Abstract
In this article, size-dependent vibrations and the stability of moving viscoelastic axially functionally graded (AFG) nanobeams were investigated numerically and analytically, aiming at the stability enhancement of translating nanosystems. Additionally, a parametric investigation is presented to elucidate the influence of various key factors such as axial gradation of the material, viscosity coefficient, and nonlocal parameter on the stability boundaries of the system. Material characteristics of the system vary smoothly along the axial direction based on a power-law distribution function. Laplace transformation in conjunction with the Galerkin discretization scheme was implemented to obtain the natural frequencies, dynamical configuration, divergence, and flutter instability thresholds of the system. Furthermore, the critical velocity of the system was evaluated analytically. Stability maps of the system were examined, and it can be concluded that the nonlocal effect in the system can be significantly dampened by fine-tuning of axial material distribution. It was demonstrated that AFG materials can profoundly enhance the stability and dynamical response of axially moving nanosystems in comparison to homogeneous materials. The results indicate that for low and high values of the nonlocal parameter, the power index plays an opposite role in the dynamical behavior of the system. Meanwhile, it was shown that the qualitative stability of axially moving nanobeams depends on the effect of viscoelastic properties in the system, while axial grading of material has a significant role in determining the critical velocity and natural frequencies of the system.
Highlights
Moving systems have a broad spectrum of applications in various engineering fields, especially in nanoscience and nanotechnology such as subminiature belts, silicon acceleration sensors, and nanowires [1,2]
It should be mentioned that the dynamical response of the system can be determined by applying the fourth-order Runge–Kutta technique
The distribution of the material properties the axially functionally graded (AFG) system along the axial direction was considered according to the power-law function
Summary
Moving systems have a broad spectrum of applications in various engineering fields, especially in nanoscience and nanotechnology such as subminiature belts, silicon acceleration sensors, and nanowires [1,2]. Mathematical modeling and vibrational analysis of these applicable structures have attracted much attention in recent decades [3,4,5] In this field, a limited number of Materials 2020, 13, 1707; doi:10.3390/ma13071707 www.mdpi.com/journal/materials. Materials 2020, 13, 1707 experimental studies have been performed and compared with the theoretical analyses [6,7] These investigations revealed that engineers could appropriately trust the results of computer simulations and mathematical modeling techniques [8,9,10]. Tan and Ying [11] theoretically and experimentally investigated the active control of the axially moving strings with various boundary conditions. They presented the closed-form expression for the lateral vibration of the system
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