Search Results (8)

In this study, the resonant characteristics of the off-center-driven Chladni plates were systematically investigated for the square and equilateral triangle shapes. Experimental results reveal that the number of the resonant modes is considerably increased for the plates under the off-center-driving in comparison to the on-center-driving. The Green’s functions derived from the nonhomogeneous Helmholtz equation are exploited to numerically analyze the information entropy distribution and the resonant nodal-line patterns. The experimental resonant modes are clearly confirmed to be in good agreement with the maximum entropy states in the Green’s functions. Furthermore, the information entropy distribution of the Green’s functions can be used to reveal that more eigenmodes can be triggered in the plate under the off-center-driving than the on-center-driving. By using the multiplication of the resonant modes in the off-center-driving, the dispersion relation between the experimental frequency and the theoretical wave number can be deduced with more accuracy. It is found that the deduced dispersion relations agree quite well with the Kirchhoff–Love plate theory. Full article

In general, sound waves propagate radially outwards from a point source. These waves will continue in the same direction, decreasing in intensity, unless a boundary condition is met. To arrive at a universal understanding of the relation between frequency and wave propagation within spatial boundaries, we explore the maximum entropy states that are realized as resonant modes. For both circular and polygonal Chladni plates, a model is presented that successfully recreates the nodal line patterns to a first approximation. We discuss the benefits of such a model and the future work necessary to develop the model to its full predictive ability. Full article

A square metal plate (Chladni plate) is excited harmonically by a vibration shaker, while the whole system is set in an anechoic chamber to stop reflections, isolate the system from sound entering from the surroundings, and deal with direct sounds only. As far as the authors are aware, such an arrangement has not been achieved so far. Vibration modes are visualized by using poppy grains scattered over the upper surface of the plate and are also recorded by a camera located above it, inserted among the acoustic wedges on the roof of the chamber, which made it possible to record the patterns and avoid unpleasant sounds associated with some of them. Four distinctive vibration modes of the plate are then originally identified using vibrational and acoustic mode identification. These responses from the plate are measured both by an accelerometer attached to the central point of the plate and by a microphone set on the same vertical line as the accelerometer but above it, measuring the direct sound. The signals from the accelerometer and the microphone are then compared in two experimental arrangements, and their forms and the frequency contents are found to be equivalent. It is shown that the existing symmetry, i.e., the exact correspondence between vibrational and acoustic responses, can be used as the identifier of the patterns formed on the plate and the associated modal frequency. Full article

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. 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 coupling strength associated with the point interaction is characterized by a dimensionless factor α. The δ potential of the point interaction is numerically modelled by a truncated basis with an upper index N. 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 $N\to \infty$. 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. Full article

A truncated basis is employed to analyze the influence of the point interaction on the eigenvalues and eigenfunctions in quantum billiards. The point interaction is numerically confirmed to cause the shift in the eigenvalue that leads the original eigenfunctions to be superposed to form the new eigenfunction. The amplitude and nodal-line patterns of the eigenfunctions are found to vary significantly with the coupling strength. It is further verified that the point-driven Chladni plates can be employed to analogously manifest the noticeable dependence of the nodal-line pattern on the coupling strength. More importantly, the dispersion relation between the frequency and the wave number for the flexural wave can be precisely determined in the process of utilizing the point interaction to model the modern Chladni plates. Full article

This study was developed during 2018 and 2019, with 10th- and 11th-grade students from the Jose Maria Obando High School (Fredonia, Antioquia, Colombia) as the target population. Here, the “art as a method” was proposed, in which, after a diagnostic, three moments were developed to establish a dialogue between art and mathematics. The moments include Moment 1: introduction to art and mathematics as ways of doing art, Moment 2: collective experimentation, and Moment 3: re-signification of education as a model of experience. The methodology was derived from different mathematical-based theories, such as pendulum motion, centrifugal force, solar energy, and Chladni plates, allowing for the exploration of possibilities to new paths of knowledge from proposing the creative act. Likewise, the possibility of generating a broad vision of reality arose from the creative act, where understanding was reached from logical-emotional perspectives beyond the rational vision of science and its descriptions. Full article

(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. Full article

We report a single transducer acoustic levitator capable of manipulating objects in two-dimensions. The levitator consists of a centrally actuated vibrating plate and a flat reflector. We show that the levitation position of the object depends not only on the vibration frequency, but also on the tilting angle between the plate and the reflector. Additionally, new levitation positions can be created by actuating the plate with a composite signal of two frequencies using frequency switching. Based on recorded levitation positions, such single transducer acoustic levitator can manipulate a cluster of levitated microspheres in predefined trajectories, with mean position error of 155 ± 84 µm. Full article