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2014, 8

V. Kezik

Equivalent parameters of a circular homogeneous membrane

language: Russian

received 22.06.2014, published 30.10.2014

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ABSTRACT

The existing technique of determination of the equivalent parameters of a circular homogeneous membrane is briefly considered. Recently suggested (in 2013) new approach to a problem of determination of the equivalent parameters of a circular homogeneous membrane is analysed. According this approach the parameters of the equivalent piston are defined from the condition of identity of laws of the motion (at forced oscillations) of the "averaged" membrane and the equivalent piston, placed to the place of the membrane i.e. in the same conditions of excitation. Parameters of the equivalent piston in this case become depending on frequency of forced excitation (except the mass of the piston). Introduction of an additional condition of equality of a kinetic energy (average for the period) of the piston and the membrane allows to determine the mass of the equivalent piston which also becomes depending on frequency. The similar actions with a potential energy of the piston and the membrane allow to define a rigidity (elastic coefficient) of the equivalent piston in a different way. Comparison of these results by means of calculation shows their complete coincidence. Comparison of a new method with the existing one by the simplified calculation of the acoustic systems including membranes is done. Calculated formulas are illustrated with the graphs for a real membrane. Examples of calculation of the acoustic oscillatory systems including a circular membrane are given. Amendments related to the radiation of sound a membrane are taken into account.

Keywords: vibrations of a circular membrane, equivalent parameters, forced oscillations, kinetic energy of a membrane, potential energy of a membrane, acoustic vibrating system, acoustic radiation of a membrane, drum

20 pages, 4 figures

Сitation: V. Kezik. Equivalent parameters of a circular homogeneous membrane. Electronic Journal “Technical Acoustics”, http://www.ejta.org, 2014, 8.

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Vladimir Kezik graduated from the Physical Faculty of the Moscow State University in 1985. He is currently working at the A.I. Burnazyan Federal Medical Biophysical Center (Moscow, Russia) as a senior researcher. Research interests are acoustic measurements (including vector-phase measurements), development of mathematical models of biophysical objects (and processes) associated with acoustics, general acoustics.

e-mail: vladimirik57(at)mail.ru