Complex eigenvalues of slotted arbitrary cylindrical cavities: Sound-soft elliptic cavity with variably placed longitudinal slit

2018 ◽  
Vol 144 (3) ◽  
pp. 1146-1153 ◽  
Author(s):  
Elena D. Vinogradova
Keyword(s):  
Complex Eigenvalues ◽  
Longitudinal Slit ◽  
Elliptic Cavity ◽  
Cylindrical Cavities

Eigenvalue Problem for the Second Order Differential Equation with Nonlocal

2006 ◽  
Vol 11 (1) ◽  
pp. 13-32 ◽  
Author(s):  
B. Bandyrskii ◽  
I. Lazurchak ◽  
V. Makarov ◽  
M. Sapagovas
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Variable Coefficient ◽  
Order Differential Equation ◽  
Integral Condition ◽  
Second Order ◽  
Computational Results ◽  
Discrete Method ◽  
Complex Eigenvalues ◽  
Nonlocal Integral Condition

The paper deals with numerical methods for eigenvalue problem for the second order ordinary differential operator with variable coefficient subject to nonlocal integral condition. FD-method (functional-discrete method) is derived and analyzed for calculating of eigenvalues, particulary complex eigenvalues. The convergence of FD-method is proved. Finally numerical procedures are suggested and computational results are schown.

Locating complex eigenvalues for analytical eddy-current models used to detect flaws

2019 ◽  
Vol 38 (6) ◽  
pp. 1800-1809
Author(s):  
Grzegorz Tytko ◽  
Łukasz Dawidowski
Keyword(s):  
Eddy Current ◽  
Design Methodology ◽  
Complex Function ◽  
Precise Determination ◽  
Argument Principle ◽  
Content Type ◽  
Conductive Material ◽  
Complex Roots ◽  
Complex Eigenvalues

Purpose Discrete eigenvalues occur in eddy current problems in which the solution domain was truncated on its edge. In case of conductive material with a hole, the eigenvalues are complex numbers. Their computation consists of finding complex roots of a complex function that satisfies the electromagnetic interface conditions. The purpose of this paper is to present a method of computing complex eigenvalues that are roots of such a function. Design/methodology/approach The proposed approach involves precise determination of regions in which the roots are found and applying sets of initial points, as well as the Cauchy argument principle to calculate them. Findings The elaborated algorithm was implemented in Matlab and the obtained results were verified using Newton’s method and the fsolve procedure. Both in the case of magnetic and nonmagnetic materials, such a solution was the only one that did not skip any of the eigenvalues, obtaining the results in the shortest time. Originality/value The paper presents a new effective method of locating complex eigenvalues for analytical solutions of eddy current problems containing a conductive material with a hole.

The Scattering of Shock Waves by Cylindrical Cavities in Liquids and Solids

1971 ◽  
Vol 38 (1) ◽  
pp. 190-196 ◽  
Author(s):  
E. Y. Harper
Keyword(s):  
Shock Wave ◽  
Asymptotic Expansion ◽  
Shielding Effect ◽  
Inviscid Fluid ◽  
Shadow Region ◽  
Shock Diffraction ◽  
Fluid Medium ◽  
Acoustic Shock Wave ◽  
Cylindrical Cavities ◽  
Logarithmic Decay

The scattering of a plane acoustic shock wave by a cylindrical cavity in an inviscid fluid medium is calculated numerically and compared with a recently obtained asymptotic expansion. In contrast to the scattering by a rigid cylinder, the cavity displays a distinctive shielding effect in the shadow region characterized by a peak exitation and an inverse logarithmic decay. Experimental results are presented which indicate a strong counterpart in plastic shock diffraction.

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