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Cybernetics and programming

Numerical method of the solution of a boundary problem for the oscillating membrane

Maier Robert Valerievich

Doctor of Pedagogy

Professor, the department of Physics and Didactics of Physics, Glazov State Pedagogical Training Institute

427628 Russia, The Udmurt Republic, Glazov, Kalinina Street 8A, unit #79

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Abstract: The article considers the simple method of the numerical solution of the two-dimensional wave equation which allows to simulate the following phenomena: 1) propagation and reflection of waves; 2) change of wavelength upon its transition from one environment to another; 3) an interference of waves from several coherent sources; 4) formation of a standing wave; 5) rounding by a wave of obstacles, diffraction of waves; 6) the forced oscillations of an elastic plate; 7) free oscillations of an elastic plate of any form; 8) self-oscillations of an elastic plate. The method of mathematical modeling, a method of the numerical solution of the differential equations in private derivatives, and also a method of color mapping of two-dimensional fields on the screen are used. Novelty of work: the article presents two simple computer programs written in Free Pascal, allowing to simulate rather big set of the phenomena connected about distribution of waves in two-dimensional environments and oscillations of an elastic plate. The given programs can be used in studying numerical methods and bases of computer modeling.

Keywords: forced oscillations, diffraction, interference, membrane oscillating, programming, wave equation, numerical methods, computer modeling, autooscillations, differential equations
This article written in Russian. You can find full text of article in Russian here .

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