Scale-dependent torsional frequency analysis of right triangle anisotropic advanced composite microscale rods

Abstract

Despite several theoretical investigations on the torsional dynamic behavior of non-circular micro/nanorods, the torsional behavior of right triangle cross-section is still unevaluated. Therefore, Timoshenko-Gere theory in conjunction with nonlocal strain gradient theory is developed for modeling the scale-dependent torsional dynamic of right triangle microscale rods. Various anisotropic materials, i.e. hexagonal, trigonal, triclinic, and monoclinic materials are regarded as the constituent material of microscale rods. The shear stress function is developed for right triangle shape and according to the calculated shear stress function, the warping function of right triangle shape is obtained. The nonlocal governing equation of the torsional dynamic of anisotropic microrods is obtained with the help of the energy approach and solved using an analytical method by regarding two different boundary conditions. The accuracy of the proposed model is validated with recent similar investigations. Because of the lack of mechanical research on right triangle microrods, the proposed methodology was validated with equilateral triangle nanowire reported in the literature. Eventually, the various remarkable variants’ effects on change of scale-dependent torsional frequency are assessed comprehensively. It is found that hexagonal and triclinic materials have the largest and smallest values of frequency. Also, nonlocal parameter, b/h ratio play a decreasing role and length scale parameters and mode number plays an increasing role.