Abstract
Eigenfrequencies inside a space significantly affect its acoustic characteristics, especially below the Schroeder frequency in the low-frequency range. In Architectural Acoustics, accurate detection and visualization of eigenmodes can be particularly useful in practical applications. One of the most important landmarks in Chania, Greece, is Neoria, a cluster of 16th-century Venetian shipyards. One existing Neoria will be converted and used as a multipurpose hall. For this objective, acoustic modeling and various measurements were performed in the space. One of the purposes of the measures and modeling was the investigation of the eigenfrequencies and the eigenmodes of the area. Finite Element Method (FEM) was used for the acoustic modeling, while the acoustic measurements were performed in various positions according to ISO 3382-1. Impulse responses were measured, and frequency responses of the space were extracted using Fourier analysis. The measurements and the acoustic modeling results show that the frequencies with the most significant effect on the area are 86.1 Hz, 150.7 Hz, and 204.6 Hz. Eigenmodes of the frequencies are visualized with the application of FEM and especially the positions of nodes and antinodes, which can be utilized appropriately for the optimum placement of absorbers and diffusers in the space.
References
Prodeus A, Didkovska M, Kukharicheva K. Comparison of speech quality and intelligibility assessments in university classrooms. Int J Archit Eng Technol 2021; 8: 52-60. https://doi.org/10.15377/2409-9821.2021.08.5
Berardi U, Iannace G, Ianniello C. Acoustic intervention in a cultural heritage: The chapel of the royal palace in caserta, Italy. Buildings. 2015; 6: 1. https://doi.org/10.3390/buildings6010001
Prodi N, Pompoli R. Acoustics in the restoration of Italian historical opera houses: A review. J Cult Herit. 2016; 21: 915-21. https://doi.org/10.1016/j.culher.2016.03.004
Đorđević Z, Novković D, Andrić U. Archaeoacoustic examination of lazarica church. Acoustics. 2019; 1: 423-38. https://doi.org/10.3390/acoustics1020024
Suárez R, Alonso A, Sendra JJ. Archaeoacoustics of intangible cultural heritage: The sound of the Maior Ecclesia of Cluny. J Cult Herit. 2016; 19: 567-72. https://doi.org/10.1016/j.culher.2015.12.003
De Muynke J, Baltazar M, Monferran M, Voisenat C, Katz BFG. Ears of the past, an inquiry into the sonic memory of the acoustics of Notre-Dame before the fire of 2019. J Cult Herit. 2022; epub ahead. https://doi.org/10.1016/j.culher.2022.09.006
Berardi U, Iannace G. The acoustic of Roman theatres in Southern Italy and some reflections for their modern uses. Applied Acoust. 2020; 170: 107530. https://doi.org/10.1016/j.apacoust.2020.107530
Savioja L, Svensson UP. Overview of geometrical room acoustic modeling techniques. J Acoust Soc Am. 2015; 138: 708-30. https://doi.org/10.1121/1.4926438
Harrison CH. Efficient modeling of range-dependent ray convergence effects in propagation and reverberation. J Acoust Soc Am. 2015; 137: 2982-5. https://doi.org/10.1121/1.4919335
Kuttruff H. Room acoustics. 6th ed., Boca Raton: CRC Press; 2016. https://doi.org/10.1201/9781315372150
Sakamoto S, Nagatomo H, Ushiyama A, Tachibana H. Calculation of impulse responses and acoustic parameters in a hall by the finite-difference time-domain method. Acoust Sci Technol. 2008; 29: 256-65. https://doi.org/10.1250/ast.29.256
Papadakis NM, Stavroulakis GE. Finite element method for the estimation of insertion loss of noise barriers: comparison with various formulae (2D). Urban Sci. 2020; 4: 77. https://doi.org/10.3390/urbansci4040077
Computational simulation in architectural and environmental acoustics. Springer; 2014. https://doi.org/10.1007/978-4-431-54454-8
Mohamady S, Raja Ahmad RK, Montazeri A, Zahari R, Abdul Jalil NA. Modeling and eigenfrequency analysis of sound-structure interaction in a rectangular enclosure with finite element method. Adv Acoust Vib. 2009; Article ID 371297. https://doi.org/10.1155/2009/371297
Papadakis N, Stavroulakis GE. Time domain finite element method for the calculation of impulse response of enclosed spaces. Room acoustics application. 12th International Workshop on the Mechanics of Hearing, AIP; 2015, p. 100002. https://doi.org/10.1063/1.4939430
Papadakis N, Stavroulakis GE. Validation of time domain finite element method via calculations of acoustic parameters in a reverberant space. 10th HSTAM International Congress on Mechanics, Chania, Crete, Greece: 25-27 May, 2013.
