A new nonlinear fractal vibration of the Euler–Bernoulli beams in a microgravity space

Abstract

Microgravity is an extreme physical environment, where many theories deduced on the earth’s surface become invalid. So a fractal vibration of Euler–Bernoulli beams in a microgravity space is presented in this paper via He’s fractal derivative. With help of the fractal two-scale transform, two methods, namely, the energy balance theory and He’s frequency–amplitude formulation are adopted to seek the solutions of the fractal vibration equation. As expected, the solutions obtained by the two methods are the same. Finally, the numerical example illustrates the effectiveness of the proposed method and the impact of different fractal orders on the vibration behavior is revealed in detail.