Chladni Figures Simulation on a Rectangular Plate

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.

Manipulation of Microrobots Using Chladni Plates and Multimode Membrane Resonators

(1) The advent of micro/nanorobotics promises to transform the physical, chemical, and biological domains by harnessing opportunities otherwise limited by size. Most notable is the biomedical field, in which the ability to manipulate micro/nanoparticles has numerous applications in biophysics, drug delivery, tissue engineering, and microsurgery. (2) Acoustics, the physics of vibrational waves through matter, offers a precise, accurate, and minimally invasive technique to manipulate microrobots or microparticles (stand-ins for microrobots). One example is through the use of flexural vibrations induced in resonant structures such as Chladni plates. (3) In this research, we developed a platform for precise two-dimensional microparticle manipulation via acoustic forces arising from Chladni figures and resonating microscale membranes. The project included two distinct phases: (i) macroscale manipulation with a Chladni plate in air; and (ii) microscale manipulation using microscale membranes in liquid. In the first phase (macroscale in air), we reproduced previous studies in order to gain a better understanding of the underlying physics and to develop control algorithms based on statistical modeling techniques. In the second phase (microscale in liquid), we developed and tested a new setup using custom microfabricated structures. The macroscale statistical modeling techniques were integrated with microscale autonomous control systems. It is shown that control methods developed on the macroscale can be implemented and used on the microscale with good precision and accuracy.

Chladni Figures in Modal Analysis of a Double-Panel Structure

Analysis of the structural vibration, under the sound excitation is an important part of the quality assurance during the design process of devices. One of the most commonly used method is Laser Doppler Vibrometry (LDV). However, under the rapid fluctuations of temperature, structural resonances are shifted into the other frequencies. In such situation LDV method may be inconvenient, due to the scanning time. In this paper the authors proposed Chladni figures to modal analysis of the double-panel structure, excited by the loudspeaker enclosed inside the casing with a rigid frame. Double-panel structure has been proven to be particularly useful for noise and vibration reduction applications. Vision images, obtained during the experiments are converted to binary patterns, using GLCM matrix, and compared with simulations performed in ANSYS.

Stochastic Models for Chladni Figures

Chladni figures are formed when particles scattered across a plate move due to an external harmonic force resonating with one of the natural frequencies of the plate. Chladni figures are precisely the nodal set of the vibrational mode corresponding to the frequency resonating with the external force. We propose a plausible model for the movement of the particles that explains the formation of Chladni figures in terms of the stochastic stability of the equilibrium solutions of stochastic differential equations.