Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material
Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material
复制标题
功能梯度材料非局部应变梯度梁的非线性弯曲和自由振动分析
DOI：
10.1016/j.ijengsci.2016.07.011
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发表时间：
2016-10-01
影响因子：
6.6
通讯作者：
Hu, Yujin
中科院分区：
文献类型：
--
作者：
Li, Li;Hu, Yujin
在非局部应变梯度理论的框架下，建立了考虑两组分功能梯度材料厚度幂函数变化的尺寸相关的非线性Euler-Bernoulli梁模型和Timoshenko梁模型，以研究材料的非线性弯曲和自由振动行为。FG梁的中面拉伸效应引起的非线性是所考虑的弯曲和自由振动问题的非线性来源。利用哈密顿原理，导出了与尺寸有关的运动方程和边界条件。梁模型包含材料长度、尺度和非局域参数，以同时考虑原子间长程力和微结构变形机制的影响。在铰-铰边界条件下，推导了非局部应变梯度Euler-Bernoulli梁和Timoshenko梁的非线性弯曲挠度和自由振动频率的解析解。研究了两组分FG材料的厚度指数变化和尺寸相关参数对非线性弯曲挠度和自振频率的影响。由于梁的中面拉伸效应带来的固有刚性效应，在相同的力作用下，梁的非线性弯曲挠度小于其线性挠度，而对于相同振幅的非线性振子，其非线性振动频率高于其线性挠度。梁中FG材料的贯通厚度对梁的非线性弯曲挠度和自振频率有较大影响。当非局部参数小于材料特性参数时，非线性FG梁表现出刚度硬化效应。当材料特性参数小于非局部参数时，FG梁表现出刚度软化效应。(C)2016爱思唯尔有限公司。保留所有权利。
Size-dependent nonlinear Euler-Bernoulli and Timoshenko beam models, which account for the through-thickness power-law variation of two-constituent functionally graded (FG) materials, are derived to investigate the nonlinear bending and free vibration behaviors in the framework of the nonlocal strain gradient theory. The nonlinearity due to the stretching effect of the mid-plane of the FG beam is the source of nonlinearity of the considered bending and free vibration problems. The size-dependent equations of motion and boundary conditions are derived by employing the Hamilton's principle. The beam models contain material length scale and nonlocal parameters to consider the effects of both inter-atomic long-range force and microstructure deformation mechanism. In the case of hinged-hinged boundary conditions, the analytical solutions for the nonlinear bending deflection and free vibration frequencies of nonlocal strain gradient Euler-Bernoulli and Timoshenko beams are deduced. The influences of the through-thickness power-law variation of a two-constituent FG material and size-dependent parameters on nonlinear bending deflection and free vibration frequencies are investigated. Due to the intrinsic stiffening effect brought by the stretching effect of the mid-plane of the beam, the nonlinear bending deflections are smaller than their linear counterparts under the action of the same force, while the nonlinear vibration frequencies are higher than their linear counterparts for the same amplitude of the nonlinear oscillator. The nonlinear bending deflections and free vibration frequencies can be affected significantly by the through-thickness grading of FG materials in the beam. When the nonlocal parameter is smaller than the material characteristic parameter, the nonlinear FG beam reveals a stiffness-hardening effect. When the material characteristic parameter is smaller than the nonlocal parameter, the FG beam reveals a stiffness-softening effect. (C) 2016 Elsevier Ltd. All rights reserved.