Papers by Keyword: Multiple Scales Method

Abstract: The effect of waving bottom on the fluid surface wave was investigated. Starting from the basic equations of potential flow theory and boundary conditions, we used the multiple scales perturbation method to deduce fluid surface waves satisfy the first-order approximate equation and second-order approximate equation. Under the second-order approximation, the fluid surface waveform was simulated with the Matlab in the presence of different waving bottom form. The results show that there are three solitary waves on the surface of the fluid. With the development of time, the amplitude of each solitary wave has not changed. It seems that they are not affected each other and propagate independently. So it suggests that the waving bottom is effective for maintaining surface wave energy balance income and expenditure in spreading process.

Abstract: Transverse vibration of an axially moving viscoelastic sandwich beam is investigated in this paper. Based on the Kelvin constitutive equation, transverse controlling equation is established. First of all, the multiple scales method is applied to obtained steady-state response. Elimination of scales terms will give us the amplitude of vibrations. Additionally, the stability conditions of trivial and non-trivial solutions are analyzed using Routh-Hurwitz criterion. Eventually, numerical results are obtained to show the thickness of core layer, mean velocity, the amplitude of fluctuation effects on natural frequencies and response curves.