Homotopy perturbation method with an auxiliary parameter for nonlinear oscillators
نویسندگان
چکیده
منابع مشابه
Nonlinear transversely vibrating beams by the homotopy perturbation method with an auxiliary term
This paper presents the high order frequency-amplitude relationship for nonlinear transversely vibrating beams with odd and even nonlinearities, using Homotopy Perturbation Method with an auxiliary term (HPMAT). The governing equations of vibrating buckled beam, beam carrying an intermediate lumped mass, and quintic nonlinear beam are investigated to exhibit the reliability and ability of the p...
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and Applied Analysis 3 Accordingly, we can construct a homotopy equation in the form ü ω2u p ( u3 −ω2u ) 0. 2.6 When p 0, we have ü ω2u 0, u 0 A, u′ 0 0, 2.7 which describes the basic solution property of the original nonlinear equation, 2.3 . When p 1, 2.6 becomes the original one. So the solution procedure is to deform from the initial solution, 2.4 , to the real one. Due to one unknown param...
متن کاملnonlinear transversely vibrating beams by the homotopy perturbation method with an auxiliary term
this paper presents the high order frequency-amplitude relationship for nonlinear transversely vibrating beams with odd and even nonlinearities using homotopy perturbation method with an auxiliary term (hpmat). the governing equations of vibrating buckled beam, beam carrying an intermediate lumped mass and quintic nonlinear beam are investigated to exhibit the reliability and ability of the pro...
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In this paper we propose a reliable algorithm for the solution of nonlinear oscillators. Our algorithm is based upon the homotopy perturbation method (HPM), Laplace transforms, and Padé approximants. This modified homotopy perturbation method (MHPM) utilizes an alternative framework to capture the periodic behavior of the solution, which is characteristic of oscillator equations, and to give a ...
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The nonlinear oscillator problem has extensive applications. In this paper, we examined the modified homotopy perturbation method to obtain the solution of the problem and to reduce the computational efforts. For the accuracy purpose the Laplace transform and Pade approximation have also been used. We construct the deformation equations by two components of the homotopy series, then by means of...
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ژورنال
عنوان ژورنال: Journal of Low Frequency Noise, Vibration and Active Control
سال: 2018
ISSN: 1461-3484,2048-4046
DOI: 10.1177/1461348418811028