RESONANCE AND THE LATE COEFFICIENTS IN THE SCATTERED FIELD OF A DIELECTRIC CIRCULAR CYLINDER

2006 ◽  
Vol 04 (04) ◽  
pp. 311-333 ◽  
Author(s):  
T. M. DUNSTER ◽  
MATTHEW YEDLIN ◽  
KIM LAM
Keyword(s):  
Scattered Field ◽  
Bessel Functions ◽  
Asymptotic Form ◽  
Regge Pole ◽  
Relative Dielectric Constant ◽  
Resonant Mode ◽  
Entire Region ◽  
Modal Expansion ◽  
Region Exterior ◽  
Modal Term

The classical modal expansion for the scattered field of a plane wave from a circular dielectric cylinder is studied. A new uniform asymptotic approximation is presented for the late coefficients in this expansion, in the case of a fixed relative dielectric constant εr, both real and complex. These new approximations for the mode values are not based on the scattering matrix but rather the classical WKBJ approximations for the Bessel functions, and are valid for the entire region exterior to the cylinder, including the transition region. Furthermore, a precise asymptotic form for the location of a certain critical Regge pole is obtained. It is shown that this pole can lead to at least one dramatic resonant modal term at certain critical values, and the exponential nature of the mode in question is determined explicitly. This is followed by an extension to complex values of εr with new uniform asymptotic approximations for the modes also being obtained, and these in turn demonstrate a heavy damping of the resonant mode.

3D ACOUSTIC ANALYSIS OF SPHERICAL CHAMBER HAVING SINGLE INLET AND MULTIPLE OUTLET: AN IMPEDANCE MATRIX APPROACH

2011 ◽  
Vol 03 (04) ◽  
pp. 685-710 ◽  
Author(s):  
A. MIMANI ◽  
M. L. MUNJAL
Keyword(s):  
Bessel Functions ◽  
Acoustic Analysis ◽  
Transmission Loss ◽  
Azimuthal Angle ◽  
Polar Angle ◽  
Impedance Matrix ◽  
Modal Expansion ◽  
3D Fea ◽  
Axisymmetric Shape ◽  
Good Agreement

The transmission loss (TL) performance of spherical chambers having single inlet and multiple outlet is obtained analytically through modal expansion of acoustic field inside the spherical cavity in terms of the spherical Bessel functions and Legendre polynomials. The uniform piston driven model based upon the impedance [Z] matrix is used to characterize the multi-port spherical chamber. It is shown analytically that the [Z] parameters are independent of the azimuthal angle (φ) due to the axisymmetric shape of the sphere; rather, they depend only upon the polar angle (θ) and radius of the chamber R0. Thus, the effects of relative polar angular location of the ports and number of outlet ports are investigated. The analytical results are shown to be in good agreement with the 3D FEA results, thereby validating the procedure suggested in this work.

scholarly journals Modal expansion of the scattered field: Causality, nondivergence, and nonresonant contribution

2018 ◽  
Vol 98 (8) ◽  
Author(s):  
Rémi Colom ◽  
Ross McPhedran ◽  
Brian Stout ◽  
Nicolas Bonod
Keyword(s):  
Scattered Field ◽  
Modal Expansion

ON THE LOGARITHMIC DERIVATIVE OF NICHOLSON'S INTEGRAL

2009 ◽  
Vol 07 (01) ◽  
pp. 73-86 ◽  
Author(s):  
T. M. DUNSTER
Keyword(s):  
Circular Cylinder ◽  
Scattered Field ◽  
Bessel Functions ◽  
Logarithmic Derivative ◽  
Asymptotic Approximations ◽  
Slowly Varying Function ◽  
Related Integral

The function [Formula: see text] is studied. By employing uniform asymptotic approximations for Bessel functions, as well as Nicholson's integral for [Formula: see text] and a related integral, uniform asymptotic approximations for Mν(x) are obtained for x → ∞, which taken together are uniformly valid for -∞ < ν < ∞. From these approximations, it follows that Mν(x) is a slowly varying function of ν for large x, a result which has ramifications in a certain quasi non-uniqueness in the scattered field of a dielectric circular cylinder.

