Quasi-variational Principles Of Initial Value Problems In Flexible Body Dynamics And Their Applications

Flexible body dynamics mainly studies the reciprocity effect or coupling of the deformation and the integral rigid movement of an object, as well as the special dynamic effects resulting from the coupling. The primary characteristics of flexible body dynamics are the concurrence and coupling of the controlled rigid displacement and the elastic vibrational displacement. It is widely applied in the important engineering fields such as spacecraft, robot (mechanical arm), high-speed precision mechanism and so on.The variational method and variational integral convolution method are adopted to study the quasi-variational principles of the initial value problems in flexible body dynamics and their applications, and the analytic discussion is carried out emphatically. The aim is to grasp the multiple subjects cross characteristics of flexible body dynamics profoundly and forecast the global dynamic phenomena of the system.First of all, the quasi-variational principles and the generalized quasi-variational principles of the initial value problems in non-conservative analytical mechanics are studied. The quasi-variational principles with one kind and the two kinds of variables, and the generalized quasi-variational principles with two and three kinds of variables of the initial value problems in non-conservative analytical mechanics are established. The quasi-stationary value conditions of the quasi-variational principles with one kind and two kinds of variables and the generalized quasi-variational principles with two and three kinds of variables are deduced. By use of the quasi-variational principles of the initial value problems in non-conservative analytical mechanics, the single and two degrees of freedom forced vibration systems with viscous damping are studied, and the vibration equations of the systems are obtained.Secondly, the quasi-variational principles and the generalized quasi-variational principles of the initial value problems in rigid body dynamics are studied. The quasi-variational principles with one kind and two kinds of variables and the generalized quasi-variational principles with two kinds of variables of the initial value problems of rigid dynamics in original space and phase space are established. The quasi-stationary value condition of the quasi-variational principles with one kind and two kinds of variables and the generalized quasi-variational principles with two kinds of variables are deduced. Examples are given to show that problems in rigid body dynamics are studied with the variational principles can add the non-holonomic constraints and controlled constraints to the rigid body dynamics systems conveniently, which embodies the superiority to the establishment of the quasi-variational principles of the initial value problems in rigid body dynamics.Thirdly, the quasi-variational principles and the generalized quasi-variational principles of the initial value problems in non-conservative elastodynamics are studied. The quasi-variational principles with one kind and two kinds of variables and the generalized quasi-variational principles with two and three kinds of variables of the initial value problems in non-conservative elastodynamics in original space and phase space are established. By the application of the generalized quasi-variational principles of the initial value problems in non-conservative elastodynamics, the dynamic characteristics for the extensional parts of the aircrafts wing surfaces are studied, and the calculation methods are given to solve the system internal force and deformation with two kinds of variables simultaneously.Fourthly, the quasi-variational principles of the initial value problems in single flexible body dynamics are studied. Based on the comparative analysis of the quasi-variational principles of the initial value problems in non-conservative analytical mechanics, rigid body dynamics and non-conservative elastodynamics, two kinds of the quasi-variational principles of the initial value problems in single flexible body dynamics with one kind and two kinds of variables are set up, and the quasi-stationary value conditions of the quasi-variational principles with one kind and two kinds of variables are deduced. By the application of the quasi-stationary value condition of the quasi-variational principles of the initial value problems in single flexible body dynamics, the dynamic equations of the interceptor launching part, maneuvering phase and under the conditions of ignoring the deformation speed are established separately. By using the quasi-variational principles of the initial value problems in single flexible body dynamics, the coupling vibration mode problems of the unbounded beams are solved properly.At last, the quasi-variational principles of the initial value problems in flexible multibody system dynamics are studied tentatively. The most common flexible multibody systems are flexible multibody cluster system and flexible multibody train system, and the former is the studied in this dissertation. The quasi-variational principles of the initial value problems in flexible multibody system dynamics with attachment that can move translationally, rotationally, and both translationally and rotationally are established separately. The quasi-stationary value condition of the quasi-variational principle is deduced, which verifies that the variational integral operation is the inverse operation of the variational differential operation. The differential kinematic equation of the aircrafts with extensional flexible beam structure is established based on the quasi-variational principles and their quasi-stationary value conditions of the initial value problems in flexible multibody system dynamics.