### Abstract

Language | English |
---|---|

Number of pages | 11 |

Journal | International Journal of Non-Linear Mechanics |

Early online date | 1 Jul 2016 |

DOIs | |

Publication status | E-pub ahead of print - 1 Jul 2016 |

### Fingerprint

### Keywords

- nonlinear oscillator
- exact solution
- Jacobi elliptic function
- external excitation

### Cite this

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**On the design of external excitations in order to make nonlinear oscillators respond as free oscillators of the same or different type.** / Rakaric, Zvonko; Kovacic, Ivana; Cartmell, Matthew.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the design of external excitations in order to make nonlinear oscillators respond as free oscillators of the same or different type

AU - Rakaric, Zvonko

AU - Kovacic, Ivana

AU - Cartmell, Matthew

PY - 2016/7/1

Y1 - 2016/7/1

N2 - This study deals with nonlinear oscillators whose restoring force has a polynomial nonlinearity of the cubic or quadratic type. Conservative unforced oscillators with such a restoring force have closed-form exact solutions in terms of Jacobi elliptic functions. This fact can be used to design the form of the external elliptic-type excitation so that the resulting forced oscillators also have closed-form exact steady-state solutions in terms of these functions. It is shown how one can use the amplitude of such excitations to change the way in which oscillators behave, making them respond as free oscillators of the same or different type. Thus, in cubic oscillators, a supercritical or subcritical pitchfork bifurcation can appear, whilst in quadratic oscillators, a transcritical bifurcation can take place.

AB - This study deals with nonlinear oscillators whose restoring force has a polynomial nonlinearity of the cubic or quadratic type. Conservative unforced oscillators with such a restoring force have closed-form exact solutions in terms of Jacobi elliptic functions. This fact can be used to design the form of the external elliptic-type excitation so that the resulting forced oscillators also have closed-form exact steady-state solutions in terms of these functions. It is shown how one can use the amplitude of such excitations to change the way in which oscillators behave, making them respond as free oscillators of the same or different type. Thus, in cubic oscillators, a supercritical or subcritical pitchfork bifurcation can appear, whilst in quadratic oscillators, a transcritical bifurcation can take place.

KW - nonlinear oscillator

KW - exact solution

KW - Jacobi elliptic function

KW - external excitation

UR - http://www.sciencedirect.com/science/journal/00207462

U2 - 10.1016/j.ijnonlinmec.2016.06.012

DO - 10.1016/j.ijnonlinmec.2016.06.012

M3 - Article

JO - International Journal of Non-Linear Mechanics

T2 - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

ER -