scholarly journals On Perturbation Solutions for Axisymmetric Bending Boundary Values of a Deep Thin Spherical Shell

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Rong Xiao ◽  
Danhui Dan ◽  
Wei Cheng
Keyword(s):  
Spherical Shell ◽  
Nonlinear Response ◽  
Fundamental Equation ◽  
Expansion Method ◽  
External Pressure ◽  
Displacement Component ◽  
Moment Theory ◽  
Axisymmetric Bending ◽  
Thin Spherical Shell ◽  
The Moment

On the basis of the general theory of elastic thin shells and the Kirchhoff-Love hypothesis, a fundamental equation for a thin shell under the moment theory is established. In this study, the author derives Reissner’s equation with a transverse shear forceQ1and the displacement componentw. These basic unknown quantities are derived considering the axisymmetry of the deep, thin spherical shell and manage to constitute a boundary value question of axisymmetric bending of the deep thin spherical shell under boundary conditions. The asymptotic solution is obtained by the composite expansion method. At the end of this paper, to prove the correctness and accuracy of the derivation, an example is given to compare the numerical solution by ANSYS and the perturbation solution. Meanwhile, the effects of material and geometric parameters on the nonlinear response of axisymmetric deep thin spherical shell under uniform external pressure are also analyzed in this paper.

A fast approach for acoustic source localization on a thin spherical shell

2021 ◽  
pp. 147592172110419
Author(s):  
Zixian Zhou ◽  
Zhiwen Cui ◽  
Tribikram Kundu
Keyword(s):  
Velocity Profile ◽  
Spherical Shell ◽  
Source Localization ◽  
Pressure Vessels ◽  
Solution Technique ◽  
Acoustic Source ◽  
Spherical Shells ◽  
Fast Approach ◽  
Acoustic Source Localization ◽  
Thin Spherical Shell

Thin spherical shell structures are wildly used as pressure vessels in the industry because of their property of having equal in-plane normal stresses in all directions. Since very large pressure difference between the inside and outside of the wall exists, any formation of defects in the pressure vessel wall has a huge safety risk. Therefore, it is necessary to quickly locate the area where the defect maybe located in the early stage of defect formation and make repair on time. The conventional acoustic source localization techniques for spherical shells require either direction-dependent velocity profile knowledge or a large number of sensors to form an array. In this study, we propose a fast approach for acoustic source localization on thin isotropic and anisotropic spherical shells. A solution technique based on the time difference of arrival on a thin spherical shell without the prior knowledge of direction-dependent velocity profile is provided. With the help of “L”-shaped sensor clusters, only 6 sensors are required to quickly predict the acoustic source location for anisotropic spherical shells. For isotropic spherical shells, only 4 sensors are required. Simulation and experimental results show that this technique works well for both isotropic and anisotropic spherical shells.

scholarly journals The estimation of electric moment in solution by the temperature coefficient method. Part I.—Experimental method and the electric moments of some benzyl compounds

1933 ◽  
Vol 142 (846) ◽  
pp. 173-197 ◽  
Keyword(s):  
Single Molecule ◽  
Polar Solvent ◽  
Fundamental Equation ◽  
Absolute Temperature ◽  
Electric Moment ◽  
Avogadro’S Number ◽  
Boltzmann Gas ◽  
Different Temperatures ◽  
The Moment ◽  
Coefficient Method

The theory of the estimation of the electric moment of molecules dissolved in a non-polar solvent is now well known. The fundamental equation is P 2∞ = 4 π /3 N (α 0 + μ 2 /3 k T) (1) in which the symbols have the following significance: P 2∞ the total polarizability of the solute per grain molecule at infinite dilution, N Avogadro’s number, α 0 the moment induced in a single molecule by unit electric field, k the Boltzmann gas constant, T the absolute temperature, and μ the permanent electric moment of the molecule. This equation is of the form P 2∞ = A + B/T, (2) where A = 4 π /3 Nα 0 and B = 4 π /9 . N μ 2 / k , from which it follows that if A and B are constant, i. e ., independent of temperature, then each may be evaluated from a series of measurements of P 2∞ at different temperatures or alternatively B (and hence μ ) may be obtained from one value of P 2∞ at one temperature, provided that A can be obtained by some independent method.

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