 52 255S112 125 186 125S320 183 320 255Z" id="g117-74"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="371" vert-adv-y="371"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,24.174,0)"><path d="M320 255C320 327 260 385 186 385S52 327 52 255S112 125 186 125S320 183 320 255Z" id="g117-74"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="371" vert-adv-y="371"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,33.355,0)"><path d="M320 255C320 327 260 385 186 385S52 327 52 255S112 125 186 125S320 183 320 255Z" id="g117-74"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="371" vert-adv-y="371"></glyph.data></g></svg> exact solution, — 2nd-order approximate solution.</div>

Mathematical Problems in Engineering

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Figure 2

Figure 2: Iterative Homotopy Harmonic Balance Approach for Determining the Periodic Solution of a Strongly Nonlinear Oscillator 