Free and forced oscillations of a gate system as proposed for the protection of Venice Lagoon: the discrete and dissipative model.

This paper describes the dynamics of a mathematical model for the mobile barriers designed to close the tidal inlets of the Venice Lagoon and to defend the city from recurrent high waters. The barriers consist of a large number of steel caissons (hereafter referred to as gates) connected to the seabed with hinges. The gates usually rest horizontally on the sea bottom allowing mass exchange between the sea and the lagoon and are brought into operation during high tides by the inflow of compressed air. When in operation the gates close the lagoon openings even though they may oscillate around their mean position. In the present contribution the barriers are modelled by vertical rigid plates which can slide along the bottom and are subjected to a recoil effect simulating Archimedes' force acting on the real gates. First, the in-phase motion of the gates produced by an incoming wave is studied. Then, by means of a linear stability analysis of this basic motion, it is shown that oscillations of the gates, such that contiguous gates oscillate out of phase, can be excited for suitable values of the wave and barrier characteristics. In particular, the existence of a critical value of the amplitude of the incoming waves is pointed out, below which the in-phase motion of the gates is stable. A quantitative comparison with previous studies of the problem which used a simple model is made.