The Effect of Wavelength on the Response of Floating Bodies
David R. B. Kraemer, Ph. D.
Assistant Professor
Mechanical Engineering
University of Wisconsin - Platteville
Resonance and frequency-domain effects are well documented for floating bodies
such as barges and moored ships. If a body’s waterplane dimensions are small in
comparison to the wavelength, it can be treated as a point absorber, and its
response can be found in terms of response amplitude operators (RAO's) which are
functions of the wave frequency. However, for wave-energy devices and
breakwaters, the waterplane dimensions of the body are often of the same order as
the wavelength, so wavelength effects become important. Simple relationships
between the wavelength and the response in different degrees of freedom would be
very useful in the design of floating structures. In the present study, a numerical
integration scheme is used to solve an initial-value problem and simulate the
motions of a floating barge in regular waves. Wave forces are calculated
numerically at each time step. Response amplitudes in heave, pitch, and surge are
plotted versus wave frequency (normalized by the barge undamped natural
frequency in the appropriate degree of freedom) and simultaneously versus
wavelength (normalized by the barge length). The simulated data agree well with
expectations, and they show that the wavelength-to-body-length ratio is an
important factor in the design of floating bodies.