Abstract
An analytical model for creating flat Chladni figures is presented. The equation of a standing wave in the simplest boundary conditions and the Fourier transform are used. Top view images are shown at different frequencies. The practical significance of the results obtained for the further development of the field of creating Chladni figures based on standing waves of different physical nature has been determined.
Highlights
Many methods have been demonstrated for creating metasurfaces for various purposes, for example, efficient absorption of solar energy [1], control of transverse vertical waves [2], multiband superabsorption and terahertz sensing [3]
The larger the coefficients at frequencies, the more inflection lines appear for standing waves, which is obvious, if we increase the generation frequency, we increase the number of standing wave peaks
This paper presents an analytical model for constructing Chladni figures for a dielectric plate using eigenvalue problem for the Laplace operator in a rectangle with Dirichlet boundary conditions
Summary
Many methods have been demonstrated for creating metasurfaces for various purposes, for example, efficient absorption of solar energy [1], control of transverse vertical waves [2], multiband superabsorption and terahertz sensing [3]. Adequate, but not universal, analytical models for the creation of Chladni figures are built, since they did not take into account the nature of the waves, the structure of the plate, the material, the parameters of environment, etc. This article discusses a method for creating metasurfaces based on Chladni figures. An analytical model for constructing a top view of Chladni figures using a stationary wave model is presented. On the basis of the analytical model, a number of Chladni figures are constructed for some combinations of the values of the model parameters. The values of the parameters were chosen from the point of view of practical interest, based on the effect of increasing the complexity of the pattern and the number of transition lines of standing waves (inflection lines of the density gradient of redistributed surface masses). Our model describes the formation of Chladni figures through simplifying assumptions, and allows their numerical simulation in terms of coefficients that can be interpreted as environmental parameters or can be derived using them
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