Papadakis NM. Application of finite element method for estimation of acoustic parameters (Ph.D Thesis). Technical University of Crete; 2018. https://doi.org/10.12681/eadd/42505
ISO B 3382-1: 2009. Acoustics-Measurement of rooms acoustic parameters-Part 1. 2009.
Papadakis NM, Stavroulakis GE. Review of acoustic sources alternatives to a dodecahedron speaker. Appl Sci. 2019; 9(18): 3705. https://doi.org/10.3390/app9183705
Papadakis NM, Stavroulakis GE. Handclap for acoustic measurements: optimal application and limitations. Acoustics. 2020; 2: 224-45. https://doi.org/10.3390/acoustics2020015
Papadakis N, Stavroulakis G. Low cost omnidirectional sound source utilizing a common directional loudspeaker for impulse response measurements. Appl Sci. 2018; 8(9): 1703. https://doi.org/10.3390/app8091703
Farina A. Simultaneous measurement of impulse response and distortion with a swept-sine technique. J Audio Eng Soc. 2000; 49: 1-24.
Antoniadou S, Papadakis NM, Stavroulakis GE. Measuring acoustic parameters with ESS and MLS: effect of artificially varying background noises. Euronoise. 2018: 771-6.
Stan GB, Embrechts JJ, Archambeau D. Comparison of different impulse response measurement techniques. J Audio Eng Soc. 2002; 50: 249-62.
Okuzono T, Otsuru T, Tomiku R, Okamoto N. Fundamental accuracy of time domain finite element method for sound-field analysis of rooms. Appl Acoust. 2010; 71: 940-6. https://doi.org/10.1016/j.apacoust.2010.06.004
Amestoy PR, Duff IS, L’Excellent J-Y. MUMPS multifrontal massively parallel solver version 2.0 1998.
Papadakis NM, Stavroulakis GE. Effect of mesh size for modeling impulse responses of acoustic spaces via finite element method in the time domain. Euronoise. 2018; 323-9.
Crocker MJ. Handbook of noise and vibration control. Wiley; 2007. https://doi.org/10.1002/9780470209707
Cucharero J, Hänninen T, Lokki T. Influence of sound-absorbing material placement on room acoustical parameters. Acoustics. 2019; 1: 644-60. https://doi.org/10.3390/acoustics1030038
Labia L, Shtrepi L, Astolfi A. Improved room acoustics quality in meeting rooms: Investigation on the optimal configurations of sound-absorptive and sound-diffusive panels. Acoustics. 2020; 2: 451-73. https://doi.org/10.3390/acoustics2030025
Arvidsson E, Nilsson E, Hagberg DB, Karlsson OJI. The effect on room acoustical parameters using a combination of absorbers and diffusers-An experimental study in a classroom. Acoustics. 2020; 2: 505-23. https://doi.org/10.3390/acoustics2030027
Choi YJ. An optimum combination of absorptive and diffusing treatments for classroom acoustic design. Build Acoust. 2014; 21: 175-9. https://doi.org/10.1260/1351-010X.21.2.175
Mir SH, Abdou AA. Investigation of sound-absorbing material configuration of a smart classroom utilizing computer modeling. Build Acoust 2005; 12: 175-88. https://doi.org/10.1260/135101005774353032
Russo D, Ruggiero A. Choice of the optimal acoustic design of a school classroom and experimental verification. Appl Acoust 2019; 146: 280-7. https://doi.org/10.1016/j.apacoust.2018.11.019
Choi Y-J. Effects of periodic type diffusers on classroom acoustics. Appl Acoust. 2013; 74: 694-707. https://doi.org/10.1016/j.apacoust.2012.11.010
Lau S-K, Powell EA. Effects of absorption placement on sound field of a rectangular room: A statistical approach. J Low Freq Noise Vib Act Cont. 2018; 37: 394-406. https://doi.org/10.1177/1461348418780027
Lau SF, Zainulabidin MH, Yahya MN, Zaman I, Azmir NA, Madlan MA, et al. Optimization of sound absorbers number and placement in an enclosed room by finite element simulation. J Phys Conf Ser. 2017; 914: 012037. https://doi.org/10.1088/1742-6596/914/1/012037
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