Dynamic modeling of preloaded size-dependent nano-crystalline nano-structures

doi:10.1007/s10483-017-2291-8

Abstract

Abstract:

The vibration behavior of size-dependent nano-crystalline nano-beams is investigated based on nonlocal, couple stress and surface elasticity theories. A nanocrystalline nano-beam is composed of three phases which are nano-grains, nano-voids, and interface. Nano-voids or porosities inside the material have a stiffness-softening impact on the nano-beam. A Eringen's nonlocal elasticity theory is applied in the analysis of nano-crystalline nano-beams for the first time. Residual surface stresses which are usually neglected in modeling nano-crystalline nano-beams are incorporated into nonlocal elasticity to better understand the physics of the problem. Also, a modified couple stress theory is used to capture rigid rotations of grains. Applying a differential transform method (DTM) satisfying various boundary conditions, the governing equations obtained from the Hamilton's principle are solved. Reliability of the proposed approach is verified by comparing the obtained results with those provided in the literature. The effects of the nonlocal parameter, surface effect, couple stress, grain size, porosities, and interface thickness on the vibration characteristics of nano-crystalline nano-beams are explored.

Key words: fuzzy mapping, probabilistic metric space, fixed point, fuzzymetric space, t-norm of h-type, fixed degree, free vibration, modified couple stress theory, nonlocal elasticity, nano-crystalline nano-beam, surface effect

2010 MSC Number:

74F10

F. EBRAHIMI, M. R. BARATI. Dynamic modeling of preloaded size-dependent nano-crystalline nano-structures. Applied Mathematics and Mechanics (English Edition), 2017, 38(12): 1753-1772.

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