Free vibration of functionally graded graphene platelet-reinforced porous beams with spinning movement via differential transformation method

This work analyzes the free vibration of a spinning functionally graded graphene platelet-reinforced metal foam (FG-GPLRMF) beam. The differential transformation method is extended to analyze flap-wise bending vibration and chordwise bending vibration with Coriolis force effect for the first time. The beam is modeled using the Euler–Bernoulli beam theory. The Halpin–Tsai micromechanics model is utilized to predict effective material properties. Various types of graphene platelet (GPL) and porosity distributions are considered. The governing equations and corresponding boundary conditions of the FG-GPLRMF beam are obtained via Hamilton’s principle. Results show that the vibration characteristics of the FG-GPLRMF beam are affected by the GPL geometry size, types of porosity, and GPL distributions. Among different types of porosity, the Porosity-A causes the highest fundamental natural frequency, while the Porosity-B corresponds to the lowest one of the spinning FG-GPLRMF beam in most cases. Moreover, the GPL pattern and porosity distribution have a coupled effect on the bending vibration of the spinning FG-GPLRMF beam.