Volterra approach – a new method to accurately calculate the non-linear and time-varying roll restoring arm of ships in irregular longitudinal seas

ABSTRACT

With several incidents of large amplitude roll motion of ships observed at sea over the past two decades, the dynamic stability of modern ship types has assumed significant importance. The move by the International Maritime Organization to develop a second generation level-2 criteria has resulted in considerable attention to the development of simplified analytical models for roll motion. Especially for the problem of parametric roll, there is still no analytical model which accurately captures the non-linear roll restoring stiffness taking into account the combined effect of incident waves and dynamic heave and pitch motions of the vessel. This paper extends our previous work to accurately capture both the linear and higher-order time-varying roll stiffness coefficients through an analytical model while taking into account incident waves and dynamic motion of the vessel. This approach called the Volterra method is compared against the existing simplified models and a non-linear time-domain simulation program to demonstrate better agreement of the proposed approach.

KEYWORDS:

• Volterra GZ
• parametric roll
• analytical roll model
• non-linear roll restoring arm
• single degree of freedom model
• grim effective wave
• SIMDYN
• non-linear time domain simulation

Acknowledgments

The authors would like to thank Dr Frans van Walree of MARIN for making available to us the hull form description for our analysis. This work has been funded by the Office of Naval Research (ONR)ONR Grant N000-14-16-1-2281. The authors thank Dr Paul Hess for facilitating the funding for this work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Office of Naval Research (ONR) [grant number N000-14-16-1-2281].

Notes on contributors

Abhilash Somayajula

Dr Abhilash Somayajula is a research assistant professor in the Department of Ocean Engineering at Texas A&M University. He received a PhD degree in ocean engineering from Texas A&M University and has authored over 15 peer reviewed conference and journal publications. He earned his bachelors and masters of technology in ocean engineering and naval architecture at Indian Institute of Technology Kharagpur. Prior to starting his academic career as a research assistant professor, Dr Somayajula has previously worked at various institutions including a naval research laboratory, two shipyards, an offshore design firm and a classification society. He has also been a part of various projects delegated by US Navy to Texas A&M University. Dr Somayajula is currently an active member of Society of Naval Architects and Marine Engineers (SNAME) and has been a member of Royal Society of Naval Architects (RINA) in the past. His research interests include ship and offshore structure hydrodynamics, parametric excitation under stochastic excitation, nonlinear dynamical systems and control of autonomous surface vehicles.

Jeffrey Falzarano

Dr Jeffrey Falzarano is a professor of ocean and civil engineering, and the director of Marine Dynamics Laboratory at Texas A&M University. He has over 25 years of experience as a tenure track naval architecture and ocean engineering faculty member. He has supervised the graduation of more than 30 graduate students and has published more than 100 publications. Based upon his significant original contributions to the study of nonlinear and stochastic dynamics of ships and marine structures, he was elected a fellow in both the Society of Naval Architects and Marine Engineers (SNAME) and American Society of Mechanical Engineers (ASME). Prior to his academic career, Dr Falzarano worked for the U.S. Coast Guard design branch where he participated in the hydrodynamic design of a proposed SWATH patrol cutter. He has also worked at various U.S. Navy labs and international academic institutions. Dr Falzarano received a PhD degree in naval architecture and marine engineering; MSE in aerospace engineering; MSE in applied mechanics, and an MSE in naval architecture and marine engineering from University of Michigan. He earned his BS degree in naval architecture and marine engineering from the Webb Institute.