33. Axial Vibration of Strain Gradient Micro-rods

In this chapter, size-dependent axial vibration response of micro-sized rods is investigated on the basis of modified strain gradient elasticity theory. On the contrary to the classical rod model, the developed nonclassical micro-rod model includes additional material length scale parameters and can capture the size effect. If the additional material length scale parameters are equal to zero, the current model reduces to the classical one. The equation of motion together with initial conditions, classical and nonclassical corresponding boundary conditions, for micro-rods is derived by implementing Hamilton’s principle. The resulting higher-order equation is analytically solved for clamped-free and clamped-clamped boundary conditions. Finally, some illustrative examples are presented to indicate the influences of the additional material length scale parameters, size dependency, boundary conditions, and mode numbers on the natural frequencies. It is found that size effect is more significant when the micro-rod diameter is closer to the additional material length scale parameter. In addition, it is observed that the difference between natural frequencies evaluated by the present and classical models becomes more considerable for both lower values of slenderness ratio and higher modes.