Piezoelectric Shell Vibration Theory

Abstract

Active piezoelectric structures capable of self—adaptation (Tzou & Anderson, 1992) and high—precision operations (Tzou & Fukuda, 1992) have drawn much attention in recent years. In this chapter, generic vibration theories of deep piezoelectric shell continua are derived. The system equations include both mechanical and electric components. The mechanical components are related to conventional elastic vibrations of shells; the electric components are electromechanical coupling effects induced by the piezoelectricity. Eliminating these electromechanical coupling terms from the generic piezoelectric system equations yields a set of conventional vibration equations for elastic shell continua. Note that the electromechanical coupling terms can also be used in sensor and actuator applications applied to distributed identification and controls of shells. (Detailed discussions will be presented in later chapters.) A background introduction and a brief review of the subject area are presented first. Detailed derivations of the piezoelectric shell theory using Hamilton’s principle are presented next. Simplification of the piezoelectric shell vibration theory to the conventional elastic shell vibration theory is also discussed. Applications of the generic theories to commonly occurring geometries, e.g., spherical shells, cylindrical shells, plates, etc., and distributed control of piezoelectric shells are demonstrated in Chapter 3.