Investigation of fluid viscosity and density on vibration of nano beam submerged in fluid considering nonlocal elasticity theory

Abstract

Predicting the dynamical behavior of nanostructures in contact with fluid is of paramount importance owing to their vast range of applications in civil engineering, aerospace, etc. Therefore, the free vibration of a nonlocal Euler-Bernoulli beam in contact with fluid is studied in this research. Using the Navier-Stokes relation, the interaction forces between the fluid and nanobeam are obtained. The equation of motion is solved using the Galerkin method of weighted residuals, and the natural frequency values in different fluids are presented, considering the viscosity effect. Further, the fluid-solid interaction model on a macroscopic scale is compared with the finite element analysis results. By considering the fluid parameters to be zero, the results of the nonlocal beam have been validated with past research. According to the obtained results, when studying the vibration of nanobeams, while density has a remarkable impact on the reduction of nanobeam natural frequencies, the fluid viscosity can be neglected. The fluid has the greatest impact on lower modes, whereas the nonlocal parameter exerts the biggest influence on higher modes. Moreover, in all vibration modes, with the increase of the nonlocal parameter, the effect of the fluid on the reduction of the natural frequencies increases, and in the nanoscale, it has a more significant role in changing the vibrational behavior of the system compared to the classical condition.

Keywords

• Nano-structures
• Vibration
• Fluid-solid interaction
• Nonlocal elasticity