Circular membrane with a centrally-located opening – analytical model using parameterisation of the non-empty torurs
Aleksandra Waszczuk-Młyńska , Stanisław Radkowski
AbstractThis paper discusses a model of the circular membrane using the second order basic partial differential equation. The aim of this work is to present a new analytical model of a membrane with an opening in its central part (damage-simulating opening). Parametrisation applied in the model is based on the parametrisation of the torus with one difference, i.e. the radius defining the torus’s circle is not a constant quantity , but it varies within the range , where is a maximal radius of the circle defining the torus. In order to build a model of a damaged membrane, only one surface of a non-empty torus is needed, that is a surface created by the torus’s circle rotation. A new partial differential equation is computed by means of the Fourier method of separation of variables, and next, by applying the Bessel substitution. The model’s correctness has been verified based on the experiment. The obtained data resulting from the model (in this case the frequency of natural vibrations) was verified as a result of the experiment.
|Journal series||ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik, ISSN 0044-2267|
|Publication size in sheets||0.5|
|Keywords in English||circular membrane, the Bessel substitution, the second order partial differential equation, torus|
|Score||= 70.0, 29-01-2020, ArticleFromJournal|
|Publication indicators||= 1; = 1; : 2017 = 1.085; : 2018 = 1.467 (2) - 2018=1.351 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.