Analysis on Acoustic Attenuation by Periodic Array Structure EH KWEE DOE 1, WIN PA PA MYO 2

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1 ISSN Vol.03,Issue.24 September-2014, Pages: Analysis on Acoustic Attenuation by Periodic Array Structure EH KWEE DOE 1, WIN PA PA MYO 2 1 Dept of Mechanical Engineering, Mandalay Technological University, Mandalay, Myanmar, whiteflower.115@gamil.com. 2 Dept of Mechanical Engineering, Mandalay Technological University, Mandalay, Myanmar, papamyo@gmail.com. Abstract: A sound enclosure with periodic arrays was constructed and tested for acoustic attenuation performance. This principle has been used to reduce the sound pressure level in one part of a structure when it is excited at another. This study has been analyzed the propagation of acoustic wave through a periodic structure by experimentally and simulation model. Such a periodic structure has been found to attenuate sound significantly in certain frequency band. Experiment has been done by two materials; glass tubes and PVC pipes. Experiments with the periodic array of glass tubes can attenuate sound pressure of 8dBA at 5 khz, 8 khz and frequencies above 14 khz. Experiments with periodic array of PVC pipes show that attenuation of 12dBA can be achieved at the frequency band of 9 khz 11 khz. In the other frequencies ranges, the sound pressure level was not significantly attenuated and most of it may be fluctuated. Keywords: Frequency Filter, Glass Tube, Periodic Structure, Sound Barrier. I. INTRODUCTION Periodic structures have a unique effect on the propagation of waves. Due to diffraction and interference of waves by the periodic structure, frequency band with different wave behavior are formed. There are frequency bands in which the waves are allowed to propagate the structure and there are certain frequency bands in which wave propagation is not allowed [1]. Noise is usually defined as annoying or unwanted sound noise from the industrial operations, cars driving and other can affect neighboring residential areas, ranging from intolerable noise level to structural vibrations. Acoustic noise problems become more and more evident as increased numbers of industrial equipment such as engines, blowers, fans, transformers, and compressors are in uses [2]. Therefore, Sound attenuation is very important and required in many situations. Attenuation is the difference in sound pressure between two points in and along the path of sound propagation. The aim of attenuation is to reduce or divert the amount of sound energy reaching the receiver. The key to attenuation is to apply noise control materials and measure that are both effective and economical [3]. The benefit of such periodic structure is that it can attenuate sound significantly in a particular frequency band. Also sound attenuation by the use of phononic structure gives a novel way to attenuate sound. The conventional method uses partition or barrier [4]. But in this method, the attenuation is due to interaction of wave with the periodic structure which is made up of glass tubes and PVC pipes. Several analytical and experimental studies haven conducted to study the behavior of sound attenuation system. The initial study of the sculpture at Madrid was done by Martinez-Sala et [5]. The sculpture consist of a periodic distribution of hollow stainless-steel cylinders in square array, with a diameter of 2.9 cm and spacing of 10 cm. the cylinder are fixed on a circular platform (4 cm in diameter ) which can rotate about a vertical axis. By experimental study on this sculpture, it was found that there is a significant sound attenuation (~15dB) at 1.67 khz. In another study was made by A Gupta [6]. In this study, the small size of periodic structure is constructed and tested in a controlled enclose. The structure used in the experiment consists of hollow acrylic cylinders with 3 cm outer diameter placed at 4.25 cm apart in a square array and the size of array was The experiment and simulation results of this study can attenuate sound was more than 8dB in three frequencies bands between khz, khz and khz. However, the acoustic analysis of this type of structures has not been done in locally. To fulfil this requirement is the main aim of this study. Specifically, the mean objectives of this study (1) to construct the periodic array structure and test it acoustic attenuation ability, (2) to obtain the numerical model for the acoustics performance simulation. II. METHODOLOGY To study the problem of acoustic wave propagation through a periodic structure with air as medium both experiment and numerical simulation are used. Experimental setup was developed to measure attenuation of 2014 SEMAR GROUPS TECHNICAL SOCIETY. All rights reserved.

