Transient Responses in a Piezoelectric Spherically Isotropic Hollow Sphere for Symmetric Problems

2003 ◽  
Vol 70 (3) ◽  
pp. 436-445 ◽  
Author(s):  
H. J. Ding ◽  
H. M. Wang ◽  
W. Q. Chen
Keyword(s):  
Hollow Sphere ◽  
Electric Potential ◽  
Present Method ◽  
Interpolation Method ◽  
Separation Of Variables ◽  
Time Variable ◽  
Spherically Symmetric ◽  
Transient Responses ◽  
Arbitrary Thickness ◽  
Piezoelectric Hollow Sphere

By virtue of the separation of variables technique, the spherically symmetric electroelastic dynamic problem of a spherically isotropic hollow sphere is transformed to an integral equation about a function with respect to time, which can be solved successfully by means of the interpolation method. Then the solution of displacements, stresses, electric displacements, and electric potential are obtained. The present method is suitable for a piezoelectric hollow sphere with an arbitrary thickness subjected to spherically symmetric electric potential and radial mechanical loads, that both can be arbitrary functions about the time variable, at the internal and external surfaces.

scholarly journals Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 830
Author(s):  
Evgeniya V. Goloveshkina ◽  
Leonid M. Zubov
Keyword(s):  
Nonlinear Theory ◽  
Hollow Sphere ◽  
Tensor Field ◽  
Exact Analytical Solution ◽  
Symmetric Tensor ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Tensor Fields ◽  
Spherically Symmetric Distribution ◽  
Nonlinear Elastic

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i. e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out.

Nonstaggered APPLE Algorithm for Incompressible Viscous Flow in Curvilinear Coordinates

2002 ◽  
Vol 124 (5) ◽  
pp. 812-819 ◽  
Author(s):  
S. L. Lee ◽  
Y. F. Chen
Keyword(s):  
Viscous Flow ◽  
Present Method ◽  
Heat Conduction Equation ◽  
Continuity Equation ◽  
Interpolation Method ◽  
Curvilinear Coordinates ◽  
Grid System ◽  
Weighted Interpolation ◽  
Incompressible Viscous Flow ◽  
Curvilinear Grid

The NAPPLE algorithm for incompressible viscous flow on Cartesian grid system is extended to nonorthogonal curvilinear grid system in this paper. A pressure-linked equation is obtained by substituting the discretized momentum equations into the discretized continuity equation. Instead of employing a velocity interpolation such as pressure-weighted interpolation method (PWIM), a particular approximation is adopted to circumvent the checkerboard error such that the solution does not depend on the under-relaxation factor. This is a distinctive feature of the present method. Furthermore, the pressure is directly solved from the pressure-linked equation without recourse to a pressure-correction equation. In the use of the NAPPLE algorithm, solving the pressure-linked equation is as simple as solving a heat conduction equation. Through two well-documented examples, performance of the NAPPLE algorithm is validated for both buoyancy-driven and pressure-driven flows.

A Innovation Identification Approach of Control System by Irrational (Fractional) Transfer

2016 ◽  
Vol 3 (2) ◽  
pp. 336
Author(s):  
Nguyen Quang Dung ◽  
Tran Hoang Quang Minh
Keyword(s):  
Control System ◽  
Transfer Function ◽  
Interpolation Method ◽  
Distributed Parameter ◽  
Computationally Efficient ◽  
Transient Responses ◽  
Adaptive Controllers ◽  
Real Interpolation Method ◽  
Identification Approach ◽  
Irrational Transfer Function

<p>In this paper, an innovative algorithm of identification of control system, described by irrational transfer function with distributed parameter characteristics - with irrational components, is proposed. Algorithm is based on real interpolation method (RIM). Parameters of irrational transfer function can be identified by its experimental transient responses. Each of them can be represented by an analytic expression, table or graph. The proposed method is computationally efficient, simple and practical, as is illustrated by numerical examples. In the furure, the method can be used for tuning the controller and for direct application construction of adaptive controllers, working on the identification principle.</p>

Functionally Graded Hollow Sphere With Piezoelectric Internal and External Layers Under Asymmetric Transient Thermomechanical Loads

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
M. Jabbari ◽  
S. M. Mousavi ◽  
M. A. Kiani
Keyword(s):  
Hollow Sphere ◽  
Legendre Polynomials ◽  
Radial Direction ◽  
Energy Equation ◽  
Separation Of Variables ◽  
Functionally Graded ◽  
Power Functions ◽  
Legendre Series ◽  
Piezoelectric Layers ◽  
Transient Thermal

In this paper, an analytical method is developed to obtain the solution for the two-dimensional (2D) (r,θ) transient thermal and mechanical stresses in a hollow sphere made of functionally graded (FG) material and piezoelectric layers. The FGM properties vary continuously across the thickness, according to the power functions of radial direction. The temperature distribution as a function of radial and circumferential directions and time is obtained solving the energy equation, using the method of separation of variables and Legendre series. The Navier equations are solved analytically using the Legendre polynomials and the system of Euler differential equations.

Analytical Solutions of Loaded Multifunctional Multilayered Plates

2013 ◽  
Vol 682 ◽  
pp. 127-134 ◽  
Author(s):  
M. Ajdour ◽  
L. Azrar
Keyword(s):  
Mechanical Loading ◽  
Analytical Solutions ◽  
Electric Potential ◽  
Numerical Results ◽  
Rectangular Plates ◽  
Multilayered Plate ◽  
Linear Elastic ◽  
Propagator Matrix ◽  
Arbitrary Thickness ◽  
Multilayered Plates

Analytical solutions are derived for multifunctional N-layered rectangular plates. The multilayered plate may consist of linear elastic or piezoelectric laminates of arbitrary thickness. The related equations and formulae are developed based on the Stroh like formalism. Solutions for multilayered plates are expressed in terms of the propagator matrix and satisfy the continuity conditions of material layers. Various types of electrical and mechanical loading may be considered. Numerical results of stresses, electric potential and displacement for some multifunctional multilayered plates are analyzed

Solution of Non-Fourier Temperature Field in a Hollow Sphere under Harmonic Boundary Condition

2015 ◽  
Vol 772 ◽  
pp. 197-203 ◽  
Author(s):  
Amin Bahrami ◽  
Siamak Hosseinzadeh ◽  
Ramin Ghasemiasl ◽  
Morteza Radmanesh
Keyword(s):  
Heat Flux ◽  
Temperature Field ◽  
Hollow Sphere ◽  
Separation Of Variables ◽  
Time Dependent ◽  
Separation Of Variables Method ◽  
Method Of Solution ◽  
Duhamel Integral ◽  
Special Case ◽  
General Time

Analytical solution of the axisymmetric two-dimensional non-Fourier temperature field within a hollow sphere is investigated considering Cattaneo-Vernotte constitutive equation with general time-dependent heat flux. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The method of solution is the standard separation of variables method. Duhamel integral is used for applying the time-dependent boundary conditions. The presented solution is applied to special case of harmonic heat flux on outer surface.

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