As a first attempt, the vibration and stability analysis of magnetically embedded spinning axially functionally graded (AFG) nanotubes conveying fluid under axial loads is performed based on the nonlocal strain gradient theory (NSGT). A detailed parametric investigation is conducted to elucidate the influence of key factors such as material distribution type and size-dependent parameters on the divergence and flutter instability borders. Also, a comparative study is conducted to evaluate the available theories in the modeling of nanofluidic systems. The material characteristics of the system are graded along the longitudinal direction based on the power-law and exponential distribution functions. To accurate model and formulate the system, the no-slip boundary condition is considered. Adopting the Laplace transform and Galerkin discretization technique, the governing size-dependent dynamical equations of the system are solved. The backward and forward natural frequencies, as well as critical fluid and spin velocities of the system, are extracted. Besides, an analytical approach is applied to identify the instability thresholds of the system. Dynamical configurations, Campbell diagrams, and stability maps are analyzed. Meanwhile, it is concluded that, in contrast to the influence of nonlocal and density gradient parameters, the increment of strain gradient and elastic modulus gradient parameters expands the stability regions and alleviate the destabilizing effect of the axial compressive load.

中文翻译：

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旋转功能梯度纳米管输送流体的振动

作为第一次尝试，基于非局部应变梯度理论 (NSGT) 对在轴向载荷下输送流体的磁性嵌入旋转轴向功能梯度 (AFG) 纳米管进行振动和稳定性分析。进行了详细的参数研究，以阐明关键因素（例如材料分布类型和尺寸相关参数）对发散和颤振不稳定边界的影响。此外，还进行了一项比较研究，以评估纳米流体系统建模中的可用理论。根据幂律和指数分布函数沿纵向对系统的材料特性进行分级。为了精确建模和制定系统，考虑了无滑移边界条件。采用拉普拉斯变换和伽辽金离散化技术，求解了系统与尺寸相关的控制动力学方程。提取系统的后向和前向自然频率，以及临界流体和自旋速度。此外，还应用了一种分析方法来识别系统的不稳定性阈值。分析了动态配置、坎贝尔图和稳定性图。同时得出结论，相对于非局部和密度梯度参数的影响，应变梯度和弹性模量梯度参数的增加扩大了稳定区域，减轻了轴向压缩载荷的失稳效应。以及系统的临界流体和自旋速度，都被提取出来。此外，还应用了一种分析方法来识别系统的不稳定性阈值。分析了动态配置、坎贝尔图和稳定性图。同时得出结论，相对于非局部和密度梯度参数的影响，应变梯度和弹性模量梯度参数的增加扩大了稳定区域，减轻了轴向压缩载荷的失稳效应。以及系统的临界流体和自旋速度，都被提取出来。此外，还应用了一种分析方法来识别系统的不稳定性阈值。分析了动态配置、坎贝尔图和稳定性图。同时得出结论，相对于非局部和密度梯度参数的影响，应变梯度和弹性模量梯度参数的增加扩大了稳定区域，减轻了轴向压缩载荷的失稳效应。