Cut-off frequencies of circumferential horizontal shear waves in various functionally graded cylinder shells

Xiaoqin Shen; Dawei Ren; Xiaoshan Cao; Ji Wang

doi:10.1016/j.ultras.2017.11.005

Cut-off frequencies of circumferential horizontal shear waves in various functionally graded cylinder shells

Ultrasonics. 2018 Mar:84:180-186. doi: 10.1016/j.ultras.2017.11.005. Epub 2017 Nov 6.

Authors

Xiaoqin Shen¹, Dawei Ren², Xiaoshan Cao³, Ji Wang⁴

Affiliations

¹ School of Civil Engineering, Xi'an University of Technology, Xi'an 710048, China; State Key Laboratories of Transducer Technology, Chinese Academy of Sciences, Shanghai 200050, China.
² School of Civil Engineering, Xi'an University of Technology, Xi'an 710048, China.
³ School of Civil Engineering, Xi'an University of Technology, Xi'an 710048, China; State Key Laboratories of Transducer Technology, Chinese Academy of Sciences, Shanghai 200050, China. Electronic address: caoxsh@xaut.edu.cn.
⁴ Piezoelectric Device Laboratory, School of Mechanical Engineering & Mechanics, Ningbo University, Ningbo 315211, China.

PMID: 29154045
DOI: 10.1016/j.ultras.2017.11.005

Abstract

In this study, cut-off frequencies of the circumferential SH waves in functionally graded piezoelectric-piezomagnetic material (FGPPM) cylinder shells with traction free, electrical and magnetic open boundary conditions are investigated analytically. The Wentzel-Kramers-Brillouin (WKB) method is employed for solving differential equations with variable coefficients for general cases. For comparison, Bessel functions and Kummer functions are used for solving cut-off frequency problems in homogenous and ideal FGPPM cylinder shells. It is shown that the WKB solution for the cut-off frequencies has good precise. The set of cut-off frequencies is a series of approximate arithmetic progressions, for which the difference is a function of the density and the effective elastic parameter. The relationship between the difference and the gradient coefficient is described. These results provide theoretical guidance for the non-destructive evaluation of curved shells based on the cut-off frequencies.

Keywords: Cut-off frequency; Cylinder shear; Functionally graded piezoelectric-piezomagnetic material; SH wave; Wentzel-Kramers-Brillouin method.