Chladni figures have stimulated numerous scientific explorations in physics including quantum chaos, self-organization of granular media, microscale acoustofluidics, and pattern formation. It is further authenticated that nearly the same resonant modes can be obtained by using a larger coupling strength α when a smaller upper index N is exploited in the calculation.Įrnst Chladni in the 18th century demonstrated a classical experiment related to acoustic phenomenon by means of vibrating a thin plate with a bow and manifesting the resonant nodal-line pattern with small sands. The asymptotic behavior for the upper index N is thoroughly explored to verify that the coupling strength of α = 1.0 can make the theoretical resonant modes agree excellently with the maximum entropy states as N → ∞. The δ potential of the point interaction is numerically modelled by a truncated basis with an upper index N. The coupling strength associated with the point interaction is characterized by a dimensionless factor α. To investigate the origin of maximum entropy states, the inhomogeneous Helmholtz equation is modified to consider the point interaction coming from the driving oscillator. The resonant modes generated from the modern Chladni experiment are systematically confirmed to intimately correspond to the maximum entropy states obtained from the inhomogeneous Helmholtz equation for the square and equilateral triangle plates.
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