Control Force Enhancement of Conical Shells Using Piezoelectric Macro-Fiber Composite

In piezoelectric coupled shells, the distributed actuation force usually consists of four components, including the membrane force and bending moment in the longitudinal direction, and the membrane force and bending moment in the circumferential direction. For commonly used bi-axial piezoelectric materials, such as PZT and PVDF, these four components may have phase difference of π or −π. This leads to force cancellation and reduces the overall control effectiveness. Supposing that one piezoelectric actuator is uni-axial, for example only d₃₁ is not equal to zero, and then this actuator will generate actuation force with the first two components or the latter two, depending on the actuator configuration and the shell geometry/modes. Accordingly the force cancellation can be avoided or minimized. In this research, the Macro-Fiber Composite (MFC) actuators are used as uni-axial actuators. The dynamic equation of a conical shell is firstly given. Then the actuation force is derived based on the converse piezoelectric effect and thin shell assumptions. Three types of the MFC actuators are considered, including MFC-P1, MFC-P2 and MFC-P3. Case studies are performed to evaluate the distributed actuation forces. Both axial and transverse vibrations of the conical shell are formulated to study the force cancellation of various shell modes, and the payload effects are considered in the analysis. The results show that, by using the MFC actuators, actuation force can be enhanced because force cancellation is avoided. The force enhancement becomes even more significant for membrane dominated modes, such as axial modes of shells with heavy payloads.