Free vibration of three-dimensional anisotropic layered composite nanoplates based on modified couple-stress theory

被引:48
作者
Guo, Junhong [1 ]
Chen, Jiangyi [2 ]
Pan, Ernian [3 ,4 ]
机构
[1] Inner Mongolia Univ Technol, Dept Mech, Hohhot 010051, Peoples R China
[2] Zhengzhou Univ, Sch Mech Engn, Zhengzhou 450001, Peoples R China
[3] Univ Akron, Dept Civil Engn, Akron, OH 44325 USA
[4] Univ Akron, Dept Appl Math, Akron, OH 44325 USA
基金
中国国家自然科学基金;
关键词
Modified couple-stress; Free vibration; Three-dimensional nanoplate; Anisotropic layered composite; Analytical solution; NONLINEAR FREE-VIBRATION; ELASTICITY THEORIES; MICROBEAMS; PLATES; MODEL; PLASTICITY; BONE;
D O I
10.1016/j.physe.2016.11.025
中图分类号
TB3 [工程材料学];
学科分类号
0805 ; 080502 ;
摘要
Based on the modified couple-stress theory, three-dimensional analytical solutions of free vibration of a simply supported, multilayered and anisotropic composite nanoplate are derived by solving an eigenvalue system and using the propagator matrix method. By expanding the solutions of the extended displacements in terms of two-dimensional Fourier series, the final governing equations of motion with modified couple-stress effect are reduced to an eigenvalue system of ordinary differential equations. Analytical expressions for the natural frequencies and mode shapes of multilayered anisotropic composite plates with modified couple-stress effect are then derived via the propagator matrix method. Numerical examples are carried out for homogeneous thick-plates and sandwich composite plates to show the effect of the non-local parameter in different layers and stacking sequence on the mode shapes. The present solutions can serve as benchmarks to various thick-plate theories and numerical methods, and could be further useful for designing layered composite structures involving small scale.
引用
收藏
页码:98 / 106
页数:9
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