Quasi-Variational Principles Of Flexilble Multi-body System Dynamics And Their Application

The development of flexible multi-body system dynamics is closely related to the development of space technology. From the multi-body point of view, flexible multi-body system dynamics is an extension of multiple rigid body system dynamics and from the perspective of dynamics, rigid body is flexible in the special circumstances. Flexible multi-body system dynamics considers more cross-link roles between the multi-body movement and flexible effects. The most common flexible multi-body system is flexible multi-body cluster system and flexible multi-body linked system. In this paper, the flexible multi-body cluster system is researched.Quasi-variational principles of flexible multi-body system dynamics covers a lot of subjects, general mechanics, solid mechanics, and other disciplines are needed.Firstly, analysis dynamics which contains the quasi-variational principle of damping non-conservative system is studied. From the basic equation, variational integral method is applied to deduce the analysis dynamics which contains the quasi-Hamilton of damping non-conservative system and the other forms of expression are given. Generalized quasi-potential energy principle and generalized quasi-complementary energy principle which include two kinds of variables are established. Generalized quasi-potential energy principle and generalized quasi-complementary energy principle which include three kinds of variables are established. Generalized quasi-variational principle which reflects constitutive relations, geometric conditions and dynamic balance equation are also built up. Analysis dynamics which contains the quasi-Hamilton principle of damping non-conservative system is applied to research the two degree of freedom on the vibration equation. Meanwhile, the author also gets the decayed solution with the damper and the steady-state solution.Secondly, quasi-variational principle and generalized quasi-variational principle in elasto-dynamics is studied. Quasi-Hamilton, quasi-complementary Hamilton principle, the first and second types generalized quasi-variational principles with two kinds of variables, and generalized quasi-variational principle with three kinds of variables in non-conservative elasto-dynamics system are established.Thirdly, quasi-variational principle of single flexible body dynamics is studied. Variational methods are applied to deduce the problems of single flexible body dynamics. At the same time, quasi-Hamilton principle of single flexible body dynamics, the quasi-Hamilton principle which include two kinds of variables are established. The concept of quasi-stationary value condition of single flexible body dynamics is proposed. Through the deduction of the quasi-stationary value condition of quasi-variational principles, quasi-variational principles have been tested. Taking the interceptor as an example, the author has explained the physical meaning of the quasi-stationary value condition and prerequisite in the quasi-Hamilton principles of single flexible body dynamics with two kinds of variables. The quasi-stationary value condition of quasi-Hamilton principles are applied to establish the vertical vibration equation when the rockets launch vertically and the author also has illustrated the features of "one force for two effects" in a single flexible body dynamics.Forthly, quasi-variational principle of flexible multi-body system dynamics is also studied. Variational methods are applied to deduce the problems of flexible multi-body system dynamics. Three kinks of movement in annex are considered: extendable translation, rotation, extendable translation and rotation. Quasi-Hamilton principles of flexible multi-body system dynamics in the three kinds of movement in annex are deduced, the quasi-Hamilton principle which include two kinds of variables are established. The concept of quasi-stationary value condition of flexible multi-body system dynamics is proposed. Through the deduction of quasi-stationary value condition of quasi-variational principles, the author has tested the quasi-variational principles. Due to the application of quasi-stationary value condition of quasi-Hamilton principle in the extendable translation annex of flexible multi-body system dynamics, the author has established vibration differential equations of extendable translation flexible beam in space vehicles, and also has got round lateral vibration frequencies. The purpose is that the quasi-stationary value condition of quasi-Hamilton principle in rotation annex of flexible multi-body system dynamics is applied to establish the spacecraft rotation flexible beam vibration differential equations and to get round lateral vibration frequencies.