Chladni Figures Research Articles

Further Study of Music Visualization: Chladni's Figure

By applying the principle of standing waves, the various scales produced by a piano within music software can be transformed into Chladni figures. These figures, which visually represent the vibration patterns of a surface, can be captured using photographic equipment. By carefully selecting the most accurate patterns and organizing them into a comprehensive table, it is possible to create a visual representation of Chladni figures corresponding to each musical syllable. This method provides a unique way to visualize the acoustic characteristics of different musical notes.

Visualization of Chladni Patterns at Low-Frequency Resonant and Non-Resonant Flexural Modes of Vibration

In this study, Chladni patterns corresponding to resonant and non-resonant vibration modes are visualized on square plates made in steel and aluminum alloys in the low frequency domain of 10–210 Hz. Using a laser sensor, the plate displacement at its central excitation point is measured, and from the obtained frequency response, the resonant and anti-resonant vibration modes are identified. Using the quality-factor method, the damping ratio corresponding to the 1st resonant peak is evaluated. Over a wide range of excitation frequencies, transitions of Chladni figures between resonant patterns via non-resonant patterns could be observed. Such Chladni figures, of the simplest geometrical configuration, can be used to achieve a certain desired movement path of the particles on the vibrating plate by controlling the excitation frequency.

Experimental, Modal, and Harmonic Response Analysis of a Chladni Plate at Ultrasonic Frequencies

Mode shapes and natural frequencies of mechanical structures can be determined with the Chladni approach. Visual patterns are generated on the Chladni plate if it is exposed to vibrations. These patterns are known as Chladni patterns/figures. Mechanical vibrators are used to excite the plates at particular frequencies for pattern generation, but based on the making and application, their range is limited up to 10 kHz. Piezoelectric transducers are a special kind of transducers that are capable of generating ultrasonic frequencies and if are attached to a plate, intricate visual patterns can be generated, based on the material properties and the shape of the plate. The current research focuses on experimenting with and simulating Chladni figures in the ultrasonic frequency range. The simulations were performed in ANSYS Workbench as a validation of the experimental work.

Modal and harmonic acoustical analysis of a circular rubber membrane and classification of resonant frequencies using deep learning

Mode shapes of a component or a structure can be determined by conducting Modal analysis. Chladni figures can also be used to determine the mode shapes of a plate. In this research comparison of these mode shapes using Chladni figures and ANSYS simulation has been carried out. Analysis systems used for ANSYS simulation are Harmonic Acoustic Analysis and modal analysis. With the help of wave equation, a mathematical formulation has been achieved. The experimental and simulation results are compared, and an error of not more than 9% for modal and 10% for harmonic acoustics is found. Classification of these Chladni figures which are obtained experimentally, using Deep Learning algorithms like Inception ResNetV2, VGG16 and Xception and have achieved 100 percent accuracy at different converging times.

Ritter’s Musical Esthetics, Der Freischütz, and the Certainty of Nature in Early Nineteenth-Century Germany1

Johann Wilhelm Ritter was a German physicist, philosopher, and chemist, who researched “invisible light” or the area beyond the visible light spectrum. Equal to his scientific interest in invisible light, Ritter was also fascinated with music, most especially the visualization of sound via the vibration plates of Ernst Chladni. This article presents Ritter’s musical esthetics in relation to the sound of nature in Carl Maria von Weber’s romantic opera Der Freischütz, which premiered in 1821 at the newly-built Königliches Schauspielhaus in Berlin. By connecting Ritter’s musical esthetics with that found in Der Freischütz, the opera can be seen as something more than a simple light work for entertainment or even a mere German nationalist text: an imaginative way of perceiving the inner workings of nature as a space of renewal and life-affirming certainty.

Dreadnought guitar top plate innovation

This paper describes the innovation of Dreadnought guitars, especially braces on top plate. The goal was to increase the dynamic range of the instruments, not only in strength but also in spectral spread. The prolongation of tones in the Sustain and Release phases was also important. Mechanical and acoustic properties of instruments from Furch Guitars' production were measured (Chladni figures, frequency response), numerical simulation of innovated top plate in program ANSYS was prepared (by the matrix) and the changes in organisation of ribs were proposed as following. The new samples of innovated Dreadnought guitars were produced by the factory, again measured, analysed and evaluated.

