This paper aims at studying the vibrational behavior and dynamical stability of small-scale axially moving beams resting on the viscoelastic-Pasternak foundation in a hygro-thermal environment, according to a nonlocal strain gradient Rayleigh beam model. The Galerkin procedure is applied to determine the eigenvalues of the dynamic system of equations together with the stability regions of the system. A comparison study of the proposed method is performed, first, against the available literature. Thus, we examine the effect of the rotary inertia, flexural stiffness, boundary conditions, scale parameters, foundation conditions, and environmental loads, on the vibrational frequencies and stability boundaries of the system. Based on the numerical results, an increased flexural stiffness and strain gradient parameter enhance the vibrational frequencies of the system. It is also demonstrated that the destructive effects of hygro-thermal conditions can be alleviated by a fine-tuning of the foundation characteristics. The outcomes of the present research can represent a useful benchmark for optimization design purposes of moving nanosystems in complex environmental conditions.

中文翻译：

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湿热环境下粘弹性-帕斯捷尔纳克基础上小尺度轴向移动支撑梁振动与稳定性响应的非局域研究

本文旨在根据非局部应变梯度瑞利梁模型，研究湿热环境下粘弹性-Pasternak 基础上的小尺度轴向移动梁的振动行为和动力稳定性。应用 Galerkin 过程来确定动态方程组的特征值以及系统的稳定区域。首先，针对现有文献对所提出的方法进行了比较研究。因此，我们研究了转动惯量、抗弯刚度、边界条件、尺度参数、基础条件和环境载荷对系统振动频率和稳定性边界的影响。根据数值结果，增加的抗弯刚度和应变梯度参数提高了系统的振动频率。还表明，通过微调地基特性可以减轻湿热条件的破坏性影响。本研究的结果可以代表一个有用的基准，用于在复杂环境条件下移动纳米系统的优化设计目的。