Acting forces exerted on a simple harmonic motion body and its movement in a wave-current interaction flow field: An analytical method by linearization of non-linear motion's equation
2017
Kimura, H. (Kochi University, Nankoku, Kochi (Japan)) | Kamii, Y.
Studying acting forces exerted on a fixed or free-moving body and its movement in a flow field, Morison's equation is widely used. Since this equation includes quadratic drag force term, engineers prefer to simplify it by linearization. This paper shows the error effect that should be tolerated by use of the Fourier coefficients. Results are as follows: 1. In case, the velocity of the body is approximately expressed by first-order component with angular velocity omega, exerted non-linear drag force is expressed by sum of the Fourier coefficients with angular velocity omega and its nth components, and it changes the non-linear equation of motion into the linear one. 2. The inertia force of Morison's equation is expressed as the first order component of the body motion with angular velocity omega and acts as the principle driving force of the body. 3. The first order component of the drag force acts as the frictional force and the higher order components of that act as the driving forces. The latter's effect results in infinity at the point of resonance (n omega=omega sub(0)) and substantially decreases when it apart from the point. 4. In case of the studied cases here, the simple harmonic action of motion with omega/omega sub(0) is possible to replicate the simple harmonic free-body motion under the estimated relative error of 10 percent by the linearized equation of motion.
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