# The Theory of Piezoelectric Shells and Plates

## Nellya N. Rogacheva

1994

xi + 247 pages

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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.

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

- 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 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

- 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

- 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

- 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 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

- 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)

- 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