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Exact analytical solutions for forced undamped Duffing oscillator
Affiliation:1. Dpto. de Aeronáutica, Facultad de Ciencias Exactas, Físicas y Naturales, Universidad Nacional de Córdoba, Avenida Vélez Sarsfield 1611–5000 Córdoba, Argentina;2. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina;3. Dpto. Física Aplicada, ETSI Aeronáuticos, Universidad Politécnica de Madrid, 28040 Madrid, Spain;1. Sant Guru Ghasidas Govt. P. G. College, Kurud, Dhamtari (Chhattisgarh), India;2. Indian Institute of Technology (Indian School of Mines, Dhanbad);1. University of Dschang, IUT-FV, LISIE, P.O. Box 134, Bandjoun, Cameroon;2. University of Yaounde I, Faculty of Science, LaMSEBP, P.O. Box 812, Yaounde, Cameroon;3. Aix-Marseille Université, DME, 5 rue Enrico Fermi Technopole de Chateau Gombert, 13453 Marseille Cedex 13, France
Abstract:The steady-state response of an undamped Duffing oscillator to periodic external forces is studied. The forcing functions are chosen such that the time course of the displacement can be described by exact analytical expressions. The displacement and forcing functions are governed by Jacobi elliptic functions and thus are periodic but generally non-harmonic. The parameter of the elliptic functions is deliberately chosen. For certain parameter choices, exact analytical expressions are found for the frequency–amplitude relation.
Keywords:Nonlinear oscillator  Non-harmonic periodic loading  Jacobi elliptic functions  Exact analytical frequency–amplitude relation
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