Elastic Waves in Generalized Thermo-Piezoelectric Transversely Isotropic Circular Bar Immersed in Fluid

2015 ◽  
Vol 8 (1) ◽  
pp. 82-103
Author(s):  
Palaniyandi Ponnusamy
Keyword(s):  
Classical Theory ◽  
Cross Sections ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Coupled System ◽  
Theory Of Elasticity ◽  
Inviscid Fluid ◽  
Displacement Potential ◽  
Modes Of Vibration

AbstractIn this paper, a mathematical model is developed to study the wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of circular cross-sections immersed in inviscid fluid. The present study is based on the use of the three-dimensional theory of elasticity. Three displacement potential functions are introduced to uncouple the equations of motion and the heat and electric conductions. The frequency equations are obtained for longitudinal and flexural modes of vibration and are studied based on Lord-Shulman, Green-Lindsay and Classical theory theories of thermo elasticity. The frequency equations of the coupled system consisting of cylinder and fluid are developed under the assumption of perfect-slip boundary conditions at the fluid-solid interfaces, which are obtained for longitudinal and flexural modes of vibration and are studied numerically for PZT-4 material bar immersed in fluid. The computed non-dimensional frequencies are compared with Lord-Shulman, Green-Lindsay and Classical theory theories of thermo elasticity for longitudinal and flexural modes of vibrations. The dispersion curves are drawn for longitudinal and flexural modes of vibrations. Moreover, the dispersion of specific loss and damping factors are also analyzed for longitudinal and flexural modes of vibrations.

Dispersion Waves in a Submerged Thermo-Piezoelectric Membrane

2020 ◽  
Vol 22 (4) ◽  
pp. 1145-1156
Author(s):  
R. Selvamani ◽  
M. Mahaveer Sreejeyan ◽  
J. Rexy ◽  
B. Sriee Malvika
Keyword(s):  
Wave Propagation ◽  
Temperature Distribution ◽  
Equations Of Motion ◽  
Electric Displacement ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Electric Conduction ◽  
Fluid Medium ◽  
Displacement Potential ◽  
Interfacial Boundary

AbstractWave propagation in a thermo piezoelectric membrane immersed in an infinite fluid medium is discussed using three-dimensional linear theory of elasticity and thermos piezoelectricity. Three displacement potential functions are introduced to uncouple the equations of motion, heat and electric conduction equations. The frequency equations are obtained for longitudinal and flexural modes at the solid fluid interfacial boundary conditions. The numerical results are analyzed for PZT-4 material and the computed stress, strain, electric displacement and temperature distribution are presented in the form of dispersion curves and its characteristics are studied.

Stress Concentrations in Three-Dimensional Electrostriction

1967 ◽  
Vol 34 (2) ◽  
pp. 431-436 ◽  
Author(s):  
T. E. Smith
Keyword(s):  
Displacement Vector ◽  
Spherical Inclusion ◽  
Crack Problem ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Uniform Electric Field ◽  
Inclusion Problem ◽  
Stress Concentrations ◽  
Displacement Potential ◽  
Penny Shaped Crack

Using the techniques employed in developing a Papkovich-Neuber representation for the displacement vector in classical elasticity, a particular integral of the kinematical equations of equilibrium for the uncoupled theory of electrostriction is developed. The particular integral is utilized in conjunction with the displacement potential function approach to problems of the theory of elasticity to obtain closed-form solutions of several stress concentration problems for elastic dielectrics. Under a prescribed uniform electric field at infinity, the problems of an infinite elastic dielectric having first a spherical cavity and then a rigid spherical inclusion are solved. The rigid spheroidal inclusion problem and the penny-shaped crack problem are also solved for the case where the prescribed field is parallel to their axes of revolution.

Application of Lifting-Surface Theory to the Prediction of Hydroelastic Response of Hydrofoil Boats

1968 ◽  
Vol 12 (04) ◽  
pp. 286-301
Author(s):  
C. J. Henry
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Mode Shapes ◽  
Operator Technique ◽  
Elastic Mode ◽  
Surface Theory ◽  
Lifting Surface ◽  
Modes Of Vibration ◽  
Elastic Modes

In this report a theoretical procedure is developed for the prediction of the dynamic response elastic or rigid body, of a hydrofoil-supported vehicle in the flying condition— to any prescribed transient or periodic disturbance. The procedure also yields the stability indices of the response, so that dynamic instabilities such as flutter can also be predicted. The unsteady hydrodynamic forces are introduced in the equations of motion for the elastic vehicle in terms of the indicia I pressure-response functions, which are de rived herein from lifting-surface theory. Thus, the predicted vehicle-response includes the effects of three-dimensional unsteady flow conditions at specified forward speed. The natural frequencies and elastic modes of vibration of the vehicle and foil system in the absence of hydrodynamic effects are presumed known. A numerical procedure is presented for the solution of the downwash integral equations relating the unknown indicial pressure distributions to the specified elastic-mode shapes. The procedure is based on use of the generalized-lift-operator technique together with the collocation method.

