The Theory of Piezoelectric Shells and Plates

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