Exact solution to diffraction on a grating with parallelogramic grooves by the true modal method

2006 ◽  
Author(s):  
M. Foresti ◽  
A. V. Tishchenko
Keyword(s):  
Exact Solution ◽  
Modal Method

Modal Analysis to Accommodate Slap in Linear Structures

2005 ◽  
Vol 128 (3) ◽  
pp. 303-317 ◽  
Author(s):  
Daniel J. Segalman ◽  
Anthony M. Roy ◽  
Michael J. Starr
Keyword(s):  
Exact Solution ◽  
Impulse Approximation ◽  
Linear Analysis ◽  
Momentum Balance ◽  
Linear Structures ◽  
Time Intervals ◽  
Piecewise Constant ◽  
Generalized Momentum ◽  
Novel Method ◽  
Modal Method

The generalized momentum balance (GMB) methods, explored chiefly by Shabana and his co-workers, treat slap or collision in linear structures as sequences of impulses, thereby maintaining the linearity of the structures throughout. Further, such linear analysis is facilitated by modal representation of the structures. These methods are discussed here and extended. Simulations on a simple two-rod problem demonstrate how this modal impulse approximation affects the system both directly after each impulse as well as over the entire collision. Furthermore, these simulations illustrate how the GMB results differ from the exact solution and how mitigation of these artifacts is achieved. Another modal method discussed in this paper is the idea of imposing piecewise constant forces over short, yet finite, time intervals during contact. The derivation of this method is substantially different than that of the GMB method, yet the numerical results show similar behavior, adding credence to both models. Finally, a novel method combining these two approaches is introduced. The new method produces physically reasonable results that are numerically very close to the exact solution of the collision of two rods. This approach avoids most of the nonphysical, numerical artifacts of interpenetration or chatter present in the first two methods.

Exact solution of a four-site crystal model for an intermediate-valence system

1986 ◽  
Vol 47 (6) ◽  
pp. 1029-1034 ◽  
Author(s):  
J.C. Parlebas ◽  
R.H. Victora ◽  
L.M. Falicov
Keyword(s):  
Exact Solution ◽  
Intermediate Valence ◽  
Crystal Model

APPLYING THE MODAL METHOD TO THERMAL MODELLING

1990 ◽  
Author(s):  
G. Lefebvre ◽  
A. Neveu ◽  
K. el Khoury ◽  
J.J. Saigon
Keyword(s):  
Thermal Modelling ◽  
Modal Method
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