Dynamic Loadings Induced Vibration of Third Order Shear Deformable FG-CNTRC Beams: Gram-Schmidt-Ritz Method

Source abstract

This research work deals with a study on dynamic behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams under various types of dynamic loads. Carbon nanotubes (CNTs) are used as the reinforcing materials that distribute continuously across the beam thickness. By using third order shear deformable theory (TSDT) in this current study, the straightness and normality of the transverse normal after deformation are unconstrained. The equations of motion based on TSDT are solved by Gram-Schmidt-Ritz method in which the displacement functions are generated via Gram-Schmidt procedure. Additionally, the time-integration of Newmark is also employed to carry out dynamic response of the beams under dynamic loads. Several effects such as material distributions, types of dynamic loads, boundary conditions and so on are taken into account. According to numerical results, it can be revealed that adding small amount of CNTs can reduce considerably the dynamic amplitude of FG-CNTRC beams. Moreover, the dynamic analysis of beam-like structures plays an important role in structural design because mass inertia matrix of the beam being involved in the equations of motion, which yields much larger deflection than that predicted by simple static analysis.