Calibration of Eringen's small length scale coefficient for initially stressed vibrating nonlocal Euler beams based on microstructured beam model

Wang, C. M., Zhang, Z., Challamel, N. and Duan, W. H. (2013) Calibration of Eringen's small length scale coefficient for initially stressed vibrating nonlocal Euler beams based on microstructured beam model. Journal of Physics D: Applied Physics, 46 34: . doi:10.1088/0022-3727/46/34/345501


Author Wang, C. M.
Zhang, Z.
Challamel, N.
Duan, W. H.
Title Calibration of Eringen's small length scale coefficient for initially stressed vibrating nonlocal Euler beams based on microstructured beam model
Journal name Journal of Physics D: Applied Physics   Check publisher's open access policy
ISSN 0022-3727
1361-6463
Publication date 2013-08-28
Sub-type Article (original research)
DOI 10.1088/0022-3727/46/34/345501
Open Access Status Not yet assessed
Volume 46
Issue 34
Total pages 6
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Language eng
Formatted abstract
In this paper, we calibrate Eringen's small length scale coefficient e 0 for an initially stressed vibrating nonlocal Euler beam via a microstructured beam modelled by some repetitive cells comprising finite rigid segments and elastic rotational springs. By adopting the pseudo-differential operator and Padé's approximation, an analytical solution for the vibration frequency in terms of initial stress may be developed for the microstructured beam model. When comparing this analytical solution with the established exact vibration solution from the nonlocal beam theory, one finds that the calibrated Eringen's small length scale coefficient e0 is given by e0 = √ (1/6)(1/12) (σ0m) where σ0 is the initial stress and σm is the mth mode buckling stress of the corresponding local Euler beam. It is shown that e0 varies with respect to the initial axial stress, 1/√12 ≈ 0.289 from at the buckling compressive stress to when the axial stress is zero and it monotonically increases with increasing initial tensile stress. The small length scale coefficient e0, however, does not depend on the vibration/buckling mode considered.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Civil Engineering Publications
 
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