2 sound. The numerical simulation was made by COMSOL Multiphysics. The results from both the methods are comparable. A. Acoustic Theory Acoustic is the science of sound, that is, wave motion in gases, liquids and solids, and the effects of such wave motion. Thus the scope of acoustic ranges from fundamental physical acoustics to say, bioacoustics, psychoacoustics and music, and technical fields such as transducer technology, sound recording and reproducing, design of theatres and concerts halls, and noise control. Sound is defined as any pressure variation heard by the human ear. This translates into a range of frequencies from 20 Hz to 20,000 Hz for a healthy human ear. In term of sound pressure, the human ear s range starts at the threshold of hearing (0 db) and ends at the threshold of pain (around 140 db). The human ear is less sensitive to sound pressure variations in the low frequencies compared to the higher frequencies. Both sound power and sound pressure level can be measured in decibels, in a manufacturers published test data. Sound levels are described on a logarithmic scale in units called decibels (db). Sound power level and sound pressure level are typically expressed in terms of decibels, as an indication that they are not absolute values, but rather, measurements relative to a reference quantity [6]. The equation can be used to calculate the sound pressure level is: P 2 SPL 10log 10 ( ) [db] (1) P Where, SPL = Sound Pressure level P = root-mean-square (rims) sound pressure (Pascals or Pa) p =international reference pressure of Pa. 0 Sound attenuation by periodic array is given by the insertion loss. IL SPL without periodicarray SPLwith periodicarray (2) 0 EH KWEE DOE, WIN PA PA MYO taken to ensure that the side walls are parallel. When the sound wave propagate through this glass tubes, some sound are reflected and back to the sound source and other are passing through to the other side of glass tubes. The end of glass tubes were not cover, there was a little vacuum between the glass tubes and acrylic structure. In this study, the main aim is to study the sound attenuation after the sound wave propagated through this glass tubes of periodic array. Sound pressure level measured in decibel (db) unit was measured first without and then with the inclusion of the glass tubes arrays. After which, the attenuation spectrum was obtained by finding the difference of the two spectra. The sound level meter (EXTECH HD 600) was used to measure the sound pressure level (SPL) of the sound after passing through the periodic structure of glass tubes and PVC pipes. The schematic diagram of acrylic structure with periodic array of glass tubes and transducer as shown in figs.1, 2 and 3. Fig.1 Schematic Diagram of Experimental Setup. B. Experimental Setup The experimental setup are discussed which are used with acrylic structure as an enclosure, glasses tubes as periodic array, transducer as sound source, transformer to generate more voltages, function generator to regulate the frequencies ranges and multi-meter to recheck the frequencies ranges and voltages during experiment. Experiments were initially carried out inside an engine room and it was constructed the enclose structure of acrylic since there was less external noise, which may affect the sound pressure level readings. In the experimental setup, the dimensions of rectangular structure which is made up of acrylic are 92.5 cm width and 33.5cm height. This structure is constructed as an enclosure to absorb the sound pressure and also to obstruct the environmental noise while measure the sound pressure during the experiment. The dimension of glass tubes is 33.5cm long and 1.5 cm inner diameter and 1.8 cm outer diameter. This glass tubes are used to reflect the sound because glasses have reflected properties. The glass tubes were mounted on a periodic grid, while care was Fig.2. Experimental Setup. Fig.3 Measuring Devices.

3 Analysis on Acoustic Attenuation by Periodic Array Structure C. Simulation Model The finite element method is a general numerical method that is used to solve differential equations with appropriate boundary condition over a domain. The present sound propagation problem can be modeled by the wave equation in linear acoustics as given by equation (6). Further, if a sinusoidal variation of pressure with time is assumed, this equation reduces to the Helmholtz equation as given by equation (7). The software COMSOL Multiphysics 3.4 is used to perform the finite element analysis in this work p p o (3) 2 2 c t Where; p is the pressure, c is the speed of sound in the medium. Fig.5. Boundary Conditions. i t If we assume p to be harmonic in time p Re[ p e ], Then, above equation reduces to Helmholtz equation. 2 p p 0 (4) Where; p complex variable is that account for amplitude and phase, and k is the wave number defined as; ω k= c (5) The model solves for the pressure field for one frequency at a time. Therefore the numerical study is the parametric study by varying the frequency from 1000 Hz to Hz at a interval of 1000 Hz. Sound attenuation caused by the structure is calculated from the pressure field, using equations (3) and (4). TABLE I: Materials Properties The initial model is too large to be solved directly because it requires lot of computational time and memory requirement. Especially at high frequencies, very small elements or mesh size is required. To model the problem as shown in Fig.4, a representative section of the array was used. Neumann boundary condition p 0is applied because n the model is symmetric and eventually translates into sound hard boundary condition. III. RESULTS A. Experimental Results 1. Experimental Result of Glass Tubes: The experimental results are shown in Fig.6 which plots attenuation versus frequency. The results show that there is significant sound attenuation at frequencies around 1 khz, 1.3 khz. In this Fig.4. Model Reduction using Periodic Property of Structure. The boundary conditions applied for the problem are shown in Fig.5. The sound source is at the left hand side boundary, while on the right hand side it is free field, no reflective wave. On the top and bottom of the faces to sound hard boundary condition is applied which is equivalent to sound hard boundary condition. Fig.6. Experiment Result of Sound Attenuation with Glass Tubes. range, the average attenuation is around 8 dba. A normal ear can perceive a change in sound pressure level of 3-5 db. Therefore an attenuation of 8 is satisfied. At frequencies around 0.2 khz to 0.8 khz where there is amplification (i.e.

