Quasi-variational Principle Research Articles

ESTABLISHMENT OF DYNAMIC EQUATIONS FOR DAMPED SYSTEMS BASED ON QUASI-VARIATIONAL PRINCIPLES

In this paper, quasi-variational principles for non-conservative damped systems are studied. A Hamiltontype quasi-variational principle for non-conservative systems in analytical mechanics and a quasi-variational principle of potential energy in non-conservative elastodynamics systems are proposed in simplified forms respectively, by using the direct variational integral method. On the basis of the standard linear solid model for viscoelastic materials, the dynamic equations of exponentially damped systems are established through the proposed quasi-variational principles. A distinction between the internal damping described by exponential damping and the external damping described by viscous one in a vibrating structure is according to different physical mechanisms, which gives some indication of the correct mechanism of damping.

Coupling Vibration of Tapered Rod

In rod's free vibration, its easy to obtain normal modes. However, if there is rigid body displacement, the problem will be much more complex. To solve these kinds of problems, single flexible body dynamics is needed. As the first part of the paper, considering rods rigid body displacement, the free vibration of tapered rod is discussed. By solving partial differential equation of rods free vibration, normal frequencies of tapered rod are obtained. As the second part of the paper, coupling vibration is discussed, in which process quasi-variational principle as the most important tool is used. Finally, first-order frequency of coupled vibration of rod is represented.

Gurtin-Type Quasi-Variational Principle of Buried Pipelines Dynamics

Because earthquakes may cause severe damage to buried pipelines, it is important to study dynamic response of buried pipelines. For dynamic response problem of buried pipelines, variational method is the suitable method. In the paper, Gurtin-type quasi-variational principle of buried pipelines dynamics is established by convolutional variational integral method, which is theoretical foundation of finite element method for solving buried pipelines dynamics problems.

Non-linear and non-conservative quasi-variational principle of flexible body dynamics and application in spacecraft dynamics

The law of conservation of energy is one of the most fundamental laws of nature. According to the law of the conservation of energy, the non-linear and non-conservative quasi-variational principle of flexible body dynamics is established. The physical meaning of the quasi-stationary value conditions has been explained in non-linear and non-conservative flexible body dynamics. In the case study, the application in spacecraft dynamics is researched.

Rigid-Elastic Coupled Dynamics and its Application

According to energy conservation law, the functional of quasi-variational principle of rigid-elastic coupled dynamics is established. Quasi-stationary value conditions of quasi-variational principle of rigid-elastic coupled dynamics are derived. The governing equations of rigid-elastic coupled dynamics are obtained. As an application of rigid-elastic coupled dynamics, an approach of coupled vibration mode determined of unrestrained beam is established. The coupled vibration mode and coupled frequency are studied by the approach.

Gurtin-Type Quasi-Variational Principle of Intelligent Structure Based on Nonlinear Theory

Intelligent structure is consistently identified as one of techniques getting much attention in the 21 century. With the research and development of intelligent material with large strain, high strength and high performance, the study on the non-linear theory of intelligent structure is a hot spot for research in the future. Based on nonlinear theory, Gurtin-type quasi-variational principle of nonlinear intelligent structure is established in this paper. Finally, some correlative problems are discussed.

Quasi-variational principles of single flexible body dynamics and their applications

The reasons for studying single flexible body dynamics are that on one hand, it is the basis of flexible multi-body dynamics. If the theory of the single flexible body dynamics has been deeply studied, the theory of flexible multi-body dynamics will be researched easily. On the other hand, it has its unique and important applications. Quasi-variational principle of non-conservative single flexible body dynamics is established under the cross-link of particle rigid body mechanics and deformable body mechanics. Taking the interceptor as an example, this paper has explained the physical meaning of the quasi-stationary value condition of the quasi-variational principle in non-conservative single flexible body dynamics. Taking the launch of rocket as an example, it has illustrated the features of “one force for two effects” in a single flexible body dynamics. With an example of the extending flexible beam coupled with the spacecraft attitude, it has shown the transition from the single flexible body dynamics to the flexible multi-body dynamics. Finally, a number of related problems are discussed.

Quasi-variational principle for the vortex-potential function of rotational flow in three-dimension pipe

The variational analysis of the Pseudo-potential function-vortex-potential function model, a new mathematical model, was developed and by which the flow field with transonic speed and curl was decided, and different sorts of the variational principle for vortex potential function were established by transforming the original equation for vortex-function, the boundary conditions for vortex-potential function was raised.

Quasi-variational principle for interface kinematics

A quasi-variational principle has been formulated for the interface motion during phase transition. We use two types of interface description: a parametric definition as a function of the arc length and the time and a new definition of the complete interface evolution through a field of the unit tangent vector of the interface. In the second case the proposed quasi-variational principle can be interpreted as the Prigogine principle of the minimum entropy production. The steady rotation of the spiral interface has been considered as an example of application of the direct variational principle.

Some Problems in the Theory of Nonconservative Elasticity

This study develops the general quasi-variational principles for nonconservative problems in the theory of elasticity such as the quasi-potential energy principle, the quasi-complementary energy principle, the generalized quasi-variational principle and quasi-Hamilton principle. The application of these quasi-variational principles to finite element analysis is also discussed and illustrated with some examples. The total variational principle for nonconservative systems of two variables is also studied.