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An experimental assessment of the added mass of some plates vibrating in water
Author(s) -
Selby A.,
Severn R. T.
Publication year - 1972
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290010207
Subject(s) - compressibility , laplace transform , added mass , mechanics , vibration , laplace's equation , structural engineering , materials science , geotechnical engineering , geology , engineering , acoustics , physics , mathematics , mathematical analysis , partial differential equation
A reservoir of water is contained by a concrete valley block, a ferrocement wall and a steel plate. Both wall and plate contain an array of pressure transducer sockets (Figures 1 and 2). Using the M.A.M.A. 1 equipment pure modes of vibration are excited. Frequency and mode shape are measured with the reservoir empty. When the reservoir is full hydrodynamic pressure is also measured. These hydrodynamic pressures are compared with Chopra's 2 two‐dimensional, series solution, which includes compressibility of water, and with two‐ and three‐dimensional finite element solutions of Laplace's equation, which do not include compressibility. Chopra's solution is unsatisfactory for modes which contain a vertical node line. The best agreement between experimental and theoretical hydrodynamic pressure is obtained when the latter is obtained from three‐dimensional solutions of Laplace's equations, indicating that compressibility does not play a significant rǒle. This conclusion is supported by agreement between experimental frequencies (reservoir full) and those calculated using added mass obtained from the Laplace solution. Similar conclusions were reached from tests on a floating steel plate, suspended in the surface of the reservoir by a soft spring. Here, dynamic pressure measurements were not made, reliance being placed on agreement between calculated and measured frequencies and mode shapes.