Resolving the formation of modern Chladni figures

Abstract

The resonant spectrum of a thin plate driven with a mechanical oscillator is precisely measured to distinguish modern Chladni figures (CFs) observed at the resonant frequencies from classical CFs observed at the non-resonant frequencies. Experimental results reveal that modern CFs generally display an important characteristic of avoided crossings of nodal lines, whereas the nodal lines of classical CFs form a regular grid. The formation of modern CFs and the resonant frequency spectrum are resolved with a theoretical model that characterizes the interaction between the plate and the driving source into the inhomogeneous Kirchhoff-Love equation. The derived formula for determining resonant frequencies is shown to be exactly identical to the meromorphic function given in singular billiards that deals with the coupling strength on the transition between integrable and chaotic features. The good agreement between experimental results and theoretical predictions verifies the significant role of the strong-coupling effect in the formation of modern CFs. More importantly, it is confirmed that the apparatus for generating modern CFs can be developed to serve as an expedient system for exploring the nodal domains of chaotic wave functions as well as the physics of the strong coupling with a point scatterer.