An extended separation-of-variable method for eigenbuckling of orthotropic rectangular thin plates

2020 ◽  
pp. 113239
Author(s):  
Y. Yuan ◽  
Y.F. Xing
Keyword(s):  
Variable Method ◽  
Thin Plates ◽  
Separation Of Variable

scholarly journals Localization of interacting fields in five-dimensional braneworld models

2017 ◽  
Vol 32 (32) ◽  
pp. 1750191 ◽  
Author(s):  
Dewi Wulandari ◽  
Triyanta ◽  
Jusak S. Kosasih ◽  
Douglas Singleton ◽  
Preston Jones
Keyword(s):  
Extra Dimension ◽  
Variable Method ◽  
Field Equations ◽  
Braneworld Model ◽  
Configuration Systems ◽  
Separation Of Variable ◽  
Better Than

We study the localization properties of fundamental fields which are coupled to one another through the gauge mechanism both in the original Randall–Sundrum (RS) and in the modified Randall–Sundrum (MRS) braneworld models: scalar–vector, vector–vector, and spinor–vector configuration systems. For this purpose, we derive conditions of localization, namely, the finiteness of integrals over the extra coordinate in the action of the system considered. We also derive field equations for each of the systems and then obtain their solutions corresponding to the extra dimension by a separation of variable method for every field involved in each system. We then insert the obtained solutions into the conditions of localization to seek whether or not the solutions are in accordance with the conditions of localization. We obtain that not all of the configuration systems considered are localizable on the brane of the original RS model while, on the contrary, they are localizable on the MRS braneworld model with some restrictions. In terms of field localizability on the brane, this result shows that the MRS model is much better than the original RS model.

scholarly journals Analyzing calculation results of non-stationary axisymmetric thermoelasticity task for a circular isotropic plate

2018 ◽  
Vol 196 ◽  
pp. 01007
Author(s):  
Dmitriy Shlyahin
Keyword(s):  
Temperature Change ◽  
High Speed ◽  
Isotropic Plate ◽  
Integral Transformation ◽  
Adjoint System ◽  
Thin Plates ◽  
Movement Vector ◽  
Calculation Results ◽  
Finite Integral ◽  
Separation Of Variable

The paper releases results of numerical calculation of axisymmetric dynamic thermoelasticity task for a fixed circular isotropic plate in case of temperature change on its front faces (boundary conditions of the 1st type). The calculated ratios are obtained by using the GL-theory of thermoelasticity (classical theory), which determines the dependence of the vector of heat flux on the velocity of change and temperature gradient. The mathematical model of the task in question includes differential equations of axisymmetric motion and thermal conductivity, formulated as regard to the component of the movement vector and the function of temperature change. Not self-adjoint system is investigated independently. For its solution, a mathematical apparatus technique of separation of variable in the form of finite integral transformations is used, that is transformations of Fourier, Hankel and generalized integral transformation (GIT). The constructed calculation ratios give an opportunity to define stress and strain state and character of distribution of a thermal field of rigidly fixed circular plate with arbitrary axially symmetrical temperature external influence. It is shown, that elastic inertial characteristics of a plate influence the law of change of movement over time only while investigating very thin plates at high-speed temperature impact.

Bending of Isotropic Thin Plates by Concentrated Edge Couples and Forces

1954 ◽  
Vol 21 (2) ◽  
pp. 129-139
Author(s):  
Yi-Yuan Yu
Keyword(s):  
Exact Solutions ◽  
Circular Plate ◽  
Complex Variable ◽  
Biharmonic Equation ◽  
Numerical Results ◽  
Complex Variable Method ◽  
Variable Method ◽  
Thin Plates ◽  
Circular Plates

Abstract In this paper the complex variable method of Muschelišvili for solving the biharmonic equation is applied to problems of bending of isotropic thin plates by concentrated edge couples and forces. The results of the method as applied to plate problems by previous authors are presented first. Methods of handling concentrated edge couples and forces are developed. These are then applied to the circular plate as an example, for which exact solutions in closed forms are obtained. Worked out in detail are three particular problems; namely, those of circular plates subjected, respectively, to two bending couples, to two twisting couples, both applied at the ends of a diameter, and to four forces applied at the ends of two diameters perpendicular to each other. Numerical results are presented in the form of graphs.

scholarly journals A novel approach of the conformal mappings with applications in biotribology

2015 ◽  
Vol 23 (1) ◽  
pp. 99-114
Author(s):  
Olivia Florea
Keyword(s):  
Conformal Mapping ◽  
Newtonian Fluid ◽  
Conformal Mappings ◽  
Viscous Fluids ◽  
Variable Method ◽  
Eccentric Cylinders ◽  
Novel Approach ◽  
Concentric Cylinders ◽  
Separation Of Variable

AbstractIn this paper, the flow of an incompressible non Newtonian fluid between two eccentric cylinders is considered. The aim of this study is to determine the flow in the case of the stationary movement of some viscous fluids between two eccentric cylinders with the generators parallel with Oz axis. Using the Mobius conformal mapping are obtained two concentric cylinders. The expression of velocity is deduced with the separation of variable method.

Resonance Acoustoelasticity Measurement of Stress in Thin Plates

1992 ◽  
Vol 4 (1) ◽  
pp. 127-138
Author(s):  
Masahiko Hirao ◽  
Hidekazu Fukuoka ◽  
Yoshinori Murakami
Keyword(s):  
Thin Plates
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