In 2002, he was a lecturer in mechanical electrical engineering with the College of the Harbin Engineering University, Harbin, China, where he is currently a professor conducting teaching and research in vibration and noise, phononic crystals and metamaterials, etc. His current research interests include seismic metamaterials. Figure 1. SM correlation quantitative broken line chart.

Piezoelectric thin rings are periodically introduced and placed on a base plate along the radial direction, forming a onedimensional thin circular plate of piezoelectric radial phononic crystals (CPPRPC). Based on flexural wave equation of thin circular plate and the transfer matrix method, the behavior of flexural waves propagating in CPPRPC is analyzed theoretically and numerically, especially in the band gaps. The transmission curves of CPPRPC and homogeneousmaterial plate are calculated for comparison. Afterwards finite element simulations are carried out to verify the theoretical results. Furthermore, the effects of the length ratio, thickness ratio, period number and control gain on the flexural wave band gap are discussed in detail. Our results show that there are band gaps of flexural wave in CPPRPC. Structural parameters and outer active control gain have important influences on the band gaps. In particular, low and broad band gaps can be obtained effectively by varying outer active control gain.

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A semi-analytic method is adopted to analyze the free vibration characteristics of the moderately thick composite laminated cylindrical shell with arbitrary classical and elastic boundary conditions. By Hamilton’s principle and first-order shear deformation theory, the governing equation of the composite shell can be established. The displacement variables are transformed into the wave function forms to ensure the correctness of the governing equation. Based on the kinetic relationship between the displacement variables and force resultants, the final equation associated with arbitrary boundary conditions is established. The dichotomy method is conducted to calculate the natural frequencies of the composite shell. For verifying the correctness of the present method, the results by the present method are compared with those in the pieces of literatures with various boundary conditions. Furthermore, some numerical examples are calculated to investigate the effect of several parameters on the composite shell, such as length to radius ratios, thickness to radius ratios and elastic restrained constants.

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.