Structronics and Actuation of Hybrid Electrostrictive/Piezoelectric Thin Shells

Certain ferroelectric materials possess dual electrostrictive and piezoelectric characteristics, depending on their specific Curie temperatures. The nonlinear electro-mechanical 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, structure-electronic (structronic) coupling and control characteristics of hybrid electrostrictive/piezoelectric dynamic systems deserve an in-depth investigation. In this study, dynamic electro-mechanical system equations and 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. These governing equations clearly reveal the coupling of electrostrictive, piezoelectric, and elastic fields and characteristics change triggered by the Curie temperature. The electric terms are used to manipulate and to control the static/dynamic behavior of hybrid electrostrictive/piezoelectric shells. To apply the hybrid shell system equations to other geometries, simplification procedures using two Lamé parameters and two radii of curvature are demonstrated in two cases: A hybrid electrostrictive/piezoelectric conical shell and a hybrid electrostrictive/piezoelectric toroidal shell. Following the same procedures, one can apply the generic system equations to other common geometries, e.g., beams, arches, plates, rings, cylindrical shells, spherical shells, etc., or specific materials, e.g., electrostrictive or piezoelectric, and further evaluate their electromechanical characteristics and actuation/control effectiveness.