Wang Zhaolin

Nonlinear phenomena of three-dimensional liquid sloshing in microgravity environment

The dynamic problem of three-dimensional liquid sloshing is numerically studied in this paper. The arbitrary Lagrange-Euler (ALE) kinematic description is introduced into the control equations system. The discrete numerical equations of finite element method are developed by Galerkin weighted residual method. The boundary condition about free-surface tension is represented in the form of weak integration that can be computed by our differential geometry method derived. The normal vector on free surface is calculated by using accurate formula presented in this paper. The numerical computations are performed and the comparison not only between numerical results and analytical results but also between numerical results and experimental results validated the effectiveness of the method. Finally, large amplitude sloshing of three-dimensional liquid in low-gravity environment is simulated and some important nonlinear characteristics are obtained. From the numerical results, it is concluded that the character of nonlinear sloshing of the liquid under low-gravity environment is much different from that of the liquid sloshing under normal gravity environment.

Stability of nonlinear vibrations of a deploying flexible beam from a spacecraft

Abstract. In this paper, stability of a complex spacecraft is studied by the use of two new models. The first, is a rigid-flexible model, which consists of a rigid body and a deploying flexible beam; while the second, includes a liquid filled rigid body with a deploying flexible beam. In particular, the deploying beam in both models is assumed to have a finite deflection profile. It has been proved that nonlinear transverse vibrations of a beam are stable when undergoing uniform extension or retrieval.

Stability of non-conservative linear gyroscopic systems

The paper investigates the stability of linear non-conservative mechanical systems subjected to potential, gyroscopic, circulatory forces and Rayleigh damping. Three stability theorems are proved by means of the Rayleigh quotients. The stability criterions given by the theorems are convenient and useful because they are independent of the Rayleigh quotients.

Viscoelastic plate-fluid interactive vibration and liquid sloshing suppression

The viscoelastic plate-fluid interaction problem was studied. Forced vibration of the interactive system was investigated, and the equivalent mechanical models were obtained. The conclusion is that, for some case, the inner damping of the viscoelastic baffle will play a major role for liquid sloshing suppression.

Output regulation of the general nonlinear discrete-time system

With the use of centre manifold and dynamic system theory, the necessary and sufficient conditions are obtained for the solvabilities of the output regulator problems for the general nonlinear discrete-time system. This work generalizes and refines the corresponding results by Isidori and Byrnes on the affine nonlinear continuous-time system.

TECHNICAL STABILITY OF NONLINEAR TIME-VARYING SYSTEMS WITH SMALL PARAMETERS *

Technical stability allowing quantitative estimation of trajectory behavior of a dynamical system over a given time interval was considered. Based on a differential comparison principle and a basic monotonicity condition, technical stability relative to certain prescribed state constraint sets of a class of nonlinear time-varying systems with small parameters was analyzed by means of vector Liapunov function method. Explicit criteria of technical stability are established in terms of coefficients of the system under consideration. Conditions under which the technical stability of the system can be derived from its reduced linear time-varying (LTV) system were further examined, as well as a condition for linearization approach to technical stability of general nonlinear systems. Also, a simple algebraic condition of exponential asymptotic stability of LTV systems is presented. Two illustrative examples are given to demonstrate the availability of the presently proposed method.

Model of centrifugal effect and attitude maneuver stability of a coupled rigid-flexible system

The influences of nonlinear centrifugal force to large overall attitude motion of coupled rigid-flexible system was investigated. First the nonlinear model of the coupled rigid-flexible system was deduced from the idea of “centrifugal potential field”, and then the dynamic effects of the nonlinear centrifugal force to system attitude motion were analyzed by approximate calculation; At last, the Lyapunov function based on energy norm was selected, in the condition that only the measured values of attitude and attitude speed are available, and it is proved that the PD feedback control law can ensure the attitude stability during large angle maneuver.

Method of large-scale system and analysis of three-axis stability of system partially filled with liquid

In the paper the method of large-scale system is investigated. The criteria of three-axis stability of a partially liquid-filled system are obtained by means of the method of large-scale system. Numerical results are given for a liquid-filled system with three-flywheels.