Comportement dynamique des lignes aériennes de transport d'électricité dû aux bris de câbles. II. Problèmes numériques associés à la modélisation mathématique

1989 ◽  
Vol 16 (3) ◽  
pp. 354-374 ◽  
Author(s):  
Ghyslaine McClure ◽  
René Tinawi
Keyword(s):  
Transmission Lines ◽  
Nonlinear Dynamic ◽  
Numerical Models ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Analysis ◽  
Small Scale ◽  
Convergence Criterion ◽  
Direct Integration ◽  
Time Step ◽  
Integration Methods

The evaluation of the response of an aerial power line section subjected to cable breakage is a complex dynamic problem in which geometric nonlinearities are important. The solution of the equations of motion of the model calls for direct integration methods for which the stability and behavior, in nonlinear situations, are difficult to predict. Seven numerical models are analyzed with the Wilson-θ and the Newmark-β algorithms and results are compared with those of small-scale tests of the American Electric Power Research Institute. This comparison emphasizes the importance of the high frequency modes in the response and the artificial damping induced by the Wilson-θ method. This method allows up to three times the time increment required by the trapezoidal rule that does not filter the contribution of higher frequencies but is limited by a convergence criterion. Many observations made in this particular study are also applicable to multi-degree-of-freedom nonlinear dynamic problems using direct time-step integration. Key words: Nonlinear dynamic analysis, direct integration methods, aerial electric transmission lines, cable breakage simulation.

scholarly journals Wavelet-based Decomposition of Ground Acceleration for Efficient Calculation of Seismic Response in Elastoplastic Structures

2020 ◽  
Author(s):  
Reza Kamgar ◽  
Noorollah Majidi ◽  
Ali Heidari
Keyword(s):  
Wavelet Transform ◽  
Dynamic Analysis ◽  
Continuous Wavelet Transform ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Continuous Wavelet ◽  
Frequency Content ◽  
Time Step ◽  
Integration Schemes ◽  
The Waves

The nonlinear dynamic analysis provides a more accurate simulation of the structural behavior against earthquakes. On the other hand, this analysis method is time-consuming since the time-step integration schemes are used to calculate the responses of the structure. Wavelet transform is also considered as one of the strong computing tools in studying the properties of the waves. The continuous wavelet transform is a time-frequency study and examines the frequency content of the waves while, the discrete wavelet transform is used to reduce sampling data and also to eliminate the noise of the waves. In this paper, the discrete and continuous wavelet transforms are used to reduce the wave sampling and therefore to reduce the required time for analysis. In this regard, eight near- and far- field earthquakes are studied. The frequency content of the earthquake is investigated by the Fourier spectrum and the continuous wavelet transform. The results show that the first five frequencies for the main earthquakes are similar to those values of earthquakes obtained by wavelet transform. Besides, it is shown that using wavelet transform for the main and decomposed earthquakes indicates that the duration of strong ground motion and the time of dominant frequency occur approximately in the same domain. Finally, it is concluded that the required calculation time reduces to about 80 % with an error less than 6 % when the main earthquake is decomposed by wavelet transform and the approximation waves are used in the nonlinear dynamic analysis.

Masonry Spires: 3D Models to Understand their Seismic Vulnerability

2019 ◽  
Vol 817 ◽  
pp. 317-324
Author(s):  
Elena Zanazzi ◽  
Eva Coïsson ◽  
Daniele Ferretti ◽  
Alessio Lorenzelli
Keyword(s):  
Dynamic Analysis ◽  
Seismic Vulnerability ◽  
Linear Time ◽  
Numerical Models ◽  
Nonlinear Dynamic Analysis ◽  
Nonlinear Static Analysis ◽  
Time Step ◽  
Epicentral Area ◽  
Finite Element Software ◽  
Bell Tower

