Size-dependent vibration of functionally graded curved microbeams based on the modified strain gradient elasticity theory

被引:62
作者
Ansari, R. [1 ]
Gholami, R. [2 ]
Sahmani, S. [1 ]
机构
[1] Univ Guilan, Dept Mech Engn, Rasht, Iran
[2] Islamic Azad Univ, Lahijan Branch, Dept Mech Engn, Lahijan, Iran
关键词
Curved microbeams; Functionally graded material; Free vibration; Modified strain gradient theory; Size effect; WALLED CARBON NANOTUBES; DYNAMIC-ANALYSIS; PLASTICITY; BEAMS; MODEL; STABILITY;
D O I
10.1007/s00419-013-0756-3
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
On the basis of the modified strain gradient elasticity theory, the free vibration characteristics of curved microbeams made of functionally graded materials (FGMs) whose material properties vary in the thickness direction are investigated. A size-dependent first-order shear deformation beam model is developed containing three internal material length scale parameters to incorporate small-scale effect. Through Hamilton's principle, the higher-order governing equations of motion and boundary conditions are derived. Natural frequencies of FGM curved microbeams corresponding to different mode numbers are evaluated for over a wide range of material property gradient index, dimensionless length scale parameter and aspect ratio. Moreover, the results obtained via the present non-classical first-order shear deformation beam model are compared with those of degenerated beam models based on the modified couple stress and the classical theories. It is found that the difference between the natural frequencies predicted by the various beam models is more significant for lower values of dimensionless length scale parameter and higher values of mode number.
引用
收藏
页码:1439 / 1449
页数:11
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