Geometric effects of cross sections on equilibrium of helical and twisted ribbon

doi:10.1007/s10483-017-2182-6

摘要/Abstract

摘要：

In the framework of elastic rod model, the Euler-Lagrange equations characterizing the equilibrium configuration of the polymer chain are derived from a free energy functional associated with the curvature, torsion, twisting angle, and its derivative with respect to the arc-length. The configurations of the helical ribbons with different crosssectional shapes are given. The effects of the elastic properties, the cross-sectional shapes, and the intrinsic twisting on the helical ribbons are discussed. The results show that the pitch angle of the helical ribbon decreases with the increase in the ratio of the twisting rigidity to the bending rigidity and approaches the intrinsic twisting. If the bending rigidity is much greater than the twisting rigidity, the bending and twisting of the helical ribbon always appear simultaneously.

关键词: closed-cell foam, plate vibration, natural frequency, cell volume distribu-tion, effective Young’s modulus, scale factor, helical and twisted ribbon, Euler-Lagrange equation, pitch angle, elastic rod model, twisting angle

Abstract:

Key words: closed-cell foam, plate vibration, natural frequency, cell volume distribu-tion, effective Young’s modulus, scale factor, pitch angle, Euler-Lagrange equation, twisting angle, elastic rod model, helical and twisted ribbon

中图分类号:

Ye XIAO, Zaixing HUANG. Geometric effects of cross sections on equilibrium of helical and twisted ribbon[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(4): 495-504.

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