Modal analysis of plate to analyze the effect of mass stiffeners using the Chladni plate approach

Modal analysis of mechanical structures or components determines the mode shapes and natural frequencies. The Chladni plate approach is used to demonstrate the mode shapes of plates. Chladni pattern formation depends on plate material, geometry, thickness, and vibration frequency. This paper studies the Chladni figures obtained by sprinkling tea powder on a square acrylic plate mounted on the mechanical vibrator. Frequencies corresponding to each Chladni figure are noted. Further, the effect of adding stiffener at antinode points of the plate is analyzed. The change in the frequency due to the addition of stiffener is also studied. Results show that the Eigenfrequency values have increased. The Chladni patterns are obtained at a higher frequency for the plate with stiffener than the plate without stiffener. Simulation results obtained in the ANSYS workbench are used to validate experimental observations. For the acrylic Chladni plate, the error between the experimental and simulation work is less than 18%.

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.

Nodes and Antinodes in Two-Color Chladni Figures

Chladni patterns are one of the most fascinating physics demonstrations. They can be produced very easily using commercially available apparatus based on metallic plates attached to a mechanical driver, similar to a loudspeaker without the membrane, and a signal generator. The figures are observed using sand sprinkled on the surface of the plate. The demonstration is even more impressive if the figures are produced by using a violin bow. In the usual demonstration the patterns show the nodal lines of the vibrating plate: the sand moves from the vibrating regions towards the nodes, where it remains at rest. This paper describes how the demonstration can be improved by using two different powders to produce two-color Chladni figures, where nodes and antinodes display different colors.

Manipulating Chladni Patterns of Ferromagnetic Materials by an External Magnetic Field

Ernst Chladni is called the father of acoustics for his work, which includes investigating patterns formed by vibrating plates. Understanding these patterns helps research involving standing waves and other harmonic behaviors, including studies of single electron orbits in atoms. Our experiment vibrates circular plates which result in well-known patterns. Alternatively to traditional experiments that used sand or salt, we use magnetic materials, namely iron filings and nickel powder. We then manipulate the patterns by applying a localized external magnetic field to one of the rings that moves a segment of the magnetic material in that ring to the next inner ring. The results show a significant decrease in magnetic field necessary to move the magnetic material at higher frequencies as well as a significant decrease in the magnetic field required to move the magnetic material as nickel powder is substituted for iron filings while keeping the mass constant.

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.

Response variation of Chladni patterns on vibrating elastic plate under electro-mechanical oscillation

Fine grain particles such as sugar, sand, salt etc. form Chladni patterns on the surface of a thin plate subjected to acoustic excitation. This principle has found its relevance in many scientific and engineering applications where the displacement or response of components under the influence of vibration is vital. This study presents an alternative method of determining the modal shapes on vibrating plate in addition to other existing methods like the experimental method by Ernst Chladni. Three (3) finite element solvers namely: CATIA 2017 version, ANSYS R15.0 2017 version and HYPERMESH 2016 version were employed in the modelling process of the 0.40 mm x 0.40 mm plate and simulation of corresponding mode shapes (Chladni patterns) as well as the modal frequencies using Finite Element Method (FEM). Result of modal frequency obtained from the experimental analysis agreed with the FEM simulated, with HYPERMESH generated results being the closest to the experimental values. It was observed that the modal frequencies obtained from the FEM and experimental approach increased as the excitation time increased. ANSYS R15.0 and HYPERMESH software clearly represented the modal lines and mode shapes for each frequency which CATIA software was somewhat limited. This study has shown that FEM is an effective tool that can save time and energy invested in acoustic experiments in determining modal frequencies and patterns.Keywords: Vibration, Chladni patterns, Modal frequency, Thin plate, Experimental analysis

Seismology’s acoustic debt: Robert Mallet, Chladni’s figures, and the Victorian science of earthquakes

ABSTRACTIn the nineteenth century, Ernst Chladni’s acoustic figures provided productive new experimental techniques for investigating natural phenomena. The movement of invisible forces, such as light, electricity, magnetism, and heat, were hard for natural philosophers to examine. But Chladni’s use of vibrating glass plates and sand to reveal the wave motions of sound offered an experimental framework through which to make natural phenomena visible. In Britain, it was Michael Faraday and Charles Wheatstone in the 1820s and 1830s who made best use of these practices and apparatus. Sound waves also provided new ways of thinking about earthquakes and seismic phenomena. This article explores how Robert Mallet, the first self-styled “seismologist”, examined earthquakes, drawing on broader philosophical work surrounding vibrations and acoustic waves. Mallet was keen to draw parallels between the movement of seismic shock waves and the movement of musical sounds, including those from a piano moving through a room. He was not alone in this respect. Charles Darwin, among others, noticed comparisons between the sonorous and the seismic. By contextualising Victorian seismology within the context of Victorian acoustic science, this article argues that the two disciplines were deeply connected.

