SUBHARMONIC AND SUPERHARMONIC RESONANCES IN THE PITCH AND ROLL MODES OF SHIP MOTIONS

We considered the motion of a ship with two degrees of freedom-pitch and roll-when second-order, static couplings are included in the equations of motion, and we obtained a nonlinear analysis of the response of the ship to a harmonic excitation (e.g., a regular sea) using the method of multiple scales. In the first part of the paper, we considered the pitch frequency to be twice the roll frequency and found that a superharmonic response exists for any value of the amplitude of the excitation, but a subharmonic response is possible only if the amplitude of the excitation is above a critical value. In the second part of the paper, we considered ships without the two-to-one frequency ratio. We found that there are five resonant situations and, depending on the value of the parameters, three can involve large motions. Some of the present results were combined with some results from a previous paper to determine the variation of the amplitude of the response with the encounter frequency. Also, the accuracy of some of the present results was established by comparing them with a numerical solution.

• Corporate Authors:

  American Institute of Aeronautics and Astronautics

  1290 Avenue of the Americas
  New York, NY  United States  10019
• Authors:
  • Mook, D I
  • Marshall, L R
  • Nayfeh, A H
• Publication Date: 1974-1

Media Info

• Features: References;
• Pagination: p. 23-40
• Serial:
  • Journal of Hydronautics
  • Volume: 8
  • Issue Number: 1
  • Publisher: American Institute of Aeronautics and Astronautics

Subject/Index Terms

• TRT Terms: Pitch (Dynamics); Rolling; Ship motion; Waves
• Old TRIS Terms: Regular waves; Roll response
• Subject Areas: Marine Transportation; Vehicles and Equipment;

Filing Info

• Accession Number: 00051873
• Record Type: Publication
• Source Agency: American Institute of Aeronautics and Astronautics
• Files: TRIS
• Created Date: Apr 9 1974 12:00AM