On the Vibrations and Stability of Moving Viscoelastic Axially Functionally Graded Nanobeams

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.

Viscoelastic stressed microbeam analysis based on Moore–Gibson–Thompson heat equation and laser excitation resting on Winkler foundation

“…However, it is clear from the numerical results and the shapes that viscosity has a clear effect on all different distributions, which agrees well with the observations obtained in previous studies, such as those referred to in Refs. 73–75.…”

Nonlocalized thermal behavior of rotating micromachined beams under dynamic and thermodynamic loads

“…Lin and Trethewey [44] investigated the dynamic arbitrary motions of a spring-mass-sweeper device of an elastic beam subject to dynamic loads by employing Euler-Bernoulli beam model. Shariati et al [45] presented the size-dependent stability analysis of moving viscoelastic functionally graded nanobeams on the basis of nonlocal elasticity theory. Jaiswal and Iyengar [46] considered the dynamic response of an endless long beam resting on a finite depth substrate subject to moving force actions.…”

“…Shariati et al. [45] presented the size‐dependent stability analysis of moving viscoelastic functionally graded nanobeams on the basis of nonlocal elasticity theory. Jaiswal and Iyengar [46] considered the dynamic response of an endless long beam resting on a finite depth substrate subject to moving force actions.…”

Stability Analysis of Nanobeams by Modified Finıie Element Transfer Matrix Method

“…Exact solutions were used for the analysis of the prismatic nanobeam. Shariati et al [2] investigated the vibrations and stability of functionally graded nanobeams by numerical and analytical methods.…”