(1)Haar wavelet discretization method for free vibration study of laminated composite beam under generalized boundary conditions
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Sung-Ryol Soa,∗ , Hoyong Yunb, Yongho Ric, Ryongsik Od, Yong-Il Yuna
a Institute of Advanced Science, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea
b Institute of Science, Kimchaek University of Technology, Pyongyang, Democratic People’s Republic of Korea
c Department of Engineering Machine, Pyongyang University of Mechanical Engineering, Pyongyang, Democratic People’s Republic of Korea
d Department of Transport Mechanical Engineering, Pyongyang University of Mechanical Engineering, Pyongyang, Democratic People’s Republic of Korea
Received 25 February 2020; received in revised form 24 March 2020; accepted 8 April 2020
Available online 14 May 2020
Abstract
Investigation on vibration of laminated composite beam (LCB) is an important issue owing to its wide use as fundamental component.
In the present work, we study the free vibration of arbitrarily LCB with generalized elastic boundary condition (BC) by using Haar wavelet
discretization method (HWDM). Timoshenko beam theory is utilized to model the free vibration of LCB. The LCB is first split into several
segments, and then the displacement for each segment is obtained from the Haar wavelet series and their integral. Hamilton’s principle is
applied to construct governing equations and the artificial spring boundary technique is adopted to obtain the general elastic boundary and
continuity conditions at two ends of LCB. The vibration characteristics of beam with different fiber orientations and lamina numbers is
investigated and its displacements are compared with those in previous works. Numerical results are shown graphically and demonstrate the
validation of our method.
© 2020 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license.(http://creativecommons.org/licenses/by-nc-nd/4.0/)
Keywords: Laminated beam; Haar wavelet discretization method; Elastic boundary condition; Free vibration; Artificial spring boundary technique