QUASI-NONUNIQUENESS IN THE SCATTERED FIELD OF A DIELECTRIC CIRCULAR CYLINDER

2010 ◽  
Vol 08 (01) ◽  
pp. 63-83 ◽  
Author(s):  
T. M. DUNSTER
Keyword(s):  
Dielectric Constant ◽  
Circular Cylinder ◽  
Scattered Field ◽  
Bessel Functions ◽  
Hankel Functions ◽  
Plane Wave Incident ◽  
The Mean ◽  
The Difference ◽  
Scattered Fields ◽  
Uniform Asymptotic Expansions

It is well known that the scattered field of a z polarized plane wave incident on a dielectric circular cylinder can be expanded as an infinite series involving Hankel functions. From numerical calculations of this expansion, Lam and Yedlin [5] observed that the mean square measure, over all space, of the difference of the scattered fields from two or more distinct values of the dielectric constant of the cylinder can take very small values, thereby almost contradicting the uniqueness property. We investigate this phenomenon rigorously using uniform asymptotic expansions of Bessel functions, and from our analysis we determine the spurious values of the dielectric constant which lead to this quasi-nonuniqueness.

AN EXPERIMENT WHICH MEASURES RESONANT MODE CONVERSION IN He II

1978 ◽  
Vol 39 (C6) ◽  
pp. C6-228-C6-229
Author(s):  
S. Garrett ◽  
S. Adams ◽  
S. Putterman ◽  
I. Rudnick
Keyword(s):  
Mode Conversion ◽  
Resonant Mode

Resonant mode in the Earth’s thermosphere

2011 ◽  
Vol 17 (6) ◽  
pp. 74-76 ◽  
Author(s):  
O.K. Cheremnykh ◽  
Keyword(s):  
Resonant Mode

Tire Vibrations

1977 ◽  
Vol 5 (4) ◽  
pp. 202-225 ◽  
Author(s):  
G. R. Potts ◽  
C. A. Bell ◽  
L. T. Charek ◽  
T. K. Roy
Keyword(s):  
Natural Frequencies ◽  
Standing Waves ◽  
Resonant Mode ◽  
Mode Shapes ◽  
Resonant Vibrations ◽  
Resonant Frequencies ◽  
Radial Tire ◽  
Analysis Techniques ◽  
Thin Ring ◽  
Good Agreement

Abstract Natural frequencies and vibrating motions are determined in terms of the material and geometric properties of a radial tire modeled as a thin ring on an elastic foundation. Experimental checks of resonant frequencies show good agreement. Forced vibration solutions obtained are shown to consist of a superposition of resonant vibrations, each rotating around the tire at a rate depending on the mode number and the tire rotational speed. Theoretical rolling speeds that are upper bounds at which standing waves occur are determined and checked experimentally. Digital Fourier transform, transfer function, and modal analysis techniques used to determine the resonant mode shapes of a radial tire reveal that antiresonances are the primary transmitters of vibration to the tire axle.

SH-Wave Scattering From the Interface Defect

2017 ◽  
Vol 5 (1) ◽  
pp. 45-50
Author(s):  
Myron Voytko ◽  
◽  
Yaroslav Kulynych ◽  
Dozyslav Kuryliak
Keyword(s):  
Half Space ◽  
Wave Diffraction ◽  
Scattered Field ◽  
Wave Scattering ◽  
Elastic Layer ◽  
Analytical Form ◽  
Structure Parameters ◽  
Sh Wave ◽  
Interface Defect ◽  
Hopf Method

The problem of the elastic SH-wave diffraction from the semi-infinite interface defect in the rigid junction of the elastic layer and the half-space is solved. The defect is modeled by the impedance surface. The solution is obtained by the Wiener- Hopf method. The dependences of the scattered field on the structure parameters are presented in analytical form. Verifica¬tion of the obtained solution is presented.

Printed Antennas Tuned by Transversely Magnetized Ferrite Operating at a Novel Resonant Mode

PIERS Online ◽  
2007 ◽  
Vol 3 (8) ◽  
pp. 1213-1216 ◽  
Author(s):  
Anestis Mavridis ◽  
George Kyriacou ◽  
J. N. Sahalos
Keyword(s):  
Resonant Mode ◽  
Printed Antennas
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