Small length scale coefficient for Eringen’s and lattice-based continualized nonlocal circular arches in buckling and vibration

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• 作者：H. Zhang^a ; ^{zhanghong@u.nus.edu} ; C.M. Wang^b ; ^{cm.wang@uq.edu.au} ; N. Challamel^c ; ^{noel.challamel@univ-ubs.fr}
• 关键词：Nonlocal arch theory ; Hencky bar-chain ; Eringen&rsquo ; s small length scale coefficient ; Buckling ; Vibration ; Finite difference
• 刊名：Composite Structures
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：165
• 期：Complete
• 页码：148-159
• 全文大小：1199 K
• 卷排序：165

文摘

This paper presents analytical buckling and vibration solutions for two nonlocal circular arch models. One model is based on Eringen’s stress gradient theory while the other model is based on continualization of a lattice system. Both nonlocal arch models contain the unknown small length scale coefficient e0. In order to calibrate e0, exact buckling and vibration solutions for Hencky bar-chain model (HBM) are first obtained. On the basis of the phenomenological similarities between the HBM and the nonlocal arch models, the matching of buckling and vibration solutions for HBMs and those for nonlocal models allows one to calibrate the e0 values. It is found that e0 for Eringen’s nonlocal circular arch (ENCA) varies with respect to geometrical property of the arch and boundary conditions. However, e0 for a continualized nonlocal circular arch (CNCA) is found to be a constant value, regardless of geometrical properties or boundary conditions.