A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation

被引：296
作者：
Bounouara, Fatima [1 ]
Benrahou, Kouider Halim [1 ]
Belkorissat, Ismahene [1 ]
Tounsi, Abdelouahed [1 ,2 ,3 ,4 ]
机构：
[1] Univ Djillali Liabes Sidi Bel Abbes, Fac Technol, Dept Civil Engn, Mat & Hydrol Lab, Bel Abbes, Algeria
[2] Univ Djillali Liabes Sidi Bel Abbes, Fac Technol, Dept Genie Civil, Lab Struct & Mat Avances Genie Civil & Travaux Pu, Bel Abbes, Algeria
[3] Univ Djillali Liabes Sidi Bel Abbes, Dept Phys, Fac Sci Exactes, Lab Modelisat & Simulat Multiechelle, Bel Abbes, Algeria
[4] Algerian Natl Themat Agcy Res Sci & Technol ATRST, Bel Abbes, Algeria
来源：
STEEL AND COMPOSITE STRUCTURES | 2016年 / 20卷 / 02期
关键词：
nonlocal elasticity theory; nanoscale-plates; free vibration; plate theory; functionally graded materials; MULTILAYERED GRAPHENE SHEETS; NEUTRAL SURFACE POSITION; WALLED CARBON NANOTUBES; FREE FLEXURAL VIBRATION; BUCKLING ANALYSIS; WAVE-PROPAGATION; BENDING ANALYSIS; SANDWICH PLATES; REFINED THEORY; BEAM;
D O I：
10.12989/scs.2016.20.2.227
中图分类号：
TU [建筑科学];
学科分类号：
0813 ;
摘要：
The objective of this work is to present a zeroth-order shear deformation theory for free vibration analysis of functionally graded (FG) nanoscale plates resting on elastic foundation. The model takes into consideration the influences of small scale and the parabolic variation of the transverse shear strains across the thickness of the nanoscale plate and thus, it avoids the employ use of shear correction factors. Also, in this present theory, the effect of transverse shear deformation is included in the axial displacements by using the shear forces instead of rotational displacements as in available high order plate theories. The material properties are supposed to be graded only in the thickness direction and the effective properties for the FG nanoscale plate are calculated by considering Mori-Tanaka homogenization scheme. The equations of motion are obtained using the nonlocal differential constitutive expressions of Eringen in conjunction with the zeroth-order shear deformation theory via Hamilton's principle. Numerical results for vibration of FG nanoscale plates resting on elastic foundations are presented and compared with the existing solutions. The influences of small scale, shear deformation, gradient index, Winkler modulus parameter and Pasternak shear modulus parameter on the vibration responses of the FG nanoscale plates are investigated.
引用
收藏
页码：227 / 249
页数：23
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