Resonant modes of the motion of a cylindrical reservoir on a movable pendulum suspension with a free-surface liquid

Received: September 28, 2018
Taras Shevchenko Kyiv National University
Taras Shevchenko National University of Kyiv

The article deals with an investigation of the system of "reservoir -- liquid with a free surface", when the reservoir is fixed on pendulum suspension, which suspension point performs a given motion. The system behavior is studied for the below-resonant, near-resonant and above-resonant modes. The description of the system behavior is done based on a nonlinear model of motion, which takes into account the combined character of motion of the system components. The numerical modeling shows that general regularities of the system behavior coincide qualitatively with known experiments.

  1. Limarchenko O. S., Yasinskiy V. V. Nonlinear dynamics of structures with liquid. National Technical University of Ukraine “KPI” (1997), (in Russian).
  2. Faltinsen O. M., Rognebakke O. M., Timokha A. N. Resonant three-dimensional nonlinear sloshing in a square-base basin. J. Fluid Mech. 487, 1–42 (2003).
  3. Ibrahim R. A. Liquid sloshing dynamics: theory and applications. Cambridge University Press (2005).
  4. Lukovskiy I. A. Introduction to nonlinear dynamics of a rigid body with cavities containing liquid. Naukova dumka, Kiev (1990), (in Russian).
  5. Faltinsen O. M., Rognebakke O. M., Timokha A. N. Transient and steady-state amplitudes of resonant three-dimensional sloshing in a square base tank with a finite fluid depth. Physics of fluids. 18 (1), 012103 (2006).
  6. Mikishev G. N., Rabinovich B. I. Dynamics of rigid bodies with cavities partially filled by liquid. Mashinostroenie, Moscow (1968), (in Russian).
  7. Pal P. Sloshing of liquid in partially filled container – an experimental study. International Journal of Recent Trends in Engineering. 1 (6), 1–5 (2009).
  8. Zhang Ch., Li Y., Meng Q. Fully nonlinear analysis of second order sloshing resonance in a three-dimensional tank. Computers & Fluids. 116, 88–104 (2015).
  9. Limarchenko O. S., Gubskaya V. V. Problem of forced nonlinear oscillations of the reservoir of truncated conic shape, partially filled with liquid. Bulletin of Kiev National University. 1 (4), 73–76 (2012).
  10. Lymarchenko O. S., Semenovych K. O. Energy redistribution between the reservoir and liquid with free surface for angular motions of the system. Journal of Mathematical Sciences. 222 (3), 296–303 (2017).
Math. Model. Comput. Vol. 5, No. 2, pp. 178-183 (2018)