| Sloshing means motion of the liquid free surface inside its container. It is caused by disturbance to partially filled liquid containers. The problem of liquid sloshing in moving or stationary containers remains of great concern to aerospace, civil, ocean engineering, designers of road tankers and ship tankers. The multidimensional modal theory is applied to solve liquid nonlinear sloshing in circular cylindrical tank used in aerospace engineering in this paper. After deriving the modal system in general form, the liquid nonlinear free sloshing, the transient response and steady response of liquid transverse forced resonant sloshing are investigated systematically and the influences of higher order modes are analyzed. A formula of liquid sloshing force, which is fit for engineering application, is also derived. The major works of this paper include four parts as follows:The free boundary value problem describing liquid nonlinear sloshing is translated into infinite dimensional modal system through the pressure integral variational principle and modes expanding method in the first part. The modal system takes on general form and is suitable for arbitrary three dimensional motion of tank. In comparing with the original complicated nonlinear boundary value problem, solving the modal system is easy greatly. At the same time, the physical meaning of the modal system is manifest. So, it is can be taken as the basis of solving all kinds of liquid nonlinear sloshing problem.The liquid nonlinear free sloshing in circular cylindrical tank is investigated in the second part. Based on the infinite dimensional modal system, the finite dimensional modal system describing liquid nonlinear free sloshing is derived. The modal system is integrated by Runge-Kutta method. By discovering many nonlinear phenomena when liquid is in free sloshing, the correctness of formula derivation and the validity of applying multidimensional modal theory to liquid nonlinear sloshing in circular cylindrical tank are proved.The third part is composed of chapter 4, chapter 5 and chapter 6, which are the emphases of the paper. The finite dimensional modal system describing liquid nonlinear resonance sloshing when the tank is in translation transverse motion is derived first in this part and the liquid transient response and steady response are investigated systematically. The influences of higher modes which are ignored are analyzed too.In Chapter 4, many important nonlinear phenomena, such as beating phenomenon, shift of nodal diameter and nonplanar motion are discovered qualitatively by direct numerical integration of the modal system and the non-ignoring of secondary modes in the describing of liquid motion are proved.Chapter 5 is the stability analysis of the modal system. The steady periodic solutions of the primary modal functions are gained first. The stability and the stable zones of the solutions are investigated by Floquet-Lyapunov method. So the different liquid transverse forced resonance sloshing wave forms—stable planar wave, stable rotary wave and unstable chaotic wave are revealed quantitatively and some significative conclusions are gained. At last, the theory results are compared with the experimental results and they agree well. So the validity of steady response analysis is proved.The influence of secondary modes on steady response and non-ignoring of higher modes in the describing of liquid motion due to secondary resonance are analyzed in Chapter 6. So the scope and localization of Narimanov-Moiseev third order asymptotic hypothesis are disclosed, which can direct future work.The fourth part faces the engineering application. Based on the work of former chapters, a formula of liquid force acted on the wall of partially filled circular cylindrical tank when the liquid produces nonlinear sloshing is derived. The physical meaning of this formula is manifest and can be used in the estimating of liquid sloshing force in engineering.
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