The Modal Method

2018 ◽  
pp. 139-196
Author(s):  
Andrei V. Lavrinenko ◽  
Jesper Lægsgaard ◽  
Niels Gregersen ◽  
Frank Schmidt ◽  
Thomas Søndergaard
Keyword(s):  
Modal Method

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

A new modal method for the grating diffraction

Optik ◽  
2021 ◽  
Vol 230 ◽  
pp. 166315
Author(s):  
Li JianLong
Keyword(s):  
Grating Diffraction ◽  
Modal Method

Advances In The Modeling And Dynamic Simulation of Reeving Systems Using The Arbitrary Lagrangian-Eulerian Modal Method

2021 ◽  
Author(s):  
José L. Escalona ◽  
Narges Mohammadi
Keyword(s):  
Finite Elements ◽  
Axial Force ◽  
Axial Direction ◽  
Rotary Inertia ◽  
Arbitrary Lagrangian Eulerian ◽  
Original Formulation ◽  
Absolute Position ◽  
Axial Forces ◽  
Modal Coordinates ◽  
Modal Method

Abstract This paper presents new advances in the arbitrary Lagrangian-Eulerian modal method (ALEM) recently developed for the systematic simulation of the dynamics of general reeving systems. These advances are related to a more convenient model of the sheaves dynamics and the use of axial deformation modes to account for non-constant axial forces within the finite elements. Regarding the sheaves dynamics, the original formulation uses kinematic constraints to account for the torque transmission at the sheaves by neglecting the rotary inertia. One of the advances described in this paper is the use of the rotation angles of the sheaves as generalized coordinates together with the rope-to-sheave no-slip assumption as linear constraint equations. This modeling option guarantees the exact torque balance the sheave without including any non-linear kinematic constraint. Numerical results show the influence in the system dynamics of the sheave rotary inertia. Regarding the axial forces within the finite elements, the original formulation uses a combination of absolute position coordinates and transverse local modal coordinates to account for the rope absolute position and deformation shape. The axial force, which only depends on the absolute position coordinates, is constant along the element because linear shape functions are assumed to describe the axial displacements. For reeving systems with very long rope spans, as the elevators of high buildings, the constant axial force is inaccurate because the weight of the ropes becomes important and the axial force varies approximately linearly within the rope free span. To account for space-varying axial forces, this paper also introduces modal coordinates in the axial direction. Numerical results show that a set of three modal coordinates in the axial direction is enough to simulate linearly varying axial forces.

Voltage Stability Criterion in New and Key Nodes and Regional Research

2012 ◽  
Vol 450-451 ◽  
pp. 582-585
Author(s):  
Qing En Li ◽  
Rui Ren ◽  
Jian Qiu
Keyword(s):  
System Theory ◽  
Stability Criterion ◽  
Voltage Stability ◽  
Power Network ◽  
Regional Power ◽  
Regional Research ◽  
Rational Analysis ◽  
Key Nodes ◽  
Roll Out ◽  
Modal Method

In recent years， as the load increasing gradually，problems in voltage stability of regional power network which is the terminal of power grid is serious. From the voltage stability machine rational analysis to roll out small interfering voltage stability criterion of new, and the modal method is used to determine the key nodes and areas of the system theory basis.

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