The May 2012 Emilia earthquake has highlighted the important vulnerability of masonry spires at the top of bell towers of churches. Indeed, almost half of those in the epicentral area have shown a typical damage mechanism consisting in the shear sliding and overturning of the top of the spire. Given the recurrence of this phenomenon, the present paper tries to provide a contribution to the comprehension of the seismic behaviour of the spires through the numerical analysis of three case studies. In particular, the work analyses the spires of the churches of San Nicola di Bari in Cortile, near Carpi (MO); Sant'Egidio in Cavezzo (MO), and Sant'Agostino in Sant'Agostino (FE). The numerical models of these masonry structures were made using Abaqus Finite Element software. After the creation of the three-dimensional geometric models, a first nonlinear static analysis of the entire bell tower was performed adopting for masonry the Abaqus “concrete damage plasticity model”. Once the stability of the bell tower was verified for dead loads, the non-linear time-step dynamic analysis was faced. This required the definition of the seismic input at the base of the tower, through the accelerograms recorded by the closest stations. The nonlinear dynamic analysis of the global model of the bell tower provided the floor response spectra at the base and at the top of the spire. Indeed the comparison between spectra at the ground and at the top highlights the filter effect of the stem of the bell tower with a significant increase in accelerations at the top. This effect may explain the widespread damage observed at the top of the spires. Eventually, three different non-invasive intervention techniques were proposed in compliance with the principles of restoration and were modelled to compare their behaviour.

The Effects of Bearing Stiffness on Nonlinear Dynamic Behaviors of Multi-Mesh Gear Train

2012 ◽  
Author(s):  
T. N. Shiau ◽  
T. H. Young ◽  
J. R. Chang ◽  
K. H. Huang ◽  
C. R. Wang
Keyword(s):  
Chaotic Motion ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Analysis ◽  
Gear Train ◽  
Time Varying ◽  
Kutta Method ◽  
Dynamic Behaviors ◽  
Runge Kutta Method ◽  
Bearing Stiffness

In this study, the nonlinear dynamic analysis of the multi-mesh gear train with elastic bearing effect is investigated. The gear system includes the three rigid shafts, two gear pairs and elastic bearings. The stiffness and damper coefficient of elastic bearing are considered. The equations of motion of nonlinear time-varying system are derived using Lagrangian approach. The Runge-Kutta Method is employed to determine the system dynamic behaviors including the bifurcation and chaotic motion. The results show that the periodic motion, quasi-periodical motion and chaos can be excited with the elastic bearing effect. Especially, the results also indicate the dynamic response will go from periodic to quasi-periodical before the chaotic motion when the bearing stiffness is increased.

scholarly journals Dynamics and Control of a Tethered Satellite System Based on the SDRE Method

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Yong-Lin Kuo
Keyword(s):  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Analysis ◽  
Satellite System ◽  
Convergence Time ◽  
Tethered Satellite ◽  
Modeling And Control ◽  
Tethered Satellite System ◽  
Dynamics And Control ◽  
And Control

This paper presents the nonlinear dynamic modeling and control of a tethered satellite system (TSS), and the control strategy is based on the state-dependent Riccati equation (SDRE). The TSS is modeled by a two-piece dumbbell model, which leads to a set of five nonlinear coupled ordinary differential equations. Two sets of equations of motion are proposed, which are based on the first satellite and the mass center of the TSS. There are two reasons to formulate the two sets of equations. One is to facilitate their mutual comparison due to the complex formulations. The other is to provide them for different application situations. Based on the proposed models, the nonlinear dynamic analysis is performed by numerical simulations. Besides, to reduce the convergence time of the librations of the TSS, the SDRE control with a prescribed degree of stability is developed, and the illustrative examples validate the proposed approach.

Comportement dynamique des lignes aériennes de transport d'électricité dû aux bris de câbles. I. Modélisation mathématique

1989 ◽  
Vol 16 (3) ◽  
pp. 335-353 ◽  
Author(s):  
Ghyslaine McClure ◽  
René Tinawi
Keyword(s):  
Mathematical Model ◽  
Dynamic Analysis ◽  
Transmission Lines ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Physical Models ◽  
Element Analysis ◽  
Electric Transmission ◽  
Electric Transmission Lines ◽  
Supporting Structures

This paper presents a mathematical model for the nonlinear dynamic analysis of aerial electric transmission lines subjected to conductor breakage. The model uses existing finite elements and validated numerical techniques available in most commercial programs capable of handling nonlinear dynamic analysis. ADINA is used in this study. In comparison with other models, the novel approach presented here focusses on the discretization of the conductors as well as the supporting structures, specially near the breakage point. Dynamic interactions between all the structural components are therefore considered and comparisons with simpler models emphasize the importance of these interactions, the effects of geometric nonlinearities present in the conductors and in the supporting structures, and the contribution of higher modes.The mathematical model is validated with 7 of 56 tests conducted on reduced-scale physical models, reported in work done for the American Electric Power Research Institute.The results of the present study are very encouraging for designers interested in validating their design criteria for longitudinal dynamic loads by use of existing nonlinear dynamic finite element analysis packages. Key words: Nonlinear dynamic analysis, electric transmission lines, conductor breakage simulation.

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