In this study, free vibration analysis of nanobeams under various non-ideal supports have presented. Size effect of nanobeams has applied by utilizing modified couple stress theory. Hamilton’s principle has been used to derive the equation of motion. Governing equation has subjected to non-ideal boundary conditions which are modeled as linear functions including an introduced weighting factor ( k ). Obtained numerical results have verified by comparing with the published results. Results show that fundamental resonance frequencies of non-ideal clamped nanobeams are significantly decreased when it is compared to ideal supports. However, non-ideal simply supports creates a minor increase effect on fundamental frequencies with respect to clamped ones. Also, nano-size effect has investigated for non-ideal supports. It has found that, the smaller cross-sectional size of nanobeam causes increasing effect of non-ideal supports on fundamental frequencies.

中文翻译：

---

基于改进耦合应力理论的非理想支撑下纳米束的自由振动

在这项研究中，提出了在各种非理想支撑下的纳米束自由振动分析。纳米束的尺寸效应已经通过利用改进的耦合应力理论得到了应用。汉密尔顿原理已被用来推导运动方程。控制方程受到非理想边界条件的影响，这些边界条件被建模为包含引入的加权因子（k）的线性函数。通过与公开的结果进行比较，已验证了获得的数值结果。结果表明，与理想支撑相比，非理想夹持纳米束的基本共振频率显着降低。但是，非理想的支座相对于钳位的支座会对基频产生较小的增加效果。同样，已经研究了纳米尺寸效应对非理想载体的影响。发现，