## Study of Subharmonic Response in Nonlinear System ModelsThe report investigates the system model G(u, u dot, . . ., u sup n, t) = F(t), where F(t) is a periodic excitation. Using an approximate solution of the form u(t) = Summation, R=0 to UH (U sub c)(R) cos R (omega sub o) t + (U sub s) (R) sin R (omega sub o) t), analytical theorems and computer results are obtained that yield information into the nature of the existence and non-existence of subharmonic components in the response. By assuming G(u, u dot ..., u sup n, t) to be a polynomial, theorems are developed that determine the conditions for the possible existence and non-existence of subharmonic response. (Author). |

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### Contents

INTRODUCTION | 1 |

Figure Page | 4 |

Figure Page | 5 |

STABILITY OF NONLINEAR DIFFERENTIAL EQUATIONS | 13 |

THE THEORY OF THE EXISTENCE OF SUBHARMONIC OSCILLATIONS | 19 |

Frequencies obtained by solving Gu ut F | 35 |

+ Kl+00 Fcl COs V and ut UCSb1b2l | 42 |

A FIRST ORDER NONLINEAR DIFFERENTIAL EQUATION | 53 |

number of Fourier parameters is increased | 62 |

A SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION | 75 |

G k Reduction of MSE for u + u k cos 3t as the number | 84 |

EQUATIONS WITH EXACT SOLUTIONS IN THE FORM OF SUBHARMONIC | 92 |

APPENDIX I | 98 |

Flow chart of ADAPT N | 101 |

REFERENCES | 105 |

This report investigates the system model Guu ut Ft | 117 |