Electromechanics and Vibrations of Piezoelectric Shell Distributed Systems

Smart piezoelectric structures, conventional passive materials integrated with piezoelectric sensors, actuators, and control electronics, have great potentials in many engineering applications. This paper is devoted to a new theoretical development of generic piezoelectric shell distributed systems. System electromechanical equations and boundary conditions for a thick piezoelectric shell continuum with symmetrical hexagonal structure (Class C_6v = 6 mm) are derived using Hamilton’s principle and linear piezoelectric theory. Further simplification leads to a set of new electromechanical system equations, three translated coordinates and two rotary coordinates, for piezoelectric shell continua including rotary inertias and transverse shears. For thin piezoelectric shells, the second set system equations are further simplified using Kirchhoff-Love’s assumptions. The converse effect induced electric forces/moments and boundary conditions can be used to control system dynamics via open or closed-loop control systems. Applications of the theories to a plate and shells of revolution (spherical, cylindrical, and conical shells) are demonstrated in case studies.