Wave propagation analysis of magnetic nanotubes conveying nanoflow

According to the nonlocal strain gradient theory, wave propagation in magnetic nanotubes conveying magnetic nanoflow under longitudinal magnetic field is inspected. The nonlocal strain gradient Timoshenko beam model is coupled with magnetic nanoflow considering slip boundary condition to model fluid structure interaction. By applying Hamilton’s principle, the size-dependent governing equations of motion have been obtained. Calculation of the wave frequency as well as phase velocity has been carried out based on the harmonic solution. The influences of strain gradient length scale, nonlocal parameter, Knudsen number, longitudinal magnetic field and magnetic nanoflow on nanotubes’ wave propagation behavior have been examined. According to analytical results, the magnetic intensity related to the longitudinal magnetic field contributes significantly to increasing nanotubes’ wave frequency as well as phase velocity. Besides, the magnetic nanotubes conveying magnetic nanoflow predict the highest phase velocity and wave frequency. Also, the wave frequency decrease when the nonlocal parameter increases or the strain gradient length scale decreases. Moreover, an increase in fluid velocity reduces the wave frequency and phase velocity. Article highlights The nonlocal strain gradient Timoshenko beam model is considered. Wave propagation in magnetic nanotubes conveying magnetic nanoflow is studied. Longitudinal magnetic field and magnetic nanoflow with considering slip boundary condition is inspected. Wave frequency decrease when the nonlocal parameter increases or the strain gradient length scale decreases. Increase in fluid velocity reduces the wave frequency and phase velocity.

A Nonlocal Strain Gradient Approach for Out-of-Plane Vibration of Axially Moving Functionally Graded Nanoplates in a Hygrothermal Environment

Vibration analyses on axially moving functionally graded nanoplates exposed to hygrothermal environments are presented. The theoretical model of the nanoplate is described via the Kirchhoff plate theory in conjunction with the concept of the physical neutral layer. By employing the nonlocal strain gradient theory, the governing equation of motion is derived based on Hamilton’s principle. The composite beam function method, as well as the complex modal approach, is utilized to obtain the vibration frequencies of axially moving functionally graded nanoplates. Some benchmark results related to the effects of temperature changing, moisture concentration, axial speed, aspect ratio, nonlocal parameter, and the material characteristic scale parameter on the stiffness of axially moving functionally graded nanoplates are obtained. The results reveal that with increasing the nonlocal parameter, gradient index, temperature changing, moisture concentration, and axial speed, the vibration frequencies decrease. The frequencies increase while increasing the material characteristic scale parameter and aspect ratio. Moreover, there is an interaction between the nonlocal parameter and material characteristic scale parameter, influencing and restricting each other.