This book presents mathematical fundaments and results on sloshing in an upright circular cylindrical tank with semi-analytical solutions. The book outlines generic mathematical and physical aspects of the multimodal method, describes milestones, and presents several versions of modal systems for an upright circular tank, both linear and nonlinear.
The book offers an extended description of the state-of-the-art theoretical sloshing with more than 200 references. It presents mathematical fundamentals of free-surface sloshing problems, details linear and nonlinear modal equations, provides analytical estimates of viscous damping, and covers stability analysis of steady-state solution.
The book is for engineers dealing with sloshing, applied mathematicians working on free-surface problems, and lecturers in fluid mechanics that need to know the fundamentals and analytical solutions from surface wave theory.
Table of Contents
1. Introduction. 2. Differential, Variational and Modal Statements of the Sloshing Problem. 3. Damping in Liquid Sloshing Dynamics. 4. Linear Modal Theory. 5. Nonlinear Asymptotic Modal Theory of the Narimanov-Moiseev Type. 6. Steady-state (periodic) Solutions of the Narimanov-Moiseev Type Modal Equations. 7. Steady-State Sloshing for the Longitudinal Forcing. 8. Steady-State Sloshing for Orbital Forcing. Appendix: Tables of hydrodynamic coefficients
Alexander Timokha obtained his PhD degree (1988) in fluid dynamics from Kyiv State University, USSR, and, later on, Full Doctoral degree in physics and mathematics (Habilitation, 1993) from Institute of Mathematics, National Academy of Sciences of Ukraine (NASU). He is Professor of Applied Mathematics (1994) and Head of Department (2017), Corresponding Member of NASU (2015). He is Senior NATO (1998-1991) and Alexander-von-Humboldt (2003-2004) Fellow, has numerous national and international awards including Petryshyn’s prize for the best work in Nonlinear Analysis (USA, 1994) and State Award in Science & Technology (Ukraine, 2012). In 2004-2012, he was a Visiting Professor at “Centre for Ship and Ocean Structures”, Norwegian University of Science and Technology (NTNU). From 2013, he is Research Professor at Centre of Excellence “Autonomous Marine Operations and Systems”, NTNU. His interests lie in the Mathematical Fluid Mechanics. He has authored more than 200 journal papers and 4 books. Ihor Raynovskyy obtained his Master Science degree from Kyiv national Taras-Shevchenko University, Ukraine, in 2015, and, later on, PhD degree in theoretical mechanics from the Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine. Since 2018, Ihor Raynovskyy occupies position of Researcher at the Institute of Mathematics of NASU, Kyiv. He has authored 7 journal papers and participated in 5 international conferences.