Journal
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
Volume 119, Issue -, Pages 383-395Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijmecsci.2016.10.031
Keywords
Buckling; Vibration; Hencky bar-chain; Central finite difference; Internal elastic spring stiffness; Exact solution
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This paper presents the Hencky bar-chain model (HBM) that allows for the presence of internal elastic springs. With the development of this general HBM, one can analyse beam-like structures with repetitive cells with allowance for internal damaged sections or bracing members. In this paper, we have derived formulas for the internal rotational and lateral spring stiffnesses of HBMs based on the finite difference model (FDM). In addition, the analytical buckling loads and vibration frequencies of the HBM and FDM with internal elastic springs are presented for the first time. These analytical solutions converge to the exact solutions for continuum beams when the HBM segmental number approaches infinity. The solutions can also be used to calibrate the Eringen's small length scale coefficient e(0) in the nonlocal beam theory based on their phenomenological similarities.
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