Dynamic analysis of actuator-driven circular arch or ring using impedance elements

Abstract

An analytical description of the dynamic characteristics of the piezoelectric actuator-drivencircular arch or ring is developed in this paper. A pair of thin curved piezoelectric patchesis perfectly bonded to the middle elastic layer and actuated out of phase, and the bendingmoments induced by the actuators drive the host structure to vibrate in plane. Thispiezo-laminated circular arch is equivalently regarded as a single-layer arch and its motionequation is given. The general solution for such a structure is obtained and a7 × 7 impedance matrix representing the dynamics of the sandwicharch is deduced. The impedance matrix can degenerate into a6 × 6 impedance matrix representing the dynamics of the elastic circular arch. These two kinds ofimpedance matrices are used to analyze three different types of smart structures, which arethe piezo-laminated circular arch, the circular arch and the circular ring withdistributed piezoelectric actuators. The above structures are meshed into the sandwicharch segments and the elastic arch segments, which are modeled as impedanceelements. The continuous conditions between the impedance elements and theelectric and mechanical boundary conditions in these structures are studied indetail. The dynamic characteristics of these smart systems are finally obtained bysolving the linear impedance equations. A piezo-laminated semicircle arch withthree different types of mechanical boundary conditions is calculated as the firstnumerical example. A cantilevered semicircle arch driven by one pair of distributedpiezoelectric actuators is analyzed as the second example. Thirdly, an elasticcircular ring excited by one or two pairs of piezoelectric segmented actuators isinvestigated respectively. The calculated results of the elastic circular ring actuatedby one pair of actuators are compared with the experimental results given byLalande et al (1997 J. Sound Vib. 20 169–87), and the other results among the threenumerical examples are compared with the FEM results using the commercialsoftware ANSYS. The comparison shows that the present method is effectivein modeling the piezoelectric actuator-driven circular arch or ring structures.