Transient and steady-state responses of an asymmetric nonlinear oscillator
| Autor: | ALEX ELIAS ZUÑIGA, 19150, OSCAR MARTINEZ ROMERO, 278430 |
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| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Steady state (electronics)
Article Subject General Mathematics Oscillators (mechanical) Duffing equation Frequency response Jacobi Elliptic function Overshoot (signal) Duffing oscillator Approximate solution Fourier series Steady-state response Mathematics lcsh:Mathematics Non-linear oscillators Mathematical analysis General Engineering Elliptic function lcsh:QA1-939 Jacobi elliptic functions Nonlinear system Classical mechanics 7 INGENIERÍA Y TECNOLOGÍA lcsh:TA1-2040 Transient (oscillation) Primary resonance response lcsh:Engineering (General). Civil engineering (General) Amplitude frequency response Dynamical response |
| Zdroj: | Mathematical Problems in Engineering Mathematical Problems in Engineering, Vol 2013 (2013) |
| Popis: | We study the dynamical response of an asymmetric forced, damped Helmholtz-Duffing oscillator by using Jacobi elliptic functions, the method of elliptic balance, and Fourier series. By assuming that the modulus of the elliptic functions is slowly varying as a function of time and by considering the primary resonance response of the Helmholtz-Duffing oscillator, we derived an approximate solution that provides the time-dependent amplitude-frequency response curves. The accuracy of the derived approximate solution is evaluated by studying the evolution of the response curves of an asymmetric Duffing oscillator that describes the motion of a damped, forced system supported symmetrically by simple shear springs on a smooth inclined bearing surface. We also use the percentage overshoot value to study the influence of damping and nonlinearity on the transient and steady-state oscillatory amplitudes. © 2013 Alex Elías-Zúñiga and Oscar Martínez-Romero. |
| Databáze: | OpenAIRE |
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