Simplification of frequency equation of multilayered cylinders and some recursion formulae of bessel functions

1999 ◽  
Vol 20 (3) ◽  
pp. 332-337 ◽  
Author(s):  
Yin Xiaochun
Keyword(s):  
Bessel Functions ◽  
Frequency Equation

Axisymmetric Free Vibration of Shallow Spherical Shells With a Circular Rigid Insert

1993 ◽  
Vol 115 (2) ◽  
pp. 207-209
Author(s):  
D. Y. Hwang ◽  
W. A. Foster
Keyword(s):  
Free Vibration ◽  
Mode Shape ◽  
Vibrational Frequency ◽  
Bessel Functions ◽  
Frequency Equation ◽  
Third Order ◽  
Spherical Shells ◽  
Fundamental Vibrational Frequency ◽  
Rigid Insert ◽  
The Relationship

A general solution for the third-order partial differential equations for the axisymmetric free vibration of thin isotropic shallow spherical shells with a rigid insert is presented in this paper. The frequency equation in terms of Bessel functions as well as modified Bessel functions is solved for the fundamental vibrational frequency and mode shape. Both linear and non-linear boundary conditions are applied and the results are compared. The relationship between the vibrational frequency, mode shape and the size of the rigid insert is discussed.

RADIAL VIBRATION CHARACTERISTICS OF SPHERICAL NANOPARTICLES IMMERSED IN FLUID MEDIUM

2013 ◽  
Vol 27 (26) ◽  
pp. 1350186 ◽  
Author(s):  
S. AHMAD FAZELZADEH ◽  
ESMAEAL GHAVANLOO
Keyword(s):  
Bessel Functions ◽  
Nonlocal Elasticity Theory ◽  
Frequency Equation ◽  
Small Scale ◽  
Complex Frequency ◽  
Radial Vibration ◽  
Radial Vibrations ◽  
Fluid Medium ◽  
Nanoparticle Radius ◽  
New Formulation

The vibrational properties of nanoparticles coupled with surrounding media are of recent interest. These nanostructures can be modeled as nanoscale spherical solids. In this paper, new formulation based on the nonlocal elasticity theory is proposed to investigate radial vibrations of the nanoparticles immersed in fluid medium. The nanoparticles with size ranging from 1 nm to 10 nm are discussed. The nanoparticles are considered elastic, homogeneous and anisotropic. Along the contact surface between the nanoparticle and the fluid, the compatibility requirement is applied and the Bessel functions are used to obtain the complex frequency equation. Numerical results are evaluated, and their comparisons are performed to confirm the validity and accuracy of the proposed method. Furthermore, the model is used to elucidate the effect of small scale on the vibration of several nanoparticles. Our results show that the small scale is essential for the radial vibration of nanoparticles when the nanoparticle radius is smaller than 2 nm.

scholarly journals Some Applications of the Wright Function in Continuum Physics: A Survey

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 198
Author(s):  
Yuriy Povstenko
Keyword(s):  
Heat Conduction ◽  
Fractional Calculus ◽  
Exponential Function ◽  
Nonlocal Elasticity ◽  
Bessel Functions ◽  
Wright Function ◽  
Mainardi Function ◽  
Integral Relations

The Wright function is a generalization of the exponential function and the Bessel functions. Integral relations between the Mittag–Leffler functions and the Wright function are presented. The applications of the Wright function and the Mainardi function to description of diffusion, heat conduction, thermal and diffusive stresses, and nonlocal elasticity in the framework of fractional calculus are discussed.

scholarly journals On Subclasses of Uniformly Spiral-like Functions Associated with Generalized Bessel Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
B. A. Frasin ◽  
Ibtisam Aldawish
Keyword(s):  
Integral Operator ◽  
Bessel Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Generalized Bessel Functions ◽  
Necessary And Sufficient

The main object of this paper is to find necessary and sufficient conditions for generalized Bessel functions of first kind zup(z) to be in the classes SPp(α,β) and UCSP(α,β) of uniformly spiral-like functions and also give necessary and sufficient conditions for z(2-up(z)) to be in the above classes. Furthermore, we give necessary and sufficient conditions for I(κ,c)f to be in UCSPT(α,β) provided that the function f is in the class Rτ(A,B). Finally, we give conditions for the integral operator G(κ,c,z)=∫0z(2-up(t))dt to be in the class UCSPT(α,β). Several corollaries and consequences of the main results are also considered.

scholarly journals A new product formula involving Bessel functions

2021 ◽  
pp. 1-17
Author(s):  
Mohamed Amine Boubatra ◽  
Selma Negzaoui ◽  
Mohamed Sifi
Keyword(s):  
Bessel Functions ◽  
New Product ◽  
Product Formula

scholarly journals Dispersive Estimates for Full Dispersion KP Equations

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Didier Pilod ◽  
Jean-Claude Saut ◽  
Sigmund Selberg ◽  
Achenef Tesfahun
Keyword(s):  
Stationary Phase ◽  
Initial Value Problem ◽  
Bessel Functions ◽  
Linear Part ◽  
Independent Interest ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Initial Value ◽  
Kp Equations ◽  
Well Posed

AbstractWe prove several dispersive estimates for the linear part of the Full Dispersion Kadomtsev–Petviashvili introduced by David Lannes to overcome some shortcomings of the classical Kadomtsev–Petviashvili equations. The proof of these estimates combines the stationary phase method with sharp asymptotics on asymmetric Bessel functions, which may be of independent interest. As a consequence, we prove that the initial value problem associated to the Full Dispersion Kadomtsev–Petviashvili is locally well-posed in $$H^s(\mathbb R^2)$$ H s ( R 2 ) , for $$s>\frac{7}{4}$$ s > 7 4 , in the capillary-gravity setting.

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