Size-dependent Effects on the Vibration Behavior of a Ti-moshenko Microbeam subjected to Pre-stress Loading based on DQM

In this paper, size-dependent effects on the vibration behavior of Timoshenko microbeams under pre-stress loading embedded in an elastic foundation, using modified strain gradient theory (MSGT) and surface stress effects, were studied. To consider the surface stress effects, the Gurtin–Murdoch continuum mechanical approach was employed. Using Hamilton’s principle, the governing equations of motion and boundary conditions were obtained and solved numerically using the differential quadrature method (DQM). The effects of pre-stress loading, surface residual stress, surface mass density, Young’s modulus applied to the surface layer, three material length scale parameters, and the elastic foundation coefficients were investigated. For higher aspect ratios, this study found that the effect of the pre-stress loading was negligible for higher modes. Considering size-dependent effects led to increase the stiffness of the matrix and enhance the dimensionless natural frequencies of the Timoshenko microbeam. The MSGT results were higher than those found using other theories. In addition, this research discovered that there were negligible surface stress effects with each of the three material length scale parameters.