On the critical forcing amplitude of forced nonlinear oscillators
Autor: | Mariano Febbo, Jinchen Ji |
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Jazyk: | angličtina |
Rok vydání: | 2013 |
Předmět: |
Frequency response
Environmental Engineering Aerospace Engineering INGENIERÍAS Y TECNOLOGÍAS critical forcing amplitude frequency-response curve Mecánica Aplicada symbols.namesake Control theory General Materials Science CRITICAL Electrical and Electronic Engineering Civil and Structural Engineering Mathematics NONLINEAR Ingeniería Mecánica Forcing (recursion theory) Mechanical Engineering FREQUENCY-RESPONSE CURVE Mathematical analysis FORCING AMPLITUDE CRITICAL FORCING AMPLITUDE Tangent Engineering (General). Civil engineering (General) Critical value Nonlinear system Amplitude purl.org/becyt/ford/2 [https] Lagrange multiplier purl.org/becyt/ford/2.3 [https] symbols Jump forced nonlinear systems TA1-2040 FORCED NONLINEAR SYSTEMS |
Zdroj: | CONICET Digital (CONICET) Consejo Nacional de Investigaciones Científicas y Técnicas instacron:CONICET Open Engineering, Vol 3, Iss 4, Pp 764-770 (2013) |
Popis: | The steady-state response of forced single degree-of-freedom weakly nonlinear oscillators under primary resonance conditions can exhibit saddle-node bifurcations, jump and hysteresis phenomena, if the amplitude of the excitation exceeds a certain value. This critical value of excitation amplitude or critical forcing amplitude plays an important role in determining the occurrence of saddle-node bifurcations in the frequency-response curve. This work develops an alternative method to determine the critical forcing amplitude for single degree-of-freedom nonlinear oscillators. Based on Lagrange multipliers approach, the proposed method considers the calculation of the critical forcing amplitude as an optimization problem with constraints that are imposed by the existence of locations of vertical tangency. In comparison with the Gröbner basis method, the proposed approach is more straightforward and thus easy to apply for finding the critical forcing amplitude both analytically and numerically. Three examples are given to confirm the validity of the theoretical predictions. The first two present the analytical form for the critical forcing amplitude and the third one is an example of a numerically computed solution. Fil: Febbo, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina Fil: Ji, Jinchen C.. University of Technology; Australia |
Databáze: | OpenAIRE |
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