## Proceedings of the ... International Conference on Offshore Mechanics and Arctic Engineering, Volumes 1-2American Society of Mechanical Engineers, 1991 - Arctic regions |

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Page 275

When

is substituted to

/ at ) , į = ( a Šat ) . these expressions , subscripts and j + 1 that the quantities ...

When

**equation**( 2 ) , expressing the dynamic boundary condition of free surface ,is substituted to

**equation**( 11 ) . the following**equation**is obtained : where 0 = ( a/ at ) , į = ( a Šat ) . these expressions , subscripts and j + 1 that the quantities ...

Page 510

PERTURBATION METHOD TO SOLVE THE NONLINEAR MATHIEU

FOR SMALL PARAMETERS Perturbation methods are usually employed to solve

a nonlinear differential

PERTURBATION METHOD TO SOLVE THE NONLINEAR MATHIEU

**EQUATION**FOR SMALL PARAMETERS Perturbation methods are usually employed to solve

a nonlinear differential

**equation**. Some research workers have used the ...Page 510

However , second and higher order approximations are needed and the

calculation becomes very complicated . Therefore , the nonlinear Mathieu

investigation further .

However , second and higher order approximations are needed and the

calculation becomes very complicated . Therefore , the nonlinear Mathieu

**equation**with large magnitude parameters needs to be solved to take thisinvestigation further .

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### Contents

SPECIAL SESSION HYDRODYNAMICS | 1 |

HYDRODYNAMIC FORCES | 29 |

SECONDORDER EFFECTS | 113 |

Copyright | |

47 other sections not shown

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### Common terms and phrases

acting amplitude analysis angle applied approach approximately assumed average body boundary cable calculated circular cylinder coefficients compared comparison components computed considered constant corresponding cylinder damping depth described determined diffraction direction distribution domain drag drift force effect element Engineering equation estimates experimental experiments expressed field Figure floating flow fluid follows free surface frequency function given height horizontal hydrodynamic incident included increase integral irregular waves length lift force linear loads mass maximum mean measured method mode mooring motion natural nonlinear obtained Ocean Offshore oscillation period phase platform points position potential predicted present pressure problem random range regular relative represents respectively response second order second-order separation ship shown shows simulation solution spectrum structure surge Table tests theory values velocity vertical vortex wave forces