At nanoscale, surface free energies of the atoms located on the free surfaces of structures significantly affect their mechanical characteristics. In this study, nonlinear large-amplitude free vibration response of nanoshells prepared from functionally graded porous materials (FGPM) is investigated by taking into account surface stress size effects and vibrational mode interactions. Non-classical shell model is constructed on the basis of the Gurtin–Murdoch type of the surface theory of elasticity having the capability of capturing surface stress size dependency. The accuracy of nonlinear vibration analysis is improved by incorporating the interaction of the main vibration mode and the first, third and fifth symmetric oscillation modes. Moreover, the closed-cell Gaussian-Random field scheme is put to use to extract the mechanical characteristics of FGPM nanoshell. Multiple timescales technique is then applied to achieve surface stress elastic-based nonlinear frequency of FGPM nanoshell analytically for different interactions between vibrational modes. It is revealed that by incorporating the interactions of the main vibration mode and higher symmetric oscillation modes, the behavior of the backbone curves belongs to the nonlinear free oscillation response of FGPM nanoshells changes from hardening to softening schema. It is found that when only the main vibration mode is taken into account, surface elasticity effects makes an enhancement in the significance of the hardening schema. However, by considering the interactions of higher symmetric oscillation modes, surface elasticity effects makes a reduction in the significance of the softening schema.

中文翻译：

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包含振动模式相互作用的FGPM纳米壳的尺寸相关大振幅自由振荡

在纳米尺度上，位于结构自由表面上的原子的表面自由能显着影响其机械特性。在这项研究中，通过考虑表面应力尺寸效应和振动模式相互作用，研究了由功能梯度多孔材料（FGPM）制备的纳米壳的非线性大振幅自由振动响应。非经典壳模型是基于Gurtin–Murdoch类型的表面弹性理论构建的，具有捕获表面应力大小相关性的能力。通过结合主振动模式与第一，第三和第五对称振动模式的相互作用，可以提高非线性振动分析的准确性。此外，利用闭孔高斯-随机场方法提取了FGPM纳米壳的力学特性。然后应用多个时间尺度技术，通过分析振动模式之间的不同相互作用，实现基于表面应力弹性的FGPM纳米壳的非线性频率。结果表明，通过结合主振动模态和较高对称振动模态的相互作用，主链曲线的行为属于FGPM纳米壳从硬化到软化转变的非线性自由振动响应。发现仅考虑主振动模式时，表面弹性效应会增强硬化方案的重要性。但是，考虑到较高对称振荡模式的相互作用，