He's frequency formulation for fractal nonlinear oscillator arising in a microgravity space

At a microgravity condition, a spaceflight might be subject to a microgravity-induced vibration. There is no theory so far to study the effect of microgravity on the vibration property. Here we give a fractal vibration model by the two-scale thermodynamics. The fractal oscillator in the microgravity space is modeled by using the fractal derivative, and its frequency is obtained by He's frequency formula. The variational principle of the fractal model is established by the fractal semi-inverse method. The example shows that the proposed method is simple, efficient, and accurate. The frequency-amplitude relationship is elucidated and the effect of the microgravity condition on vibration property is discussed.