Free vibration analysis of sigmoid functionally graded nanobeams based on a modified couple stress theory with general shear deformation theory

被引：36
|
作者：
Khorshidi, Majid Akbarzadeh [1 ]
Shariati, Mahmoud [1 ]
机构：
[1] Ferdowsi Univ Mashhad, Dept Mech Engn, Mashhad, Iran
来源：
JOURNAL OF THE BRAZILIAN SOCIETY OF MECHANICAL SCIENCES AND ENGINEERING | 2016年 / 38卷 / 08期
关键词：
Nanostructures; Smart materials; Vibration; Modified couple stress theory; NONLINEAR FREE-VIBRATION; GRADIENT ELASTICITY THEORY; TIMOSHENKO BEAM MODEL; ULTRA-THIN FILMS; LAMINATED COMPOSITE; DYNAMIC-ANALYSIS; BERNOULLI; BEHAVIOR; TORSION; PLATES;
D O I：
10.1007/s40430-015-0388-3
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
Free vibration of nano-scale beams made of sigmoid functionally graded material is studied based on the modified couple stress theory. In the context of the modified couple stress theory, a material length scale parameter is used to describe the size effect. The classical, first-order and some higher order beam theories are considered to assess the effect of shear deformation. Differential equations of motion and boundary conditions are derived using Hamilton's principle. The equations of motion are discretized by generalized differential quadrature method. Finally, a comprehensive solution for the present problem with general shear deformation theory and with different boundary conditions is provided. Then effects of the shear deformation, boundary conditions, Poisson's ratio, and material composition are studied.
引用
收藏
页码：2607 / 2619
页数：13
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