Size-dependent transverse vibration of microbeams

Abstract

In this chapter, a new microstructure-dependent higher-order shear deformation beam model is introduced to investigate the vibrational characteristics of microbeams. This model captures both the size and shear deformation effects without the need for any shear correction factors. The governing differential equations and related boundary conditions are derived by implementing Hamilton's principle on the basis of modified strain gradient theory in conjunction with trigonometric shear deformation beam theory. The free vibration problem for simply supported microbeams is analytically solved by employing the Navier solution procedure. Moreover, a new modified shear correction factor is firstly proposed for Timoshenko (first-order shear deformation) microbeam model. Several comparative results are presented to indicate the effects of material length-scale parameter ratio, slenderness ratio, and shear correction factor on the natural frequencies of microbeams. It is observed that effect of shear deformation becomes more considerable for both smaller slenderness ratios and higher modes.