Excitation of motion modes

It was noted earlier that within the linearised problem there is no mechanism for the excitation of sloshing trapped modes when the structure is allowed to move freely. The same is not true of motion modes and this is illustrated in the figure below. Here a two-dimensional motion trapping structure is displaced vertically and released from rest. The dashed line shows the displacement of the structure and the solid line the displacement of the mid point of the internal free surface, both as a function of time. After an initial transient has died away both time traces show oscillations of constant amplitude with the same frequency; Fourier analysis shows that this is the trapped-mode frequency. A motion trapped mode can be excited by the release from rest of a displaced structure.

The second figure below shows the result of the incidence of a wave packet on a motion trapping structure that is initially at rest. Again, the dashed line shows the displacement of the structure and the solid line the displacement of the mid point of the internal free surface, both as a function of time. The wave packet excites the structure as it passes but no persistent oscillation is established. An incident wave cannot excite a motion trapped mode.