期刊
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
卷 51, 期 14, 页码 2676-2686出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijsolstr.2014.03.043
关键词
Cellular solids; Vibration; Couple-stress; Size effects
类别
资金
- National Natural Science Foundation of China [11002031, 11172052, 11202042]
- National Basic Research Program (973 Program) of China [2011CB610304]
- Liaoning Province Doctor Startup Fund [20101008]
- Liaoning Excellent Talents in University [LJQ2012040]
Cellular solids are usually treated as homogeneous continuums with effective properties. Nevertheless, these mechanical properties depend strongly on the ratio of the specimen size to the cell size. These size effects may be accounted for according to preliminary static analysis of effective continuums based on couple-stress theory. In this paper an effective dynamic continuum model, based on couple-stress theory, is proposed to analyze the behavior of free vibrations of periodic cellular solids. In this continuum model, the effective mechanical constants of the effective continuum are deduced by an equivalent energy method. The cellular solid structure is then replaced with the equivalent couple-stress continuum with same overall dimension and shape. Moreover, the finite element formulation of the couple-stress continuum for the generalized eigenvalue analysis is developed to implement the free vibration analysis. The eigenfrequencies of the effective continuum are then obtained via the shear beam theory or the finite element method. A conventional finite element analysis by discretizing each cell of the cellular solids is also carried out to serve as an exact solution. Several structural cases are calculated to demonstrate the accuracy and effectiveness of the proposed continuum model. Good agreement on structural eigenfrequencies between the effective continuum solutions and the exact solutions shows that the proposed continuum model can accurately simulate the dynamic behavior of the cellular solids. (C) 2014 Elsevier Ltd. All rights reserved.
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