### Abstract

We consider a class of parametrically driven nonlinear oscillators: x+k_{1}x+k_{2}f(x,x)P(Ωt)=0, P(Ωt+2π)=P(Ωt) (*) which can be used to describe, e.g., a pendulum with vibrating length, or the displacements of colliding particle beams in high energy accelerators. Here we study numerically and analytically the subharmonic periodic solution of (*), with frequency 1/ m≅√k_{1}, m=1,2,3,.... In the cases of f(x, x)=x^{3} and f(x,x)=x^{4}, with P(Ωt)=cost, all of these so-called synchronized periodic orbits are obtained numerically, by a new technique, which we refer to here as the indicatrix method. The theory of generalized averaging is then applied to derive highly accurate expressions for these orbits, valid to the second order in k_{2}.

Original language | English |
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Pages (from-to) | 721-728 |

Number of pages | 8 |

Journal | Journal of Applied Mechanics, Transactions ASME |

Volume | 55 |

Issue number | 3 |

Publication status | Published - Sep 1988 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials

### Cite this

*Journal of Applied Mechanics, Transactions ASME*,

*55*(3), 721-728.