Generalized variational principles and nondifferentiable potentials in analytical mechanics

1984 ◽  
Vol 25 (3) ◽  
pp. 491-493 ◽  
Author(s):  
Helge‐Otmar May
Keyword(s):  
Variational Principles ◽  
Analytical Mechanics ◽  
Generalized Variational Principles

Generalized variational principles in the finite-element method.

AIAA Journal ◽  
1969 ◽  
Vol 7 (7) ◽  
pp. 1254-1260 ◽  
Author(s):  
B. E. GREENE ◽  
R. E. JONES ◽  
R. W. McLAY ◽  
D. R. STROME
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variational Principles ◽  
The Finite Element Method ◽  
Generalized Variational Principles ◽  
Element Method

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

2016 ◽  
Vol 40 (5) ◽  
pp. 859-870
Author(s):  
Yuhua Pan ◽  
Yuanfeng Wang ◽  
Li Su
Keyword(s):  
Variational Principle ◽  
Variational Principles ◽  
Dynamic Equations ◽  
Analytical Mechanics ◽  
Variational Integral ◽  
Physical Mechanisms ◽  
Standard Linear Solid Model ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Damped Systems

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.

Sign in / Sign up

Export Citation Format

Share Document