Based on the surface elasticity theory established by Gurtin and Murdoch, one-dimensional (1D) multi-field coupling model incorporating surface effects for piezoelectric semiconductor (PS) nanostructures is developed, in which the surface effect is treated as a non-classical mechanical boundary condition. With the derived equations, we conduct a theoretical analysis of static bending and free vibration of a simply supported n-type PS beam with open-circuit and electrically isolated boundary conditions at two ends. Numerical results show that the surface effect can stiffen the PS beam, and thus enhance its natural frequencies. Due to the influence of surface effects, the physical quantities such as the effective rigidity and natural frequencies of the PS beam exhibit a considerably significant size-dependent property when the radius R of the PS beam’s cross-section is smaller than 400 nm. For the free vibration of the PS beam, the motion of electrons causes a damping effect. Both the surface effect and initial concentration of electrons have an effect on the quasi-damping ratio of the PS beam. The surface effect tends to enhance the damping effect.

基于 Gurtin 和 Murdoch 建立的表面弹性理论，开发了包含表面效应的压电半导体 (PS) 纳米结构的一维 (1D) 多场耦合模型，其中将表面效应视为非经典力学边界状况。利用导出的方程，我们对两端开路和电隔离边界条件的简支n型PS梁的静态弯曲和自由振动进行了理论分析。数值结果表明，表面效应可以使 PS 梁变硬，从而提高其固有频率。由于表面效应的影响，PS梁的有效刚度和固有频率等物理量表现出相当显着的尺寸相关性，当半径为PS 光束横截面的R小于 400 nm。对于 PS 梁的自由振动，电子的运动会产生阻尼效应。电子的表面效应和初始浓度都对 PS 光束的准阻尼比有影响。表面效应倾向于增强阻尼效应。