1560. A series solution for the in‑plane vibration of sector plates with arbitrary inclusion angles and boundary conditions

Kaipeng Zhang1, Dongyan Shi2, Xiaoyan Teng3, Yunke Zhao4, Qian Liang5

College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin, China

2Corresponding author

E-mail: 1zhangkaipeng@hrbeu.edu.cn, 2shidongyan@hrbeu.edu.cn, 3tengxiaoyan@hrbeu.edu.cn, 4zhaoyunke@hrbeu.edu.cn, 5liangqian@hrbeu.edu.cn

(Received 15 September 2014; received in revised form 12 January 2015; accepted 20 January 2015)

Abstract. In this investigation, a Spectro-Geometric Method (SGM) is presented for the in‑plane vibration analysis of sector plates with an arbitrary inclusion angle, and general boundary conditions along each of its edges. Unlike in most existing studies where solutions are often developed for a particular type of boundary conditions, the current method can be generally applied to a wide range of boundary conditions with no need of modifying solution algorithms and procedures; that is, the in-plane displacement functions are invariably expressed as an accelerated trigonometric series expansion and different boundary conditions can be easily dealt with through modifying the stiffness values for restraining springs in the same way as varying other model parameters such as Young’s modulus and mass density. The expansion coefficients are considered as the generalized coordinates, and determined using the Rayleigh‑Ritz technique. The effectiveness and reliability of the current method are demonstrated by the calculated modal properties for sector plates with a range of different combinations of boundary conditions and inclusion angles up to .

Keywords: sector plates, in-plane vibration, arbitrary inclusion angles, arbitrary boundary conditions, spectro‑geometric method (SGM).

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Cite this article

Zhang Kaipeng, Shi Dongyan, Teng Xiaoyan, Zhao Yunke, Liang Qian A series solution for the in‑plane vibration of sector plates with arbitrary inclusion angles and boundary conditions. Journal of Vibroengineering, Vol. 17, Issue 2, 2015, p. 870‑882.

 

© JVE International Ltd. Journal of Vibroengineering. Mar 2015, Volume 17, Issue 2. ISSN 1392-8716