In the current paper, size-dependent mechanical analysis of functionally graded porous (FGP) nanobeams resting on Pasternak foundation in thermal environment is presented based on nonlocal strain gradient theory and Gurtin-Murdoch surface elasticity theory. The nanobeam is modeled based on Euler-Bernoulli beam theory, Timoshenko beam theory and Reddy's third-order shear deformation theory and the set of the governing equations are solved for a clamped-clamped FGP nanobeam using generalized differential quadrature method. Numerical results show that as porosity parameter increases, static deflection increases and critical buckling load decreases, but its effect on the fundamental frequency strongly depends on the porosity distribution pattern. It was revealed that among all studied porosity distribution patterns, the minimum value of the static deflection and maximum values of critical buckling load and fundamental frequency can be achieved using symmetric distribution pattern of pores. It is concluded that tensional residual stress reduces static deflection and increases both critical buckling load and fundamental frequency and temperature rise has reverse effects.

中文翻译：

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结合表面效应的 Pasternak 基础上 FG 多孔纳米梁的弯曲、屈曲和振动分析

在本文中，基于非局部应变梯度理论和Gurtin-Murdoch表面弹性理论，提出了基于Pasternak基础的功能梯度多孔（FGP）纳米梁在热环境中的尺寸依赖性力学分析。基于欧拉-伯努利梁理论、Timoshenko 梁理论和 Reddy 的三阶剪切变形理论对纳米束进行建模，并使用广义微分求积法求解了夹紧-夹紧 FGP 纳米束的控制方程组。数值结果表明，随着孔隙度参数的增加，静态挠度增加，临界屈曲载荷减小，但其对基频的影响很大程度上取决于孔隙度分布模式。结果表明，在所有研究的孔隙度分布模式中，静态挠度的最小值和临界屈曲载荷和基频的最大值可以通过孔隙的对称分布模式来实现。得出的结论是，拉伸残余应力降低了静态挠度并增加了临界屈曲载荷和基频，温升具有相反的效果。