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

چکیده مقاله

In this paper, size-dependent effect on vibration behavior of Timoshenko micro-beam under pre-stress loading embedded in an elastic foundation using modified strain gradient theory (MSGT) and surface stress effect is studied. To consider the surface stress effect, the Gurtin–Murdoch continuum mechanic approach is employed. Using Hamilton’s principle, the governing equations of motion and boundary conditions are obtained and solved numerically using differential quadrature method (DQM). The effects of pre-stress load, surface residual stress, surface mass density, Young’s modulus of surface layer, three material length scale parameters and elastic foundation coefficients are investigated. It is concluded that for higher aspect ratio, the effect of pre-stress load is negligible in higher modes. Also, with considering the size dependent effect, the stiffness of matrix increases and then the dimensionless natural frequencies of Timoshenko micro beam increase. This result for MSGT is higher than that for the other theories. Also, the results of this research for surface stress effect with respect to three material length scale parameters are negligible.