Vibration Analysis of Porous Cu-Si Microcantilever Beams in Fluids Based on Modified Couple Stress Theory

Abstract

The vibrations in functionally graded porous Cu-Si microcantilever beams are investigated based on physical neutral plane theory, modified coupled stress theory, and scale distribution theory (MCST&SDT). Porous microcantilever beams define four pore distributions. Considering the physical neutral plane theory, the material properties of the beams are computed through four different power-law distributions. The material properties of microcantilever beams are corrected by scale effects based on modified coupled stress theory. Considering the fluid driving force, the amplitude-frequency response spectra and resonant frequencies of the porous microcantilever beam in three different fluids are obtained based on the Euler–Bernoulli beam theory. The quality factors of porous microcantilever beams in three different fluids are derived by estimating the equation. The computational analysis shows that the presence of pores in microcantilever beams leads to a decrease in Young’s modulus. Different pore distributions affect the material properties to different degrees. The gain effect of the scale effect is weakened, but the one-dimensional temperature field and amplitude-frequency response spectra show an increasing trend. The quality factor is decreased by porosity, and the degree of influence of porosity increases as the beam thickness increases. The gradient factor n has a greater effect on the resonant frequency. The effect of porosity on the resonant frequency is negatively correlated when the gradient factor is small (n1) but positively correlated when the gradient factor is large (n>1).

Keywords

• vibration
• porosity
• scale effects
• microcantilever beams
• quality factor