整合連體力學與熱動力學之變分原理(1/3)
Date Issued
2004-07-31
Date
2004-07-31
Author(s)
鮑亦興
DOI
922212E002066
Abstract
In dealing with the mechanics of material bodies modeled by
particles, rigid body, or deformable body subject to various types of
constraint, variational principles can usually provide a suitable path to
obtain the solutions. The main objective of this project is to seek
additional applications and possible extensions on the basis of the
Principle of Virtual Power, and to explore whether the proposed principle
can be unified with the law of thermodynamics to form a unified
variational principle. After nearly one-year term of endeavor, we are able
to obtain the desired Principle by choosing the velocity and the velocity
gradient as fundamental variables in mechanics, and the entropy and the
hear flux as the fundamental quantities in theomodynamics. The Principle
indeed unify the theory of thermodynamics and continuum mechanics,
from which a variational equation can be established. The Cauchy’s laws
of linear and angular momentum and the newly developed variational
constitutive law are then deduced. By selecting appropriate internal
energy function and dissipating function, we could derive the constitutive
equations for elastic body or viscous fluid in mechanics, and Fourier law
and Maxwell-Catteneo Equation, which are treated as the constitutive
equation in thermodynamics. See Part I of this report for more detailed.
On the other hand, to perform tracking control, we divide the system
coordinates into two sets: privileged coordinates and non-privileged
coordinates. While all the coordinates have their desired trajectory, two
control loops are designed. The inner loop drives the privileged
coordinates to their desired value. The relations between privileged
coordinates and non-privileged coordinates are then used to change the
desired values of privileged coordinates so that the non-privileged ones
can be tracked. We apply the strategy to the trajectory tracking control of
a three-wheeled vehicle and the performance is quite well. The results are
shown in Part II of this report.
Subjects
Continuum Mechanics
Thermodynamics
Principle of Virtual
Power
Power
Privileged Coordinates
Tracking Control
Publisher
臺北市：國立臺灣大學應用力學研究所
Type
report
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