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On the elliptic balance method. (English) Zbl 1047.70001
From the summary: The objective is to apply a novel perturbation technique called the elliptic balance method (EBM) to obtain an approximate solution for nonlinear two-degree-of-freedom systems. Two examples are presented to compare the EBM solution with numerical integration. The first is related to a damped nonlinear system with two degrees of freedom that describes the dynamical behavior of a viscohyperelastic simple shear suspension system with an undamped linear absorber, and the second is related to a damped nonlinear mechanical model. It is shown that its amplitude-time response can be accurately described by the EBM solution even for moderate values of damping coefficients $$\nu_i$$ and a nonlinear parameter $$\varepsilon$$.

MSC:
 70-08 Computational methods for problems pertaining to mechanics of particles and systems 70K60 General perturbation schemes for nonlinear problems in mechanics 74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
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