Resistive Ballooning Modes in Three-Dimensional Configurations

1982 ◽  
Vol 37 (8) ◽  
pp. 848-858 ◽  
Author(s):  
D. Correa-Restrepo
Keyword(s):  
Growth Rates ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Coupled System ◽  
Small Constant ◽  
Ballooning Mode ◽  
The Stability ◽  
The Magnetic Field ◽  
Symmetric Systems ◽  
The Ideal

Resistive ballooning modes in general three-dimensional configurations are studied on the basis of the equations of motion of resistive MHD. Assuming small, constant resistivity and perturbations localized transversally to the magnetic field, a stability criterion is derived in the form of a coupled system of two second-order differential equations. This criterion contains several limiting cases, in particular the ideal ballooning mode criterion and criteria for the stability of symmetric systems. Assuming small growth rates, analytical results are derived by multiple-length-scale expansion techniques. Instabilities are found, their growth rates scaling as fractional powers of the resistivity

scholarly journals The torsion of a semi-infinite elastic solid by an elliptical stamp

1968 ◽  
Vol 9 (1) ◽  
pp. 36-45
Author(s):  
Mumtaz K. Kassir
Keyword(s):  
Field Equation ◽  
Classical Theory ◽  
Cross Sections ◽  
Plane Surface ◽  
Boundary Surface ◽  
Elastic Solid ◽  
Theory Of Elasticity ◽  
Circular Area

The problem of determining, within the limits of the classical theory of elasticity, the displacements and stresses in the interior of a semi-infinite solid (z ≧ 0) when a part of the boundary surface (z = 0) is forced to rotate through a given angle ω about an axis which is normal to the undeformed plane surface of the solid, has been discussed by several authors [7, 8, 9, 1, 11, and others]. All of this work is concerned with rotating a circular area of the boundary surface and the field equation to be solved is, essentially, J. H. Mitchell's equation for the torsion of bars of varying circular cross-sections.

Aeroelastic Stability of Wide Webs and Narrow Ribbons in Cross Flow

2008 ◽  
Vol 75 (4) ◽  
Author(s):  
Rahul A. Bidkar ◽  
Arvind Raman ◽  
Anil K. Bajaj
Keyword(s):  
Three Dimensional ◽  
Cross Flow ◽  
Coupled System ◽  
Inviscid Fluid ◽  
Aeroelastic Stability ◽  
Aeroelastic Flutter ◽  
Panel Methods ◽  
Divergence Instability ◽  
Applied Tension ◽  
The Web

Aeroelastic flutter can lead to large amplitude oscillations of tensioned wide webs and narrow ribbons commonly used in the paper-handling, textile, sheet-metal, and plastics industries. In this article, we examine the aeroelastic stability of a web or a ribbon, which is submerged in an incompressible and inviscid fluid flow across its free edges. The web or ribbon is modeled as a uniaxially tensioned Kirchhoff plate with vanishingly small bending stiffness. A Galerkin discretization for the structural dynamics together with panel methods for the unsteady three dimensional potential flow are used to cast the coupled system into the form of a gyroscopic, nonconservative dynamical system. It is found that wide webs mainly destabilize through a divergence instability due to the cross-flow-induced conservative centrifugal effects. However, for certain values of applied tension, the wake-induced nonconservative effects can destabilize the web via a weak flutter instability. Contrarily, narrow ribbons in cross flow are nearly equally likely to undergo flutter or divergence instability depending on the value of applied tension.

Axial Loading of Annular Bonded Rubber Blocks

2003 ◽  
Vol 76 (5) ◽  
pp. 1194-1211 ◽  
Author(s):  
J. M. Horton ◽  
G. E. Tupholme ◽  
M. J. C. Gover
Keyword(s):  
Experimental Data ◽  
Stress Distribution ◽  
Closed Form ◽  
Cross Section ◽  
Classical Theory ◽  
Cross Sections ◽  
Axial Loading ◽  
Theory Of Elasticity ◽  
Governing Equations ◽  
Annular Cross Section

Abstract Closed-form expressions are derived using a superposition approach for the axial deflection and stress distribution of axially loaded rubber blocks of annular cross-section, whose ends are bonded to rigid plates. These satisfy exactly the governing equations and conditions based upon the classical theory of elasticity. Readily calculable relationships are derived for the corresponding apparent Young's modulus, Ea, and the modified modulus, Ea′, and their numerical values are compared with the available experimental data. Elementary expressions for evaluating Ea and Ea′ approximately are deduced from these, in forms which are closely analogous to those given previously for blocks of circular and long, thin rectangular cross-sections. The profiles of the deformed lateral surfaces of the block are discussed and it is confirmed that the assumption of parabolic lateral profiles is not valid generally.

Asymptotic Distribution of Eigenfunctions and Eigenvalues of the Basic Boundary-Contact Oscillation Problems of the Classical Theory of Elasticity

1999 ◽  
Vol 6 (2) ◽  
pp. 107-126
Author(s):  
T. Burchuladze ◽  
R. Rukhadze
Keyword(s):  
Elastic Medium ◽  
Asymptotic Distribution ◽  
Classical Theory ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Asymptotic Formulas ◽  
Closed Surfaces ◽  
Isotropic Elastic Medium ◽  
Boundary Contact ◽  
Basic Boundary

Abstract The basic boundary-contact oscillation problems are considered for a three-dimensional piecewise-homogeneous isotropic elastic medium bounded by several closed surfaces. Using Carleman's method, the asymptotic formulas for the distribution of eigenfunctions and eigenvalues are obtained.

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