Imaging Chladni Figure of Plasmonic Charge Density Wave in Real Space

The future photonic age largely depends on our ability to manipulate optical waves in confined systems. Particularly, understanding the behavior of a plasmonic charge density wave (p-CDW) in optical resonators is vital for engineering 2D plasmonic devices. In this study, the standing p-CDW on the surface of a gold triangle resonator is examined through diffraction limited all-optical far field power loss microscopy. The scattering light map captured by this microscopy, named plasmonic Chladni figure, is directly proportional to the entire in-plane photonic local density of state. The theoretical model of the plasmonic Chladni figure proposed in this study is related to the 2D standing p-CDW node pattern, which is similar to the mechanical Chladni, but follows a special node selection rule. Investigating the plasmonic Chladni phenomenon provides an in-depth understanding of fundamental plasmonic physics and plasmonic chemistry and presents various possibilities for plasmonic application, such as 2D dimensi...

Standard and inverse microscale Chladni figures in liquid for dynamic patterning of microparticles on chip

We report on experimental demonstrations of the first sub-100 μm scale standard and inverse Chladni figures in both one- (1D) and two-dimensional (2D) fashions in liquid, and on exploiting these micro-Chladni figures for patterning microparticles on chip, via engineering multimode micromechanical resonators with rich, reconfigurable 1D and 2D mode shapes. Silica microparticles (1–8 μm in diameter) dispersed on top of resonating doubly-clamped beams (100 × 10 × 0.4 μm3) are observed to aggregate at antinodal points, forming 1D inverse Chladni figures, while microbeads atop square trampoline resonators (50 × 50 × 0.2 μm3) cluster at nodal lines/circles, creating 2D standard Chladni figures such as “,” “○,” “×,” and “\.” These observations suggest two distinct micro-Chladni figure patterning mechanisms in liquid. Combining analytical and computational modeling, we elucidate that streaming flow dominates the inverse Chladni pattern formation in the 1D beam experiments, while vibrational acceleration dictates the standard Chladni figure generation in the 2D trampoline experiments. We further demonstrate dynamical patterning, switching, and removal of 2D micro-Chladni figures in swift succession by simply controlling the excitation frequency. These results render new understandings of Chladni patterning genuinely at the microscale, as well as a non-invasive, versatile platform for manipulating micro/nanoparticles and biological objects in liquid, which may enable microdevices and functional device-liquid interfaces toward relevant sensing and biological applications.

Signatura rerum: Chladni’s Sound Figures in Schelling, August Schlegel, and Brentano

The sound figures were an oscillating metal plate that produced two-dimensional shapes in the sand when musical notes were played through it. Ernst Chladni, the German acoustician who discovered the phenomenon in 1789, exhibited it at public demonstrations around Europe. But despite the support of Napoleon himself, the sound figures could not be explained mathematically. So in these sound figures, F. W. J. Schelling found confirmation of dynamic physics and posited a Signatura rerum. August Schlegel built this claim into his lectures on art history and aesthetics, and Clemens Brentano celebrated the experiment in his poetry. Thus did philosophy and literature express the full significance of an insoluble problem in mechanical physics, illuminating the reciprocity of science and culture at the turn of the eighteenth century.

The state of percussion research in musical acoustics: How we got here and where it is going

Drums are among the most ancient of all musical instruments and have been found in nearly all cultures across the world. This work covers a selection of major investigations of the acoustics of percussion instruments by a variety of scientists throughout history. Ernst Chladni’s efforts to characterize the vibration of plates are well known in acoustics and often replicated by students in the laboratory. Other scientists who made early contributions to the understanding of percussion instruments include Lord Rayleigh and C. V. Raman. Rayleigh’s observations of the acoustics of the kettledrum and bells represented only a fraction of his contributions to acoustics. Raman, who is remembered more for his work in spectroscopy, made detailed studies of the traditional Indian drum, the tabla. Modal analysis techniques used to investigate the acoustics of percussion instrument have evolved significantly in recent years. A brief review of current modal analysis techniques for studying percussion instruments is pre...

