The Generalized Quasi-Variational Principles of NCS and Its Application in Mechanical Vibration

2007 ◽  
Author(s):  
Lifu Liang ◽  
Liming Dai ◽  
Qingyong Guo
Keyword(s):  
Phase Space ◽  
Variational Principles ◽  
Mechanical Vibration ◽  
Internal Force ◽  
Energy Principle ◽  
Force System ◽  
Conservative Systems ◽  
Generalized Displacements ◽  
Complementary Energy Principle ◽  
Two Kinds Of Variables

According to the corresponding relations between generalized forces and generalized displacements, the basic equations of elasto-dynamics in phase space are multiplied by corresponding virtual quantities, integrated and then added algebraically. By considering the character of fellow body and surface forces, the generalized quasi-variational principles of non-conservative systems are established in elasto-dynamics in phase space. By doing inverse Laplace transformation, the convolutional generalized quasi-variational principles of non-conservative systems of elasto-dynamics are established in original space. Applying the generalized quasi-complementary energy principle to the mechanical vibration problem of two kinds of variables, the authors of this paper present a calculation method for solving two kinds of variables simultaneously: the internal force and the displacement of a typical fellow force system.

Quasi-Variational Principles of Large Elastic Deformation in Non-Conservative Systems Based on Base Forces Theory and its Application

2008 ◽  
Author(s):  
Zongmin Liu ◽  
Lifu Liang ◽  
Tao Fan
Keyword(s):  
Elastic Deformation ◽  
Variational Principles ◽  
Analytic Solutions ◽  
Energy Principle ◽  
Conservative Systems ◽  
Generalized Displacements ◽  
Large Elastic Deformation ◽  
Base Forces ◽  
Basic Equations ◽  
Theory Framework

Based on base forces theory framework, the basic equations of time boundary value problem of large elastic deformation in non-conservative systems are defined. According to the corresponding relations between generalized forces and generalized displacements, the basic equations of elasto-dynamics are multiplied by corresponding virtual quantities, integrated and then added algebraically. Considering that both body forces and surface forces are fellow forces, the generalized Hamilton-type quasi-variational principles with three kinds of variables of large elastic deformation based on base forces theory in non-conservative systems are established. Then they are degenerated. Applying the Hamilton-type quasi-potential energy principle, analytic solutions of large deformation cantilever beam problem in non-conservative systems is obtained. Finally, some correlative problems are discussed.

Some Problems in the Theory of Nonconservative Elasticity

1986 ◽  
Vol 10 (1) ◽  
pp. 28-33
Author(s):  
Qi-hao Zhang ◽  
Dian-kui Liu
Keyword(s):  
Finite Element Analysis ◽  
Variational Principle ◽  
Variational Principles ◽  
Theory Of Elasticity ◽  
Complementary Energy ◽  
Element Analysis ◽  
Energy Principle ◽  
Nonconservative Systems ◽  
Potential Energy Principle ◽  
Complementary Energy Principle

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.

Hamilton Principle and Generalized Variational Principles of Linear Thermopiezoelectricity

2000 ◽  
Vol 68 (4) ◽  
pp. 666-667 ◽  
Author(s):  
Ji-Huan He
Keyword(s):  
Inverse Method ◽  
Variational Principles ◽  
Complementary Energy ◽  
Energy Principle ◽  
Hamilton Principle ◽  
Complementary Energy Principle ◽  
Generalized Variational Principles

Via the semi-inverse method, a family of various variational principles is established for thermopiezoelectricity, including a Hamilton principle and a minimum complementary energy principle.

Generalized phase space and conservative systems

2013 ◽  
Vol 88 (1) ◽  
pp. 457-459 ◽  
Author(s):  
B. I. Sadovnikov ◽  
N. G. Inozemtseva ◽  
E. E. Perepelkin
Keyword(s):  
Phase Space ◽  
Conservative Systems ◽  
Generalized Phase Space

CHAOTIC DIFFUSION IN MULTIDIMENSIONAL CONSERVATIVE MAPS

2012 ◽  
Vol 22 (10) ◽  
pp. 1250237 ◽  
Author(s):  
PABLO M. CINCOTTA ◽  
CLAUDIA M. GIORDANO
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Resonance Interaction ◽  
Chaotic Diffusion ◽  
Conservative Systems

In the present paper, we provide results and discussions concerning the processes that lead to local and global chaotic diffusion in the phase space of multidimensional conservative systems. We investigate and provide a measure of the extent of the domain over which diffusion may occur. All these issues are thoroughly discussed by dealing with a multidimensional conservative map that would be representative of the dynamics of a resonance interaction, which is an important mechanism in many dynamical systems.

Internal Force System and Current Secondary Moment Concept in Prestressed Structures

2014 ◽  
Vol 501-504 ◽  
pp. 611-619
Author(s):  
Jian Yu Zeng ◽  
Xiao Zu Su
Keyword(s):  
Prestressed Concrete ◽  
Internal Force ◽  
Computation Method ◽  
Basic Principles ◽  
Force System ◽  
Traditional Concept ◽  
Internal Forces ◽  
The Relationship ◽  
Theoretical Analyses ◽  
Prestressed Structures

The internal forces in a prestressed concrete structure are of special nature due to the existence of tendons. And flaws can be found in the traditional concept of secondary moment such that common computation method of secondary moment may produce unreasonable results. This article aims at getting a better understanding of internal forces in prestressed structures and solving the relevant problems. Starting from the basic principles of internal force analysis, a new system of internal forces is put forward by which the relationship between the compression resultant on concrete cross-section and the sectional internal forces is made clear. On this basis, a definition on the concept of current secondary moment (Mcs) is proposed and its superiority pointed out. Finally, theoretical analyses are carried out on the method for calculating Mcs in the posttentioned continuous beams with unbonded and bonded prestressing tendons.

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