An analytical description of the dynamic characteristics of the piezoelectric actuator-driven circular arch or ring is developed in this paper. A pair of thin curved piezoelectric patches is perfectly bonded to the middle elastic layer and actuated out of phase, and the bending moments induced by the actuators drive the host structure to vibrate in plane. This piezo-laminated circular arch is equivalently regarded as a single-layer arch and its motion equation is given. The general solution for such a structure is obtained and a 7 × 7 impedance matrix representing the dynamics of the sandwich arch is deduced. The impedance matrix can degenerate into a 6 × 6 impedance matrix representing the dynamics of the elastic circular arch. These two kinds of impedance matrices are used to analyze three different types of smart structures, which are the piezo-laminated circular arch, the circular arch and the circular ring with distributed piezoelectric actuators. The above structures are meshed into the sandwich arch segments and the elastic arch segments, which are modeled as impedance elements. The continuous conditions between the impedance elements and the electric and mechanical boundary conditions in these structures are studied in detail. The dynamic characteristics of these smart systems are finally obtained by solving the linear impedance equations. A piezo-laminated semicircle arch with three different types of mechanical boundary conditions is calculated as the first numerical example. A cantilevered semicircle arch driven by one pair of distributed piezoelectric actuators is analyzed as the second example. Thirdly, an elastic circular ring excited by one or two pairs of piezoelectric segmented actuators is investigated respectively. The calculated results of the elastic circular ring actuated by one pair of actuators are compared with the experimental results given by Lalande et al (1997 J. Sound Vib. 201 169-87), and the other results among the three numerical examples are compared with the FEM results using the commercial software ANSYS. The comparison shows that the present method is effective in modeling the piezoelectric actuator-driven circular arch or ring structures.
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