Point-driven modern Chladni figures with symmetry breaking

Point-driven modern Chladni figures subject to the symmetry breaking are systematically unveiled by developing a theoretical model and making experimental confirmation in the orthotropic brass. The plates with square shape are employed in the exploration based on the property that the orientation-dependent elastic anisotropy can be controlled by cutting the sides with a rotation angle with respect to the characteristic axes of the brass. Experimental results reveal that the orientation symmetry breaking not only causes the redistribution of resonant frequencies but also induces more resonant modes. More intriguingly, the driving position in some of new resonant modes can turn into the nodal point, whereas this position is always the anti-node in the isotropic case. The theoretical model is analytically developed by including a dimensionless parameter to consider the orientation symmetry-breaking effect in a generalized way. It is numerically verified that all experimental resonant frequencies and Chladni patterns can be well reconstructed with the developed model. The good agreement between theoretical calculations and experimental observations confirms the feasibility of using the developed model to analyze the modern Chladni experiment with orientation symmetry breaking. The developed model is believed to offer a powerful tool to build important database of plate resonant modes for the applications of controlling collective motions of micro objects.

A Study to Explore the Effects of Sound Vibrations on Consciousness

Sound is a form of energy produced by vibrations caused by movement of particles. Sound can travel through solids (such as metal, wood, membranes), liquids (water) and gases (air). The sound vibrations that reach our ear are produced by the movement of particles in the air surrounding the source of sound. The movement or vibration of particles produces waves of sound. Sound waves are longitudinal and travel in the direction of propagation of vibrations. The pitch of sound is related directly to its frequency, which is given by the number of vibrations or cycles per second. The higher the pitch of sound, the higher is its frequency, and the lower the pitch, the lower is its frequency. Human ear can hear sounds of frequencies ranging from 20 – 20,000 cycles per second (or Hertz – Hz). Sound waves can be visually seen and studied using 'Chladni' plates, which was devised and experimented by Ernst Chladni, a famous physicist with a passion for sound/music. In this experiment the source of sound is connected via a wave driver to the Chladni metal plate with fine sand strewn on it. The sound vibrations cause the plate to vibrate at the same frequency, which causes movement of the sand particles to form patterns of the sound generated. The visual patterns comprise of nodes or regions where the sand particles accumulate, and antinodes or regions where the sand particles drift away from. Each frequency of sound causes a particular pattern to be formed on the plate. The study of wave phenomena is also called 'Cymatics' (Raghu, 2016). Sound vibrations can come in contact physically through the body and have an effect on our consciousness at the mental, emotional and spiritual levels. Sounds that are musical can be categorized as consonant sounds that are pleasant, and dissonant sounds that are unpleasant or not so pleasant. Musical sounds are comprised of notes in increasing or decreasing order of pitch (frequency). The interval between notes can give rise to consonance and dissonance. Example, an interval of an octave -a range of seven notes - is said to be consonant, whereas an interval between adjacent notes can be dissonant. These are studied by experimenting with musical notes and intervals, their visual patterns and their effect on consciousness. While consonant intervals can cause happiness, joy, courage or calmness, dissonant intervals can cause tension, anger, fear or sadness, thereby affecting the emotional aspect of consciousness.

Vibroacoustic analysis of table tennis rackets and balls: The acoustics of ping pong

Table Tennis rackets (ping-pong paddles) exhibit a large number of structural vibration modes which follow patterns first observed by Ernst Chladni and Mary Waller for elliptical plates. Vibrational mode shapes and frequencies obtained through experimental modal analysis will be shown. Acoustic analysis reveals that one structural mode of the paddle, in particular, dominates the sound produced by the ball-paddle impact. The rubber padding provides some damping, and a significant mass loading to the paddle vibrations. The hollow cellulose nitrate balls exhibit a number of vibrational mode shapes typical of a hollow spherical shell, starting at frequencies around 5900 Hz; these will be demonstrated from experimental and computational results. However, the contact time between ball and paddle is such that the lowest acoustic modes of the ball do not contribute to the radiated sound. Instead, the ball appears to radiate sound at a much higher frequency sound (10-12 kHz) most likely due to snap-through buckling common to spherical shells undergoing deformation while impacting a rigid surface at high speeds.