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Computational Study of Cymatics with Experimental Analysis

时间:2024-12-22

Shennal HARSHANA, Nimali T. MEDAGEDARA

(Department of Mechanical Engineering Faculty of Engineering Technology,The Open University of Sri Lanka Nawala, Nugegoda, Sri Lanka.)

Abstract: Cymatics is a visual representation of sound and vibrations, on surfaces of plates, diaphragms, and membranes in the forms of auditory-images. The surfaces that are exposed to these vibrations are sprinkled with fine particles that accumulate at nodes, to create visualizations of specific geometry unique to the particular frequency. This paper discusses the designing of an experimental platform, dedicated towards observing the behavior of cymatics, through analysis of such visualizations (Chladni patterns). This is further investigated by performing a numerical modelling using finite element simulation. Two millimeter thickness Aluminum (Al)plates of three shapes consisting of surfaces with equal areas were used for both experimental and finite element analysis (FEA). FEA was performed using ANSYS simulation software and patterns were derived for different vibrational frequencies. The results demonstrated that the 60% of the experimental imagery conforms with the visualization generated by ANSYS software. Additionally, the lowest average frequency differences with respect to the simulation results an average deviation for similar images was found to be 9.2% and 2.8mm for the triangular shape plate, validating that the shape of the plate plays a paramount role in cymatics analysis.An image processing technique was used to determine the deviation between the images created by experimental platform and FEA for all the three shapes. The results demonstrate that Chladni patterns are best represented by a triangular shaped plate.

Keywords: Cymatics, Finite Element Analysis, Chladni Patterns, Vibration, Resonance

1 Introduction

Cymatics is the study of sound and vibration made visible, typically on the surface of plates or liquid.Each frequency of sound causes a particular pattern to be formed on the plate. This study of vibrational wave phenomena is also called 'Cymatics' (Raghu, 2016).Every object or system in this universe acquire an infinite number of resonant frequencies which increase the amplitude of the system. This frequency is equal or close to the natural frequency of the system. Even though the resonance causes a massive vibration, specific regions of the object or system become stationary.When there are particles placed over this vibrating system, they will vibrate until they find those tranquil regions. These regions of standing waves have minimum frequencies called nodal frequency where the particles gather, and form quite complex patterns called Chladni patterns. The basic phenomenon of cymatics is to shows how vibrations interact to create the node shapes for different frequencies. When a membrane vibrates at its natural frequency, it shows specific dynamic behavior. Therefore, contemplating the nature of cymatics assists in determining the be-havior and characteristics of invisible acoustic phenomenon.

Behavior of the cymatics refers to the phenomenon of sand particles on a flexural vibrating plate moving and aggregating at the nodal positions of the plate[1,2]. That demonstrates the effects of the resonance phenomenon over two dimensional objects.Although Chladni effect has applications in the visualization of vibration modes and ultrasonic motor[3],and potential applications in micro and nano manipulations[4], research on its characteristics is deficient.Recent contemporary advancement of computer technologies facilitates the simulation of complex natural occurrences that exist in the world[5]and for solving and validating engineering problems.

The cymatics patterns represent the effects of vibration, with specific force and frequency, over one or many objects. Cymatics can have multiple applications,including cloaking of flexural vibrations in a structured plate that has been investigated in D. Misseroni et al.[5]They have used finite element simulation to validate their model. Cymatics or sound vibrations can come in contact physically through the body and have an effect on our consciousness at the mental, emotional, and spiritual levels. John et al.[6]used cymatics as a sound visualization tool. Cymatics has been used as a sound therapy in spirituality and consciousness[6]. This phenomenon is used in medical industry as a method of healing by exposing sounds to patients and this provides effective relief of stress, injury and chronic pain[7]. More over cymatics is used in the field of education to accelerate the learning process and brain activity to overcome disturbances in the learning process[8]and also as an elegant natural art form.

To identify the behaviour of the cymatics and to create the Chladni patterns, specific resources and techniques are required. Conducting of experiments is limited by the physical properties and accuracy of the experimental equipment[9]. The application of computational technology in this scenario would ease the process of investigating this phenomenon, and would not only save time and resources, but would allow for the creation of conditions which would be difficult to recreate using existing technology[8,10].

Modal analysis is a process of representing various natural features of a geometry (structure) which may include damping, mass, modes shapes and frequency (Polytech, 2001). Modal analysis is significant in evaluating the mode shapes generated by a component under vibrational excitation. These mode shapes of cymatics visualization can be used to determine the displacement or response of the component under the influence of vibrations in day today applications. Results obtained from the modal analysis will generate a number of resonances, for which the frequency can be determined by measurement. Vibrations may be exceptionally high when a structure vibrates at frequencies higher or closer to the natural frequency of the body[11]. This phenomenon is used to identify the behaviour of the cymatics with reference to the nodal frequencies.

2 Methodology

This section presents the design and implementation of the system to determine the various images according to the frequencies and its significant components. The section introduces the finite element analysis, selection of material and details of the fabricated experimental set up. The schematic diagram(Fig.1) illustrates the overall methodology of the study.

2.1 Finite Element Analysis (FEA)

Finite Element analysis (FEA) is widely used to predict the behavior of engineering designs under given boundary conditions. We can use this analysis for determining the impact of pressure, heat, vibration etc. on a design and for solving problems in mathematical models. Moreover, the FE analysis precisely can be used in solving complicated differential equations with numerical solutions. Therefore, FE model analysis has been used to calculate the natural frequencies of vibrating models[11]. There are many simulation software that are being used for different purposes. Modal analysis using ANSYS is an effective method of determining vibration characteristics[12].ANSYS enables the harmonic analysis which is used to

Table 10 Comparison of Experimental and FE Results for Triangular Shape

Table 11 Comparison of Experimental and FE Results for Circular Shape

Average difference of frquencies with respect to FEA results for rectangular shape plate is 31.3 (%) and average image deviation between experimental results and FEA results is 15.1.

5 Conclusion

The fabricated prototype produced results which are close to the phenomenon of cymatics and the visualization of Chladni patterns, even when thousands of particles are involved. For this phenomenon of cymatics, modal analysis is significant in evaluating the mode shapes generated by the test platform under vibrational excitation. Results obtained from the modal analysis was generated due to number of resonances and therefore the frequency for each pattern was recorded by measurement for both test and FE analysis.Sand with approximately 440μm diameter were used as the particles for measurement. Experimentally generated modal shapes (images) were compared with the results by FE analysis for square, triangular and circular shapes. Both experimental and FE analysis were performed using 2mm thick aluminum plates with same dimensions. ANSYS software was used for the simulation and the experimental analysis was performed using a fabricated test platform. The results from experimental were on par with simulated results. A total of 56 Chladni patterns were created experimentally and 60% of them were similar to patterns generated by the ANSYS software. Results shows that, the average frequency difference with respect to the finite element analysis was found to be 12.5% for square plates, 9.2% for triangular plates and 31.3% for circular plates. An image processing technique was used to evaluate the deviation between the images created by the test platform and FEA for all three shapes. The results show that the average deviation between the images of experimental and FEA is for square shape 9.1mm, for triangular shape 2.8mm and for circular shape 15.1mm. Therefore, studies of the behaviour of cymatics of various frequencies for different shapes of plates, demonstrated that for the triangular shaped plate, the experimental results are in good agreement with the FEA results for formation of chladani patterns.

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