Nonlinear forced vibration of clamped-free beam reinforced by carbon nanotubes with an attached mass

Due to the different application of the beam-attached mass structures, and also increment of the importance of nanocomposite materials, in this paper, the study on nonlinear vibrations of composite cantilever beam with tip mass under the harmonic excitation is presented. The equations of motion are derived using a geometrically exact formulation based on the Cosserat theory for rods. The Muri-Tanaka model is implemented to formulate the mechanical properties of carbon nanotube reinforced beam. The Galerkin approach is implemented to derive the linear natural frequencies and corresponding mode shapes of the mentioned beam with tip mass. The extracted mode shapes are employed to discretize the equation of motion. The discretized equations of motion, which includes geometrical and inertial non-linearitites, are solved using the method of multiple scales and the frequency response is extracted. The effect of attached mass, carbon nanotube volume fraction and the excitation force amplitude on the frequency response of the system is investigated.