Shock and Vibration
Volume 2016, Article ID 6758291, 8 pages
http://dx.doi.org/10.1155/2016/6758291
Research on Radial Vibration of a Circular Plate
College of Power and Energy Engineering, Harbin Engineering University, Harbin, China
Received 25 May 2016; Revised 13 September 2016; Accepted 29 September 2016
Academic Editor: Giorgio Dalpiaz
Copyright © 2016 Wei Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Radial vibration of the circular plate is presented using wave propagation approach and classical method containing Bessel solution and Hankel solution for calculating the natural frequency theoretically. In cylindrical coordinate system, in order to obtain natural frequency, propagation and reflection matrices are deduced at the boundaries of free-free, fixed-fixed, and fixed-free using wave propagation approach. Furthermore, radial phononic crystal is constructed by connecting two materials periodically for the analysis of band phenomenon. Also, Finite Element Simulation (FEM) is adopted to verify the theoretical results. Finally, the radial and piezoelectric effects on the band are also discussed.