Electromechanical Coupling,Distributed Sensing And Control Of Flexoelectric/Piezoelectric Smart Structures

The structure integrated with in situ sensors, actuators and controllers has been becoming an effective technique in the aerospace field to enhance structural adaptability and performance. Due to light weight, fast response and wide bandwidth, piezoelectric-based smart structures are widely used in practical engineering. As compared with piezoelectric materials, flexoelectric dielectrics have advantages such as a wide range of material selection and non-requirement of pre-poling, which avoids issues induced by the complicated pre-poling and aging effect. Thus, combination of flexoelectricity and piezoelectricity can not only enhance the electromechanical coupling, but also make the coupling effect available in case of absence of piezoelectric effect, which is promising for distributed sensing and active control.Based on Hamilton’s principle and variation method, a dynamic model of flexoelectric double-curvature shell continua is systematically established with additional consideration of energy contributions due to the strain gradient-electric field and electric field gradient-strain coupling. Dynamic equations of generic flexoelectric thick/thin shells are derived based on the linear assumption. Classical theories of piezoelectric shell continua (or elastic shells) can be obtained when the flexoelectric effect (and piezoelectric effects) is removed, which verifies the proposed theory. The thin shell theory is applied to several kinds of shells and non-shells typically used in practical engineering. The direct/converse flexoelectric effects represented by the matrix notation is defined in orthogonal curvilinear coordinate system.Mathematical modeling of distributed sensing on generic shell structures is conducted and expression of flexoelectric sensing signal in either open or closed circuit condition is obtained. Features of flexoelectric sensing are discussed on beams and rings in detail. The sensing signals with different design parameters are evaluated. Sensing signals induced by the flexoelectric and piezoelectric effects are compared based on ring shells. Generally, flexoelectric sensors are preferred to be laminated on structures that are much thinner and smaller, especially for bending-dominant vibration.A point-layer design of flexoelectric actuator is proposed. The flexoelectric actuator is set on a cantilever beam to actively control its static deflection. The analytical expression of control force is derived and the control effectiveness is obtained. Comparison between the flexoelectric and the piezoelectric control results proves the feasibility of static shape control due to the converse flexoelectric effect. Mobile actuator and muti-actuators are also proposed, showing that the point-layer actuator has advantage in local control applications with high precision, as well as flexibility and intelligence.In order to experimentally study the flexoelectric coupling effect, an method based on the open-circuit voltage model is proposed. An equivalent flexoelectric constant is measured. The inferred constant is comparable with the reported data proving efficiency of the method. Distributed sensing behaviors are experimentally verified on the flexoelectric cantilever beam. Signal output versus excitation frequency is also experimentally studied and predictions by the theoretical model match well with experimental results.On purpose of active vibration control of parabolic cylindrical shells, the shell laminated with distributed piezoelectric sensors and actuators is proposed. A new mode shape function is defined to analytically study a flexible simply-supported shell. Sensing/actuation behaviors of distributed sensor/actuator are analyzed and modal sensing signal/control force induced by the sensor/actuator are derived. Two shell cases are considered to reveal the curvature effect on neural sensing signals and microscopic actuation effectiveness. Localized behavior is the most crucially distinctive characteristic and it becomes more prominent as the shell deepens.A collocated pair of piezoelectric sensor and actuator are laminated on the parabolic cylindrical shell to realize the active vibration control with LQ optimal control law. Based on sensing/actuation behaviors of piezoelectric sensors/actuators, optimal control gain and control voltage are solved. Simulation results show that the LQ optimal control law combined with the distributed piezoelectric sensors and actuators is effective to enhance the damping of whole system and thus to actively suppress the vibration.