The nonlinear oscillations of a tank partially filled with a fluid under a horizontal harmonic force are studied. The generation of waves on the free liquid surface is studied using a nonlinear multimode (twelve modes) model that describes the combined motion of the tank and the fluid under external forces. It is shown that the oscillations of the system do not reach a steady state in classical sense, which is confirmed experimentally. Using an advanced model reveals a multi-frequency dynamic process, effect of high-frequency modes, and shift of the frequencies of antisymmetric modes
Similar content being viewed by others
References
K. S. Kolesnikov, Dynamics of Rockets [in Russian], Mashinostroenie, Moscow (1980).
O. S. Limarchenko, “Studying the nonlinear waveformation in the fluid in a moving cylindrical tank,” Mat. Fiz. Nonlin. Mekh., No. 8, 12–19 (1987).
O. S. Limarchenko and V. V. Yasinskii, Nonlinear Dynamics of Structures with Fluid [in Russian], NTTU KPI, Kyiv (1997).
O. S. Limarchenko and V. V. Gubs’ka, “Problem of the force vibrations of a truncated conical tank partially filled with a fluid,” Visn. Kyivsk. Nats. Univ. im. Tarasa Shevchenka, 1, No. 4, 73–76 (2012).
I. A. Lukovskii, Introduction to the Nonlinear Dynamics of a Rigid Body with Cavities Containing a Fluid [in Russian], Naukova Dumka, Kyiv (1990).
G. N. Mikishev and B. I. Rabinovich, Dynamics of a Rigid Body with Cavities Partially Filled with a Fluid [in Russian], Mashinostroenie, Moscow (1968).
G. S. Narimanov, L. V. Dokuchaev, and I. A. Lukovskii, Nonlinear Dynamics of an Aircraft with Fluid [in Russian], Mashinostroenie, Moscow (1977).
H. Abramson (ed.), The Dynamic Behavior of Liquid in Moving Container, NASA SP-106, Washington (1966).
M. Akbarzade and A. Farshidianfar, “Application of the amplitude–frequency formulation to a nonlinear vibration system typified by a mass attached to a stretched wire,” Int. Appl. Mech., 50, No. 4, 476–482 (2014).
O. M. Faltinsen, O. M. Rognebakke, and A. N. Timokha, “Transient and steady-state amplitudes of resonant three-dimensional sloshing in a square base tank with a finite fluid depth,” Physics of Fluids, 1, No. 18, 1–14 (2006).
R. A. Ibrahim, Liquid Sloshing Dynamics: Ttheory and Applications, Cambridge University Press, Cambridge (2005).
P. S. Koval’chuk, L. A. Kruk, and V. A. Pelykh, “Stability of composite cylindrical shells with added mass interacting with the internal fluid flow,” Int. Appl. Mech., 50, No. 5, 566–574 (2014).
M. La Rocca, G. Sciortino, C. Adduce, and M. A. Boniforti, “Experimental and theoretical investigation on the sloshing of a two-liquid system with free surface,” Physics of Fluids, 17, 062101, 1–17 (2005).
O. S. Limarchenko and R. V. Tkachenko, “Influence of spring attachment on the dynamics of a fluid-filled cylindrical tank on a moving platform,” Int. Appl. Mech., 50, No. 3, 289–294 (2015).
J. Miles, “Nonlinear surface waves in closed basins,” J. Fluid. Mech., 75, No. 3, 419–448 (1976).
P. Pal, “Sloshing of liquid in partially filled container—an experimental study,” Int. J. of Recent Trends in Engineering, 1, No. 6, 1–5 (2009).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika, Vol. 52, No. 5, pp. 94–105, September–October, 2016.
Rights and permissions
About this article
Cite this article
Konstantinov, A.V., Limarchenko, O.S. Nonlinear Dynamics of the Combined Motion of a Tank and a Fluid Partially Filling It. Int Appl Mech 52, 520–528 (2016). https://doi.org/10.1007/s10778-016-0772-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-016-0772-4