Micro-Structronics and Control of Hybrid Electrostrictive/Piezoelectric Thin Shells

Certain ferroelectric materials possess dual electrostrictive and piezoelectric characteristics, depending on their specific Curie temperatures. These materials exhibit piezoelectric characteristics in the ferroelectric phase when the temperature is below the Curie point. However, they become electrostrictive in the paraelectric phase (non-polar phase) as the temperature exceeds the Curie point. The (direct) electrostrictive effect is a quadratic dependence of stress or strain on applied electric field. The nonlinear electromechanical effect of electrostrictive materials provides stronger actuation performance as compared with that of piezoelectric materials. Due to the complexity of the generic ferroelectric actuators, micro-electromechanics and control characteristics of generic electrostrictive/piezoelectric dynamics system deserve an in-depth investigation. In this study, electro-mechanical dynamic system equations and generic boundary conditions of hybrid electrostrictive/piezoelectric double-curvature shell continua are derived using the energy-based Hamilton’s principle, elasticity theory, electrostrictive/piezoelectric constitutive relations, and Gibb’s free energy function. Moreover, the second converse electrostrictive effect and the direct piezoelectric effect are all considered in the generic governing equations. Simplifications of the generic theory to other common geometries or specific materials are demonstrated and their electromechanical characteristics are also evaluated.