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Shock and Vibration
Volume 2014, Article ID 738162, 9 pages
http://dx.doi.org/10.1155/2014/738162
Research Article

The Analysis of Curved Beam Using B-Spline Wavelet on Interval Finite Element Method

1The State Key Laboratory for Manufacturing Systems Engineering, Xi’an 710049, China
2School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China
3College of Mechanical and Electrical Engineering, Xi’an University of Architecture and Technology, Xi’an 710049, China

Received 30 January 2013; Accepted 26 October 2013; Published 25 February 2014

Academic Editor: Reza Jazar

Copyright © 2014 Zhibo Yang 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

A B-spline wavelet on interval (BSWI) finite element is developed for curved beams, and the static and free vibration behaviors of curved beam (arch) are investigated in this paper. Instead of the traditional polynomial interpolation, scaling functions at a certain scale have been adopted to form the shape functions and construct wavelet-based elements. Different from the process of the direct wavelet addition in the other wavelet numerical methods, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space by aid of the corresponding transformation matrix. Furthermore, compared with the commonly used Daubechies wavelet, BSWI has explicit expressions and excellent approximation properties, which guarantee satisfactory results. Numerical examples are performed to demonstrate the accuracy and efficiency with respect to previously published formulations for curved beams.