Response Time Reduction for Tracking Systems with Complex Roots of Characteristic Equation by Use of Set-point Action

2000 ◽  
Vol 32 (2) ◽  
pp. 34-41
Author(s):  
Grigoriy F. Zaitsev ◽  
Nelya V. Gradoboyeva ◽  
Evgeniy V. Zakharenkov
2018 ◽  
Vol 6 (1) ◽  
pp. 6 ◽  
Author(s):  
Jana Scharfen ◽  
Diego Blum ◽  
Heinz Holling

2021 ◽  
Author(s):  
Kenya Suzuki ◽  
Kazushige Yonenaga ◽  
Noboru Takachio ◽  
Toshiki Tanaka ◽  
Osamu Moriwaki ◽  
...  

1996 ◽  
Vol 63 (2) ◽  
pp. 264-270 ◽  
Author(s):  
J. C. Sung ◽  
J. Y. Liou

The order of stress singularities at the tip of a crack terminating normally at an interface between two orthotropic media is analyzed. Characteristic equation in complex form for the power of singularity s, where 0 < Re{s} < 1, is first set up for two general anisotropic materials. Attention is then focused on the problem that is composed by two orthotropic media where one of them (say, material #2 ) the material principal axes are aligned while the other one (say, material #1) the principal axes can have an angle γ relative to the interface. For such a problem, a real form of the characteristic equation is obtained. The roots are functions of γ in general. Two real roots exist for most values of γ; however, there are possible ranges of γ that the complex roots will occur. The roots s are found to be independent of γ when material #1 has the property that δ(1) = 1. When γ = 0, two roots are always real. Furthermore, each of these two roots is associated with symmetric or antisymmetric mode and they become equal when Δ = 1. Many other features of the effects of the material parameters on the behaviors of the roots s are further investigated in the present work, where the six generalized Dundurs’ constants, expressed in terms of Krenk’s parameters, play an important role in the analysis.


2009 ◽  
Vol 41 (5) ◽  
pp. 448-466 ◽  
Author(s):  
Navneet Vidyarthi ◽  
Samir Elhedhli ◽  
Elizabeth Jewkes

2021 ◽  
pp. 87-97
Author(s):  
Birane Koundoul ◽  
Youssou Kasse ◽  
Fatoumata Balde ◽  
Bamba Gueye
Keyword(s):  

2017 ◽  
Vol 09 (01) ◽  
pp. 1750001 ◽  
Author(s):  
Chi-Wei Kuo ◽  
C. Steve Suh

Guided modes admissible in elastic hollow pipes are derived to establish their dispersion and attenuation characteristics in the presence of multi-layered viscoelastic coatings. Longitudinal waves propagating in the axial direction in response to displacement continuity boundary conditions signifying perfect interfacial bonds are evaluated against a baseline uncoated tubing. Viscoelastic bitumen and epoxy are coating materials applied to improve pipeline reliability. The impact of viscoelastic coating layers on wave dispersion and attenuation are investigated by incorporating complex material properties in the characteristic equation. The real and complex roots of the corresponding characteristic equation are determined, allowing the phase velocity and attenuation dispersion to be depicted as functions of the propagation frequency. The effects of varying attenuation parameter and coating thickness are also examined. Viscoelastic protective materials are found to have a substantial impact on the propagation and attenuation of longitudinal waveguide modes.


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