TRANSIENT RESPONSE OF ONE-DIMENSIONAL DISTRIBUTED SYSTEMS: A CLOSED FORM EIGENFUNCTION EXPANSION REALIZATION

1997 ◽  
Vol 208 (5) ◽  
pp. 763-776 ◽  
Author(s):  
B. Yang ◽  
X. Wu
Keyword(s):  
Distributed Systems ◽  
Closed Form ◽  
Transient Response ◽  
Eigenfunction Expansion ◽  
One Dimensional

scholarly journals Transient Solutions for One-Dimensional Problems With Strain Softening

1987 ◽  
Vol 54 (3) ◽  
pp. 513-518 ◽  
Author(s):  
T. Belytschko ◽  
Xiao-Jun Wang ◽  
Z. P. Bazant ◽  
Y. Hyun
Keyword(s):  
Strain Rate ◽  
Closed Form ◽  
Transient Response ◽  
Softening Point ◽  
Strain Softening ◽  
Stress Strain ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Transient Solutions

Closed-form solutions are presented for the transient response of rods in which strain softening occurs and the stress-strain laws exhibit nonvanishing stresses after the strain-softening regime. It is found that the appearance of any strain softening results in an infinite strain rate if the material is inviscid. For a stress-strain law with a monotonically decreasing stress the strains are infinite also. If the stress increases after the strain-softening portion, the strains remain finite and the strain-softening point moves through the rod.

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.

Closed-Form Transient Response of One-Dimensional Continua

1997 ◽  
Author(s):  
Xuqiang Wu ◽  
Bingen Yang
Keyword(s):  
Closed Form ◽  
Transient Response ◽  
Modal Expansion ◽  
One Dimensional ◽  
Circulatory Effects ◽  
Internal Forces ◽  
Space Formulation ◽  
Adjoint Operators ◽  
Eigenvalue Dependent Boundary Conditions ◽  
Spatial State

Abstract Exact and closed-form transient response of general one-dimensional distributed dynamic systems subject to arbitrary external, initial and boundary disturbances is determined. Non-self-adjoint operators characterizing damping, gyroscopic and circulatory effects, and eigenvalue-dependent boundary conditions are considered. Through introduction of augmented operators, a closed-form modal expansion of the displacement and internal forces of the distributed system is derived. The eigenfunction expansion is realized in a spatial state-space formulation, which systematically yields exact eigensolutions, eigenfunction normalization coefficients, and modal coordinates. The proposed method is illustrated on a cantilever beam with end mass, damper and spring.

scholarly journals TRANSIENT RESPONSE OF A DISTRIBUTED RLC INTERCONNECT BASED ON DIRECT POLE EXTRACTION

2009 ◽  
Vol 18 (07) ◽  
pp. 1263-1285 ◽  
Author(s):  
GUOQING CHEN ◽  
EBY G. FRIEDMAN
Keyword(s):  
Closed Form ◽  
Transient Response ◽  
Transmission Lines ◽  
Average Error ◽  
Proposed Model ◽  
Newton Raphson ◽  
On Chip ◽  
Interconnect Systems ◽  
Interconnect System ◽  
Raphson Method

With higher operating frequencies, transmission lines are required to model global on-chip interconnects. In this paper, an accurate and efficient solution for the transient response at the far end of a transmission line based on a direct pole extraction of the system is proposed. Closed form expressions of the poles are developed for two special interconnect systems: an RC interconnect and an RLC interconnect with zero driver resistance. By performing a system conversion, the poles of an interconnect system with general circuit parameters are solved. The Newton–Raphson method is used to further improve the accuracy of the poles. Based on these poles, closed form expressions for the step and ramp response are determined. Higher accuracy can be obtained with additional pairs of poles. The computational complexity of the model is proportional to the number of pole pairs. With two pairs of poles, the average error of the 50% delay is 1% as compared with Spectre simulations. With ten pairs of poles, the average error of the 10%-to-90% rise time and the overshoots is 2% and 1.9%, respectively. Frequency dependent effects are also successfully included in the proposed method and excellent match is observed between the proposed model and Spectre simulations.

System Properties of One-Dimensional Distributed Systems

1977 ◽  
Vol 99 (2) ◽  
pp. 85-90 ◽  
Author(s):  
L. S. Bonderson
Keyword(s):  
Distributed Systems ◽  
Sufficient Conditions ◽  
State Variables ◽  
One Dimensional ◽  
First Order ◽  
Lumped Element ◽  
Order Form ◽  
Power Product ◽  
System Properties ◽  
Necessary And Sufficient

The system properties of passivity, losslessness, and reciprocity are defined and their necessary and sufficient conditions are derived for a class of linear one-dimensional multipower distributed systems. The utilization of power product pairs as state variables and the representation of the dynamics in first-order form allows results completely analogous to those for lumped-element systems.

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