The disturbance on the free surface of the liquid when the liquid-filled tanks are excited is called sloshing. This paper examines the nonlinear sloshing response of the liquid free surface in partially filled two-dimensional rectangular tanks using finite element method. The liquid is assumed to be inviscid, irrotational, and incompressible; fully nonlinear potential wave theory is considered and mixed Eulerian-Lagrangian scheme is adopted. The velocities are obtained from potential using least square method for accurate evaluation. The fourth-order Runge-Kutta method is employed to advance the solution in time. A regridding technique based on cubic spline is employed to avoid numerical instabilities. Regular harmonic excitations and random excitations are used as the external disturbance to the container. The results obtained are compared with published results to validate the numerical method developed. 1. Introduction It is common everyday knowledge to each of us that any small container filled with liquid must be moved or carried very carefully to avoid spills. For example, one has to be careful while carrying a cup of coffee while moving, because the motion of the person makes coffee spill. Such a motion on the free surface of the liquid, due to external excitation in the liquid-filled containers, is called sloshing. Sloshing is likely to be seen whenever we have a liquid with a free surface in the presence of gravity. At equilibrium the free surface of the liquid is static and coincides with a gravitational equipotential surface. When the surface is perturbed, an oscillation is set up in which the energy oscillates between kinetic energy and gravitational potential energy. The phenomenon called sloshing occurs in a variety of engineering applications such as sloshing in liquid-propellant launch vehicles, sloshing in liquids used in industries to store oil, water, chemicals, liquefied natural gases, and so forth, and sloshing in the nuclear reactors of pool type, nuclear fuel storage tanks under earthquake. The liquid sloshing may cause huge loss of human, economic, and environmental resources owing to unexpected failure of the container; for example the spillage of toxic chemicals stored in tanks in industries can cause contamination of soil and the environment. Thus, understanding the dynamic behaviour of liquid free surface is essential. As a result, the problem of sloshing has attracted many researchers and engineers targeting to understand the complex behaviour of sloshing and to design the structures to withstand its effects. Abundant
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