Closed-Form Transient Response of Distributed Damped Systems, Part I: Modal Analysis and Green’s Function Formula

1996 ◽  
Vol 63 (4) ◽  
pp. 997-1003 ◽  
Author(s):  
Bingen Yang
Keyword(s):  
Green’S Function ◽  
Modal Analysis ◽  
Closed Form ◽  
Distributed System ◽  
Transient Response ◽  
Green's Function ◽  
Eigenfunction Expansion ◽  
Distributed Parameter ◽  
Modal Expansion ◽  
Damped Systems

An analytical method is developed for closed-form estimation of the transient response of complex distributed parameter systems that are nonproportionally damped, and subject to arbitrary external, initial, and boundary excitations. A new modal analysis leads to the Green’s function formula for the distributed system and an eigenfunction expansion of the system Green’s function. The legitimacy of the modal expansion is also shown.

Distributed System Identification: A Green’s Function Approach

1976 ◽  
Vol 98 (2) ◽  
pp. 146-151 ◽  
Author(s):  
G. R. Spalding
Keyword(s):  
Green’S Function ◽  
Distributed System ◽  
Green's Function ◽  
Function Method ◽  
System Response ◽  
Distributed Parameter ◽  
Discrete Form ◽  
Modeling Process ◽  
Spatial Coordinates ◽  
Spatial Operators

A method is presented for identifying linear distributed parameter systems. Emphasis is placed on identification as a function of spatial coordinates by considering time-transformed, noise-free systems. Measurements of system response are combined with the Green’s function method of analysis to obtain integral equations that can be solved for unknown spatial operators or coefficients. A discrete form of the theory is developed, utilizing Chebyshev polynomials. This allows prior estimates to be used to determine the number and location of spatial measurements. Where estimates are of sufficient order, the modeling process is exact.

Modal Analysis of Multi-Stepped Distributed-Parameter Rotor-Bearing Systems Using Exact Dynamic Elements

2001 ◽  
Vol 123 (3) ◽  
pp. 401-403 ◽  
Author(s):  
Seong-Wook Hong ◽  
Jong-Heuck Park
Keyword(s):  
Modal Analysis ◽  
Closed Form ◽  
Complete Analysis ◽  
Distributed Parameter ◽  
Analysis Method ◽  
Closed Form Solutions ◽  
Analysis Scheme ◽  
Rotor Bearing ◽  
The Matrix ◽  
Transcendental Functions

Although the exact dynamic elements have been suggested by the authors [1] and proved to be useful for the dynamic analysis of distributed-parameter rotor-bearing systems, difficulty remains in computation because of the presence of transcendental functions in the matrix. This paper proposes a complete analysis scheme for the exact dynamic elements, a generalized modal analysis method, to obtain exact and closed form solutions of time and frequency domain responses for multi-stepped distributed-parameter rotor-bearing systems. A numerical example is provided for validating the proposed method.

Coulomb Green's Function in Closed Form

1963 ◽  
Vol 10 (11) ◽  
pp. 469-470 ◽  
Author(s):  
Levere Hostler ◽  
R. H. Pratt
Keyword(s):  
Green’S Function ◽  
Closed Form ◽  
Green's Function ◽  
Coulomb Green’S Function
Sign in / Sign up

Export Citation Format

Share Document