Abstract
Piezoelectric rings are periodically introduced and inserted in a base plate along the radial direction, forming a one-dimensional circular plate of piezoelectric radial phononic crystals (CPPRPC). The transfer matrix of the torsional wave between adjacent units is derived in cylindrical coordinates. Then, by introducing Lyapunov exponents, the phenomenon of the torsional wave band gap is analyzed with consideration of outer control. Furthermore, the effects of some factors, namely, radial span ratio, inner radius of the plate, open-circuit, and short-circuit statuses of the piezoelectric ceramics, on the torsional wave band gap are also discussed in detail. The results show that the distinct band gaps are obtained for torsional waves propagating in CPPRPC. Together with the outer control gain, structural and piezoelectric parameters have significant effects on the band gaps. In particular, middle-low frequency band gaps can be effectively obtained by rationally varying the outer active control gain.
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