In this study, a rational beam-elastic substrate model with inclusion of nonlocal and surface-energy effects is developed for bending and buckling analyses of nanobeams lying on elastic substrate media. The beam-section kinematics follows Euler–Bernoulli beam hypothesis. The thermodynamics-based strain gradient theory is employed to represent the beam-bulk nonlocality while the Gurtin–Murdoch surface theory is utilized to account for the surface-free energy. Interaction between the beam and its underlying substrate medium is described by the Winkler foundation model. The governing equilibrium equation and admissible natural boundary conditions are consistently obtained using the virtual displacement principle. To characterize bending and buckling responses of the new beam-elastic substrate model, three numerical examples are employed: the first demonstrates the capability of the proposed model in eliminating the paradoxical behavior present in the Eringen nonlocal differential model; the second characterizes the bending response of the free–free nanobeam-elastic substrate system; and the third examines the influences of several model parameters as well as the size-dependent effect on the buckling response of the simply supported nanobeam-elastic substrate system.

在这项研究中，开发了一种包含非局部和表面能效应的合理的梁弹性基底模型，用于对位于弹性基底介质上的纳米束的弯曲和屈曲进行分析。横梁截面运动学遵循欧拉-伯努利横梁假设。基于热力学的应变梯度理论用于表示梁体的非局部性，而Gurtin-Murdoch表面理论则用于解释表面自由能。Winkler基础模型描述了光束与其下层基板介质之间的相互作用。使用虚拟位移原理一致地获得控制平衡方程和容许的自然边界条件。为了表征新的梁弹性基底模型的弯曲和屈曲响应，采用了三个数值示例：第一个证明了所提出的模型具有消除Eringen非局部微分模型中存在的自相矛盾行为的能力。第二个特征是自由-自由纳米束-弹性基底系统的弯曲响应。第三部分研究了几个模型参数的影响以及尺寸依赖性对简单支撑的纳米束-弹性基底系统屈曲响应的影响。