Dynamic Loadings Induced Vibration of Third Order Shear Deformable FG-CNTRC Beams: Gram-Schmidt-Ritz Method (Advances in Applied Mathematics and Mechanics, 2022)
This research work deals with a study on dynamic behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams under varioustypes of dynamic loads. Carbon nanotubes (CNTs) are used as the reinforcing materials that distribute continuously across the beam thickness. By using third order sheardeformable theory (TSDT) in this current study, the straightness and normality of thetransverse normal after deformation are unconstrained. The equations of motion basedon TSDT are solved by Gram-Schmidt-Ritz method in which the displacement functions are generated via Gram-Schmidt procedure. Additionally, the time-integrationof 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-likestructures plays an important role in structural design because mass inertia matrix ofthe beam being involved in the equations of motion, which yields much larger deflection than that predicted by simple static analysis.