4 negative attenuation). In the simulation, there is no such negative attenuation. Therefore it may be due to some phenomenon that needs to be studied further. Environmental change is probably due to the variation in the experiment, other physical disturbance in the experimental setup on different days and uncertainty in the measurement equipment. EH KWEE DOE, WIN PA PA MYO 2. Experimental Result of PVC pipes: The attenuation with and without 2 6 periodic array structure of PVC pipes as shown in fig.7. The x axis was frequencies (khz) and y axis was attenuation (dba). This figure shows that the sound pressure was significantly attenuated around 12 dba in the band of frequency 8 khz 12 khz compared to other frequencies. In the other frequencies ranges, sound pressure level was not significantly attenuated and most of it may be fluctuated. Fig.8. Sound Pressure Level without Periodic Array, at 3233 Hz. Fig.7. Experimental Result of Sound Attenuation with PVC Pipes. B. Simulation Results 1. Surface Plot of Rectangular Box with Periodic Array and without Periodic Array: Fig.8 shows the sound wave propagation though within the given geometry in COMSOL Multiphysics. The sound pressure level expressed with colors in range. The blue color expressed the low SPL and red color shows the maximum SPL. This simulation in this thesis was based on sound pressure level. The sound pressure level without periodic array structure at frequency of 2.3 khz as showed in fig.8. As can be seen in figure, the sound pressure level is not changed significantly in the geometry. The color was almost in constant from the given sound source to the end. Figure shows the form of sound wave propagate through into the medium in the given crosssectional area. The form of sound wave propagate through the medium with constructed the periodic array of glass tubes as shown in fig.9. In this figure, some of the sound wave that propagate though the glass tubes were reflected back to the sound source and other passed through to the other side of the glass tubes. Therefore, the color of sound wave is slightly changed after it propagates through the array. This result can be checked with the experimental result. Fig.9. Sound Pressure Level at 3233Hz with Periodic Array. Fig.10 Simulation Results of Sound Pressure Level with array and without array.

5 The simulation results of sound pressure were then collected at all frequencies within the range. The results are show in Fig.10 for both cases with and without periodic array. As seen in the picture, the sound pressure level significantly attenuate at 5 khz, 8 khz and frequencies above 12 khz. In the other frequencies bands sound pressure is not attenuated to a considerable level. 2.Comparison the Result of Simulation and Experiment: The experiment and simulation results are plotted together in figs.11 and 12 below. The graphs show a plot of the sound pressure levels versus frequency. From fig.11, it can be seen that the simulation and the experimental results with periodic array match up very well especially at frequencies above 4 khz. However, the trend does not match at frequencies lower than 4 khz. Analysis on Acoustic Attenuation by Periodic Array Structure experimental results of sound pressure level is measured with only sound pressure trend from simulation. The exact modeling is still needed to be conducted for full verification purpose. V. DISCUSSION The experiments with and without periodic array structures were discussed. Further tests and studies sound attenuation by placing the glass tubes in different rows and columns to investigate the widths of band gaps in details. However, the attenuation graphs of all experiments were mostly similar to each other, not significantly quite differ. The structure of these experiments can attenuate sound pressure level around 8 dba. After that the experiment had also been done by using PVC pipes with 2 6 periodic array. This result shows that the sound pressure level was attenuate around 12 dba. So that the PVC pipes can attenuate sound pressure level more 4 dba than glass tubes. Fig.11. Comparison of Experiment and Simulation Results of Sound Pressure Level with Structure. Fig.12. Comapresion of Experimental and Simulation Results of Sound Pressure Level without structure. The comparison for the case without periodic array is shown in Fig 12. The trends of experimental and simulation results match very well for all frequencies except at 7 khz. Therefore, simulation model can be verified using experimental results. However, it must be noted that the VI. CONCLUSION In conclusion, results from the experiments with and without periodic array structure of glass tubes show that attenuation peaks were not distinct. This could be due to several reasons including unwanted echoing in an enclosed rectangular structure of which made of acrylic. Sound propagation through a periodic structure made of glass tube was studies. It was found that periodic array structure attenuates the sound in particular frequency bands. For the periodic structure, finite element simulation was also performed and the results matched up well with the experiment results between 5 khz to 19 khz. The experimental results of sound pressure with PVC pipes was significantly attenuated around 12 dba in the band of frequency 8 khz 12 khz compared to other frequencies. Sound attenuation using periodic structure gives an efficient way to attenuate sound while, allowing for the air flow and convective heat transfer where needed. VII. REFERENCES [1] Kittle, C., Introduction to Solid State Physics. 1971, New York: Wiley. [2] Finn Jacobsen, Torben Poulsen, Fundamental of Acoustics and Noise Control, Nov, [3] Acoustics, April, [4] A. Gupta, Effect of Periodic Structure on Sound Propagation, Department of Mechanical Engineering, National University of Singapore, Singapore, 2012 [5] Martinez-Sala, R., et al., Control of noise by trees arranged like sonic crystals. Journal of Sound and Vibration, (1-2): p [6] Martinez-Sala, R., et al., Control of noise by trees arranged like sonic crystals. Journal of Sound and Vibration, (1-2): p