The Theory of Piezoelectric Shells and Plates

Nellya N. Rogacheva

1994

xi + 247 pages

This is the first book devoted to a systematic description of the linear theory of piezoelectric shells and plates. In the first part of the book, the theories for electroelastic thin-walled elements of arbitrary form with different directions of preliminary polarization are presented in an easy form for practical use. The approximate methods for integrating the equations of piezoelectric shells and plates are developed and applied for solving some engineering problems.

In the second part, the theory of piezoelectric shells and plates is substantiated by the asymptotic method. The area of applicability for different kinds of electroelastic shell theories is studied. A new problem concerning the electroelastic phenomena at the edge of a thin-walled element is raised and solved.

Contents

Statics and Dynamics of Piezoelectric Shells and Plates

Three-Dimensional Equations of Electroelasticity

Preliminary Information
Basic Equations
Boundary Conditions in Electroelasticity Theory
General Theorems on Electroelasticity

Equations of the Theory of Piezoceramic Shells

Two-Dimensional Equilibrium Equations
Hypotheses of the Theory of Nonelectric Shells and the Saint Venant Principle
Shells with Thickness Polarization (Electrode-Covered Faces)
Shells with Thickness Polarization (Faces without Electrodes)
Shells with Tangential Polarization (Faces without Electrodes)
Shells with Tangential Polarization (Electrode-Covered Faces)
Free Shells with Thickness Polarization
Bimorphic Shells and Plates
The Theory of Piezoceramic Plates with Thickness Polarization
Plates with Tangential Polarization

The Method of Partitioning a Static Electroelastic Static Preliminary Remarks

The Membrane Theory of Shells with Thickness Polarization
The Membrane Theory of Shells with Tangential Polarization
The Principal Stressed State of Shells with Tangential Polarization and Electrode-Covered Faces
Pure Moment Electroelastic State of a Shell with Thickness Polarization Simple Edge Effects in Electroelastic Shells with
Thickness Polarization
Simple Edge Effects in Shells with Tangential Polarization
Boundary Conditions for the Principal Electroelastic State and Simple Edge Effect

Approximate Methods for Computing Free and Forced Vibrations of Electroelastic Shells

Free Vibrations of Shells with Thickness Polarization
Free Vibrations of Shells with Tangential Polarization
The Refined Membrane Dynamic Theory
Forced Vibrations of Shells with Thickness Polarization

Some Dynamic Problems in the Theory of Piezoceramic Plates and Shells

Forced Vibrations of a Circular Cylindrical Shell with Longitudinal Polarization (Axisymmetric Problem) Forced Vibrations of a Circular Cyndrical Shell with
Longitudinal Polarization (Nonaxisymmetric Problem)
Two Nonclassical Problems for Shells with Tangential Polarization
Axisymmetric Tangential Vibrations of Circular Plates with Thickness Polarization
Active Suppression of Vibrations in Electroelastic Bars and Round Plates by Means of Piezoeffect
Resonance Method for Measuring Fluid Viscosity Using a Piezoelement
Using a Piezoceramic Element with Thickness Polarization as a Strain Gauge

Asymptotic Method as Applied to Electroelastic Shell Theory

Constructing Equations in the Theory of Piezoceramic Shells

Shells with Thickness Polarization
Pure Moment Electroelastic State of Shells with Thickness Polarization
Shells with Tangential Polarization (Electrode-Covered Faces)
Shells with Tangential Polarization (Faces without Electrodes)

The Theory of Electroelastic Boundary Layer

The Boundary Layer of a Shell with Thickness Polarization
Boundary Layer at the Edge alpha 2 = alpha 10 (Preliminary Polarization along the alpha 2-Lines)
Boundary Layer near the Edge alpha 2 = alpha 20 (Preliminary Polarization along the alpha 2-Lines)
The Saint Venant Principle Generalized to Electroelasticit

Interaction Between the Internal Electroelastic State and the Boundary Layer

Two-Dimensional Electroelastic State with Great Variability in the Direction Normal to the Edge
Boundary Conditions in the Theory of Shells with Thickness Polarization (Electrode-Covered Faces)
Boundary Conditions for a Shell with Thickness Polarization (Faces without Electrodes)
Boundary Conditions in the Theory of Shells with Tangential Polarization (Electrode-Covered Faces)
Boundary Conditions in the Theory of Shells with Tangential Polarization (Faces without Electrodes)

Some Problems of Boundary Layers

Antiplane Boundary Layer at a Free Edge of a Shell with Thickness Polarization
Antiplane Boundary Layer at a Free Edge of a Shell with Tangential Polarization
Antiplane Boundary Layer at a Rigidly Fixed Edge of a Shell with Tangential Polarization
Plane Boundary Layer at a Rigidly Fixed Edge of a Shell with Tangential Polarization