Dynamic Thermal Analysis of Laminated Cylinder with a Piezoelectric Layer Based on Three-Dimensional Elasticity Solution

2012 ◽  
Vol 186 ◽  
pp. 16-25
Author(s):  
A.R. Daneshmehr ◽  
S. Akbari ◽  
A. Nateghi
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Piezoelectric Layer ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Longitudinal Direction ◽  
Elasticity Solution ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Three Dimensional Elasticity

Three-dimensional elasticity solution is presented for finite length, simply supported, laminated cylinder with a piezoelectric layer under dynamic thermal load and pressure. The piezoelectric layer can be used as an actuator or a sensor. The ordinary differential equations are obtained from partial differential equations of motion by means of trigonometric function expansion in longitudinal direction. Galerkin finite element method is used to solve the resulting ordinary differential equations. Finally numerical results are discussed for different situations.

Elasticity Solution of Laminated Cylindrical Shell with Piezoelectric Layer under Local Ring Load

2007 ◽  
Vol 334-335 ◽  
pp. 917-920 ◽  
Author(s):  
M.H. Yas ◽  
Morteza Shakeri ◽  
M.R. Saviz
Keyword(s):  
Cylindrical Shell ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Local Ring ◽  
Longitudinal Direction ◽  
Variable Coefficients ◽  
Elasticity Solution ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
External Forces

Elasticity solution is presented for simply-supported, orthotropic, piezoelectric cylindrical shell with finite length under local ring load in the middle of shell and electrostatic excitation. The highly coupled partial differential equations (p.d.e.) are reduced to ordinary differential equations(o.d.e.) with variable coefficients by means of trigonometric function expansion in longitudinal direction for displacement and external forces. The resulting ordinary differential equations are solved by Galerkin finite element method. Numerical examples are presented for [0/90/P] lamination with sensor and actuator for different thicknesses.

Dynamic analysis of functionally graded shell with piezoelectric layers based on elasticity

2009 ◽  
Vol 223 (9) ◽  
pp. 2039-2047 ◽  
Author(s):  
M Javanbakht ◽  
M Shakeri ◽  
S N Sadeghi
Keyword(s):  
Differential Equations ◽  
Piezoelectric Layer ◽  
External Surface ◽  
Internal Surface ◽  
Longitudinal Direction ◽  
Variable Coefficients ◽  
Functionally Graded ◽  
Galerkin Finite Element ◽  
Piezoelectric Layers ◽  
Functionally Graded Shell

A study on the elasticity solution of the functionally graded (FG) shell with two piezoelectric layers is presented. In this article, the structure is finitely long, simply supported, and FG with two piezoelectric layers under pressure and electrostatic excitation. The equations of equilibrium, which are coupled partial differential equations, are reduced to ordinary differential equations (o.d.e.) with variable coefficients by means of trigonometric function expansion in the longitudinal direction. The resulting o.d.e. are solved by the Galerkin finite-element method and the Newmark method. Numerical results are presented for a FG cylindrical shell with a piezoelectric layer as an actuator in the external surface and a piezoelectric layer as a sensor in the internal surface.

Three-dimensional elasticity solution for laminated cross-ply panel under localized moment

2007 ◽  
Vol 221 (8) ◽  
pp. 859-866
Author(s):  
A Alibeigloo ◽  
M Shakeri
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Three Dimensional ◽  
Axial Direction ◽  
Variable Coefficients ◽  
Cylindrical Panel ◽  
Fourier Series Expansion ◽  
Simply Supported ◽  
Elasticity Solutions ◽  
Three Dimensional Elasticity

Three-dimensional elasticity solutions have been presented for thick laminated crossply circular cylindrical panel. The panel is under localized patch moment in axial direction and is simply supported at all edges with finite length. Ordinary differential equations with variable coefficients are obtained by means of Fourier series expansion for displacement field and loading in the circumferential and axial directions. Resulting ordinary differential equations are solved using Taylor series. Numerical results are presented for (0/90°) and (0/90/0°) lay-up, and compared with the results for simple form of loading published in literatures.

The Response Analysis of the Piezoelectric Shell Panel Actuators Based on the Theory of Elasticity

Volume 2 ◽  
2004 ◽  
Author(s):  
A. Daneshmehr ◽  
M. Shakeri
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Variable Coefficients ◽  
Theory Of Elasticity ◽  
Response Analysis ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Piezoelectric Layers ◽  
Shell Panel ◽  
Piezoelectric Shell

A study on the elasticity solution of shell panel piezoelectric actuators is presented. In this paper, the structure is infinitely long, simply-supported, orthotropic and under pressure and electrostatic excitation. The equations of equilibrium, which are coupled partial differential equations, are reduced to ordinary differential equations with variable coefficients by means of trigonometric function expansion in circumferential direction. The resulting ordinary differential equations are solved by Galerkin finite element method. Numerical results are presented for [0/90/P] lamination. Finally the results are compared with the assumption of piezoelectric layers in published results.

Methods for Automated Dynamic Analysis of Discrete Mechanical Systems

1973 ◽  
Vol 40 (3) ◽  
pp. 809-811 ◽  
Author(s):  
Y. O. Bayazitoglu ◽  
M. A. Chace
Keyword(s):  
Differential Equations ◽  
Dynamic Analysis ◽  
Ordinary Differential Equations ◽  
Mechanical System ◽  
Dynamic Systems ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Constrained Systems ◽  
Lower Pair ◽  
Linear And Nonlinear

The equations of motion for any discrete, lower pair mechanical system can be obtained by analyzing a branched, three-dimensional compound pendulum of indefinite length. In this paper, a set of expressions which provides the equations of motion of arbitrary mechanical dynamic systems directly as ordinary differential equations are presented. These expressions and the associated technique is applicable to linear and nonlinear unconstrained dynamic systems, kinematic systems and multidegree-of-freedom constrained systems.

Nonsteady Three-Dimensional Stagnation-Point Flow

1971 ◽  
Vol 38 (1) ◽  
pp. 282-287 ◽  
Author(s):  
E. H. W. Cheng ◽  
M. N. O¨zis¸ik ◽  
J. C. Williams
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stagnation Point ◽  
Potential Flow ◽  
Blunt Body ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Special Cases ◽  
Layer Flow ◽  
Two Parameters

The equations of motion for the three-dimensional nonsteady flow of incompressible viscous fluid in the vicinity of a forward stagnation point are reduced to three ordinary differential equations for a potential flow field chosen to vary inversely as a linear function of time. The resulting ordinary differential equations contain two parameters C and D, the former characterizes the type of curvature of the surface around the stagnation point and the latter the degree of acceleration or deceleration of the potential flow. The simple stagnation-point problems which have been studied previously are obtainable as special cases of the present analysis by assigning particular values to C and D. Exact solutions have been computed numerically for the velocity field and the pressure distribution in the boundary-layer flow around the stagnation point of a three-dimensional blunt body for the values of the parameter C from 0–1.

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