scholarly journals ETHOD OF COMPENSATING LOADS FOR SOLVING OF ANISOTROPIC MEDIUM PROBLEMS

2018 ◽  
Vol 14 (1) ◽  
pp. 71-77
Author(s):  
Elena B. Koreneva
Keyword(s):  
Closed Form ◽  
Anisotropic Medium ◽  
Bessel Functions ◽  
Circular Plates ◽  
Cylindrical Anisotropy

The work applies the method of compensating loads (MCL) for solution of statics and vibrations problems of plates with cylindrical anisotropy. For receiving of basic and compensating solutions Nielsen’s equation is used. The solution expressed in terms of Bessel functions is obtained. Such way can be used in con-sideration of symmetric, antisymmetric and unsymmetric flexure of orthotropic circular plates resting on an elastic Winkler’s subgrade. The similar method can be also utilized for examination of the symmetric vibrations of the orthotropic circular plates as well as for the cases of vibrations with one or a few nodal diameters. The solutions are obtained in closed form in terms of the cylindrical functions.

scholarly journals FORCED VIBRATIONS OF ANISOTROPIC ELASTIC SOLIDS SUBJECTED TO AN ACTION OF COMPLICATED LOADS

2019 ◽  
Vol 15 (3) ◽  
pp. 77-83
Author(s):  
Elena Koreneva ◽  
Valery Grosman
Keyword(s):  
Closed Form ◽  
Bessel Functions ◽  
Forced Vibrations ◽  
Dynamic Loads ◽  
New Technique ◽  
Circular Plates ◽  
Elastic Solids ◽  
Anisotropic Elastic ◽  
A New Technique

The work studies the forced vibrations of anisotropic elastic circular plates caused by dynamic loads uniformly distributed along concentric circumferences and over ring surfaces. The method of compensating loads (MCL) is used to solve the formulated problems. A new technique is used to construct basic and compen­sating solutions. The Nielsen’s equation is taken into consideration. The solutions are obtained in closed form in terms of Bessel functions. Formulae of addition of cylindrical functions are used.

ASYMPTOTICS OF ZEROS OF CERTAIN ENTIRE FUNCTIONS

2007 ◽  
Vol 05 (03) ◽  
pp. 291-299
Author(s):  
MOURAD E. H. ISMAIL
Keyword(s):  
Closed Form ◽  
Bessel Functions ◽  
Entire Functions

We derive representations for some entire q-functions and use it to derive asymptotics and closed form expressions for large zeros of a class of entire functions including the Ramanujan function, and q-Bessel functions.

Approximated Fundamental Frequency for Thin Circular Plates Clamped or Pinned at the Edge

2007 ◽  
Author(s):  
George Weiss
Keyword(s):  
Circular Plate ◽  
Fundamental Frequency ◽  
Bessel Functions ◽  
Unit Area ◽  
Continuous System ◽  
Modified Bessel Functions ◽  
Circular Plates ◽  
Numerical Parameter ◽  
Elliptical Plate ◽  
Distributed Load

Calculating the exact solution to the differential equations that describe the motion of a circular plate clamped or pinned at the edge, is laborious. The calculations include the Bessel functions and modified Bessel functions. In this paper, we present a brief method for calculating with approximation, the fundamental frequency of a circular plate clamped or pinned at the edge. We’ll use the Dunkerley’s estimate to determine the fundamental frequency of the plates. A plate is a continuous system and will assume it is loaded with a uniform distributed load, including the weight of the plate itself. Considering the mass per unit area of the plate, and substituting it in Dunkerley’s equation rearranged, we obtain a numerical parameter K02, related to the fundamental frequency of the plate, which has to be evaluated for each particular case. In this paper, have been evaluated the values of K02 for thin circular plates clamped or pinned at edge. An elliptical plate clamped at edge is also presented for several ratios of the semi–axes, one of which is identical with a circular plate.

A closed form solution for bending/stretching analysis of functionally graded circular plates under asymmetric loading using the Green function

2010 ◽  
Vol 224 (6) ◽  
pp. 1153-1163 ◽  
Author(s):  
A R Saidi ◽  
A Naderi ◽  
E Jomehzadeh
Keyword(s):  
Green Function ◽  
Closed Form ◽  
Volume Fraction ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Form Solution ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Circular Plates ◽  
Equilibrium Equations

In this article, a closed-form solution for bending/stretching analysis of functionally graded (FG) circular plates under asymmetric loads is presented. It is assumed that the material properties of the FG plate are described by a power function of the thickness variable. The equilibrium equations are derived according to the classical plate theory using the principle of total potential energy. Two new functions are introduced to decouple the governing equilibrium equations. The three highly coupled partial differential equations are then converted into an independent equation in terms of transverse displacement. A closed-form solution for deflection of FG circular plates under arbitrary lateral eccentric concentrated force is obtained by defining a new coordinate system. This solution can be used as a Green function to obtain the closed-form solution of the FG plate under arbitrary loadings. Also, the solution is employed to solve some different asymmetric problems. Finally, the stress and displacement components are obtained exactly for each problem and the effect of volume fraction is also studied.

scholarly journals A Review of Procedures for Summing Kapteyn Series in Mathematical Physics

2009 ◽  
Vol 2009 ◽  
pp. 1-34 ◽  
Author(s):  
R. C. Tautz ◽  
I. Lerche
Keyword(s):  
Closed Form ◽  
Bessel Functions ◽  
Mathematical Physics ◽  
Short Review ◽  
Quantum Systems ◽  
Review Article ◽  
Functional Behavior ◽  
Basic Physics ◽  
Kapteyn Series ◽  
Physics Problems

Since the discussion of Kapteyn series occurrences in astronomical problems the wealth of mathematical physics problems in which such series play dominant roles has burgeoned massively. One of the major concerns is the ability to sum such series in closed form so that one can better understand the structural and functional behavior of the basic physics problems. The purpose of this review article is to present some of the recent methods for providing such series in closed form with applications to: (i) the summation of Kapteyn series for radiation from pulsars; (ii) the summation of other Kapteyn series in radiation problems; (iii) Kapteyn series arising in terahertz sideband spectra of quantum systems modulated by an alternating electromagnetic field; and (iv) some plasma problems involving sums of Bessel functions and their closed form summation using variations of the techniques developed for Kapteyn series. In addition, a short review is given of some other Kapteyn series to illustrate the ongoing deep interest and involvement of scientists in such problems and to provide further techniques for attempting to sum divers Kapteyn series.

MODELING NON-LINEAR COHERENT STATES IN FIBER ARRAYS

2011 ◽  
Vol 09 (supp01) ◽  
pp. 349-355 ◽  
Author(s):  
R. DE J. LEÓN-MONTIEL ◽  
H. MOYA-CESSA
Keyword(s):  
Closed Form ◽  
Coherent States ◽  
Bessel Functions ◽  
Displacement Operator ◽  
Fiber Arrays ◽  
Non Linear ◽  
Phase Operators

A class of nonlinear coherent states related to the Susskind-Glogower (phase) operators is obtained. We call these nonlinear coherent states as Bessel states because the coefficients that expand them into number states are Bessel functions. We give a closed form for the displacement operator that produces such states.

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