On Analysis of Cable Network Vibrations Using Galerkin’s Method

1970 ◽  
Vol 37 (3) ◽  
pp. 606-611 ◽  
Author(s):  
A. I. Soler ◽  
H. Afshari
Keyword(s):  
Field Equation ◽  
System Response ◽  
Galerkin’S Method ◽  
Small Oscillations ◽  
Dirac Delta ◽  
Galerkin's Method ◽  
Cable Network ◽  
Cable Networks ◽  
Delta Functions ◽  
Vibrating Membrane

Built-up systems consisting of rectangular cable networks covered by or embedded in a membrane matrix are considered; small oscillations about an initially flat, pretensioned state are studied. By employing Dirac delta functions to aid in representation of preload and weight distribution acting on the system, the system response is shown to be given by a generalized version of the equation for a vibrating membrane. A solution of the field equation is effected using Galerkin’s method and approximating functions are suggested for a wide class of boundary shapes. As an illustration of the method a rectangular boundary shape is considered and results are obtained for typical values of preload, cable distribution, etc. Results are compared with previous analyses of similar systems, and advantages of the present approach are discussed.

Variational Modal Identification of Conservative Nongyroscopic Systems

1989 ◽  
Vol 111 (2) ◽  
pp. 160-171 ◽  
Author(s):  
L. Silverberg ◽  
S. Kang
Keyword(s):  
Longitudinal Vibration ◽  
Modal Identification ◽  
System Response ◽  
Bending Vibration ◽  
Free System ◽  
Dirac Delta ◽  
Vibration Problem ◽  
Identification Method ◽  
Delta Functions ◽  
Admissible Functions

A new modal identification method for Conservative Nongyroscopic Systems is proposed. The modal identification method is formulated as a variational problem in which stationary values of a functional quotient are sought. The computation of the functional quotient is carried out using a set of admissible functions defined over the spatial domain of the system. Measurements of the free system response at discrete points are carried out using any combination of displacements, velocities, and/or accelerations. Three types of admissible functions have been considered—global functions, spatial Dirac-delta functions, and finite element interpolation functions. The variational modal identification method is applied to a pure bending vibration problem, to a pure longitudinal vibration problem, and to a combined bending and longitudinal vibration problem. The effectiveness of the variational modal identification method using different sets of admissible functions is examined.

Steady-state modelling method for matrix-reactance frequency converter with boost topology

2011 ◽  
Vol 60 (2) ◽  
pp. 137-148
Author(s):  
Igor Korotyeyev ◽  
Beata Zięba
Keyword(s):  
Fourier Series ◽  
Steady State ◽  
Differential Equations ◽  
Numerical Method ◽  
Frequency Converter ◽  
Double Fourier Series ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Modelling Method ◽  
Three Phase

Steady-state modelling method for matrix-reactance frequency converter with boost topologyThis paper presents a method intended for calculation of steady-state processes in AC/AC three-phase converters that are described by nonstationary periodical differential equations. The method is based on the extension of nonstationary differential equations and the use of Galerkin's method. The results of calculations are presented in the form of a double Fourier series. As an example, a three-phase matrix-reactance frequency converter (MRFC) with boost topology is considered and the results of computation are compared with a numerical method.

Galerkin’s method revisited and corrected in the problem of Jaworski and Dowell

2021 ◽  
Vol 155 ◽  
pp. 107604
Author(s):  
Isaac Elishakoff ◽  
Marco Amato ◽  
Alessandro Marzani
Keyword(s):  
Galerkin’S Method ◽  
Galerkin's Method

scholarly journals Impact of Cross-Tie Properties on the Modal Behavior of Cable Networks on Cable-Stayed Bridges

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Javaid Ahmad ◽  
Shaohong Cheng ◽  
Faouzi Ghrib
Keyword(s):  
Analytical Model ◽  
Design Parameters ◽  
Reference Base ◽  
Cable Network ◽  
Cable Networks ◽  
Modal Behavior ◽  
Stiffness And Damping ◽  
Main Cables ◽  
The Impact ◽  
Selection Of

Dynamic behaviour of cable networks is highly dependent on the installation location, stiffness, and damping of cross-ties. Thus, these are the important design parameters for a cable network. While the effects of the former two on the network response have been investigated to some extent in the past, the impact of cross-tie damping has rarely been addressed. To comprehend our knowledge of mechanics associated with cable networks, in the current study, an analytical model of a cable network will be proposed by taking into account both cross-tie stiffness and damping. In addition, the damping property of main cables in the network will also be considered in the formulation. This would allow exploring not only the effectiveness of a cross-tie design on enhancing the in-plane stiffness of a constituted cable network, but also its energy dissipation capacity. The proposed analytical model will be applied to networks with different configurations. The influence of cross-tie stiffness and damping on the modal response of various types of networks will be investigated by using the corresponding undamped rigid cross-tie network as a reference base. Results will provide valuable information on the selection of cross-tie properties to achieve more effective cable vibration control.

Dirac Delta Functions in the Laplace‐Type Expansion of rnYlm(θ, φ)

1969 ◽  
Vol 51 (6) ◽  
pp. 2359-2362 ◽  
Author(s):  
Kenneth G. Kay ◽  
H. David Todd ◽  
Harris J. Silverstone
Keyword(s):  
Dirac Delta ◽  
Delta Functions ◽  
Laplace Type
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