Küçük hacimlerde durağan dalgaların (modların) oda geometrisi ve oda oranları ile ilişkisinin incelenmesi
Examination of standing waves (modes) via relations room geometry and room ratio in small rooms
Yazar: İLKAY SEFER
Danışman: PROF. DR. SEVTAP YILMAZ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Mimarlık Ana Bilim Dalı / Çevre Kontrolü ve Yapı Teknoloji Bilim Dalı
Derece: Yüksek Lisans, 2020
Konu: Mimarlık = Architecture
Dizin: Mimari akustik = Architectural acoustic

Özet:
Mimari tasarımda oda oranları 20'inci yüzyılın ikinci yarısından itibaren tasarımın iyi ve kötü olarak nitelendirilmesine yönelik olarak tartışılmaya başlandı. Platon, Pisagor, Euclid gibi filozofların doğada bulunan oranlara ilişkin matematiksel yaklaşımları, bu tartışmanın epey öncesinde başlamıştır. Matematiksel oranların mimari tasarıma uygulanması bu düşünceler ışığında önemli bir konu haline geldi. Rönesans dönemi boyunca sanat üretiminde kullanılan altın oran, Fibonacci serisi ile tanımlanan matematiksel oranlar; doğanın düzeni ve kanunu olan karşılıklı anlaşma ve uyum olarak ifade edilir. Sanatta güzellik kavramı yalın olarak optik bir olayı değil, daha derin bir anlamı (karşılıklı anlaşma ve uyum) ifade eder. Modern mimari, Rönesans dönemi mimari anlayışından farklı olarak, mekânın sade, yalın ve net olarak üretir. Mekânın yüzeyleri, köşeleri, tavan, duvar, döşeme ve mobilya tasarımı net yüzeyler ile kurgulanır. Bu form değişimi sesin mekândaki davranışlarını da değiştirir. Sesin yayılmasını sağlayacak yüzeyler bu tasarım anlayışında yoktur. Bu durum özellikle küçük hacimlerde oda modlarını ortaya çıkarır.
Bu çalışmada, küçük hacimlerde oldukça önemli bir olay olan oda modlarının, hacmin şekil ve boyut özellikleri ile ilişkisi ve oda oranlarının modlar üzerindeki etkisi incelenmiştir. Çalışmanın birinci bölümü, mimaride kullanılan oda oranlarını inceler. İkinci bölüm, küçük oda tanımını ve küçük odaların akustik parametrelerini ayrıntılı olarak ele alır. Üçüncü bölüm, literatür araştırması sonucunda belirlenen çalışma matrisinin bilgisayar ortamında benzetiminin yapılmasıdır. Elde edilen sonuçlar üzerinden, modal karakteristiği en kötü olan hacim çalışmanın ikinci aşamasında incelenir. İkinci aşamada hacmin köşe ve yüzeylerine farklı şekil değişiklikleri uygulanarak modal karakteristiğindeki değişimler incelenmiştir. 
Yedi elemanlı matris (eşit hacimde yedi adet oda) üzerinde yapılan çalışma, birbirinin tam sayı katlarına sahip oranlı hacimlerin modal davranışlarının ve ses yayılımının akustik kusurlar içerdiğini gösterir. En kötü sonucu 1:1:1 oranlı küp hacim verir. En iyi sonucu ise 1:0.57:1.28 oranlı hacim verir. İkinci aşamada küp hacim, birim olarak kabul edilir. Hacmin köşe ve yüzeylerine uygulanan değişiklikler sonucunda modal karakteristiğin nasıl etkilendiği incelenmiştir. Çalışmanın iki aşamasında da yüzeylere malzeme bilgisi girilmez. Çalışma, tasarım sürecinin malzeme kararlarının verilmediği ilk aşamasında, şekil ve boyut özelliklerinin akustik kaliteye etkisini incelemeyi amaçlar.
Yapılan çalışma sonucunda, hacme uygulanan köşe değişiklikleri olay modun dalga boyu ile ilişkili olarak etki gösterdiği görülmüştür. En etkin akustik durum, hacimde yüzey paralelliklerinin bozulduğu örnekte görülmektedir. Paralelliğin bozulması hacmin modal karakteristiği üzerinde olumlu sonuçlar verir.

Abstract:
The room ratios in architectural design has started to be discussed since in the second half of the 20th century in order to can be characterized the design as good and bad. The mathematical approaches of philosophers such as Plato, Pythagoras and Euclid about of the proportions in nature has started well before this discussion. The application and using of mathematical proportions to architectural design has become an important subject in the light of these thoughts. The golden ratio and Fibonacci series used in art production during the Renaissance period; It is expressed as mutual agreement and harmony, which is the order and law of nature. The concept of beauty in art do not expresses only an optical event. It expresses a deeper meaning (mutual agreement and harmony). Unlike the architectural understanding of the Renaissance period, modern architecture produces the own architectural space with basic, simple and clear surfaces. The surfaces, corners, ceiling, wall, floor and furniture of the space are designed with clear surfaces. This design approach also changes the behavior of the sound in the architectural space. The surfaces that will diffuse the sound are absent in this design concept. This situation reveals room modes, especially in small volumes.
In this study, relation of the room modes, which is a very important acoustics criterion in small rooms, with the shape and size characteristic/property of the volume and the effect of room ratios on the modes were investigated. The first part of the study investigates the room ratios which used in architecture. The second part discusses a definition of the small room and the acoustics criterion of small rooms. The third part simulate room ratios which is determined as a result of the literature research. In the second stage of the study, the room has a worst modal characteristics is investigated. In the second stage, how can be change modal characteristics of the room with applying different treatments to the corners and surfaces of the room were investigated.
The simulation of the room was done in COMSOL Multiphysic software, which works according to the wave theory of sound. The wave theory is an effective in the small room acoustics. Mode frequencies and pressure values (Pascal and decibel) were obtained with using the software's Pressure Acoustics, Frequency Domain (acpr) physics calculation unit. Room response graphs were created by combining frequency and pressure level values.
Architectural ratio (Alberti, Golden Ratio, Fibonacci) and acoustic ratio (Europan, Harmonic) types in the literature were used to find the rooms. In the first part of the study, 3 architectural / visual ratio, 3 acoustic ratio and cube totally 7 different room ratios were studied.
Some design parameters have been kept constant. The constant parameters: volume, reverberation time. The design parameters whose effect will be investigated have been changed. Parameters whose effects are investigated: room ratio, surface and shape changes.
The images of the modes are obtained as a result of the simulation using Comsol Multiphysic software. Frequency values and pressure values of the modes are obtained by simulation. The frequency values of the modes were also calculated with the formulas for control purposes.
The frequency response curve is created by exporting the sound pressure level value and the frequency value which is corresponding to these pressure value obtained as a result of the simulation and reworking them in Excel software to make them graphic. The value on the curve represent the value of the frequency axis. Frequency response curve graphs start from the dB type of 1 Pa for each volume.
The subset was created, which has seven element. The subset is intersection of architectural room ratio set (defined by Alberti and architect/artist) and acoustics room ratio set (defined by Bonello and acoustician) which is defined by literature research. The cube room (1:1:1) was analyzed as a control unit. The number of modes in the rooms, the mode frequencies, the number of modes depending on the frequency, the distances between the modes, the positions of the modes and the shape features were investigated. The room response curve of the volumes are expressed as a graph for making comparison.
The integer multiplication between the dimensions of the room gives acoustically bad results. Overlapping mode can be created by the common divisor of the dimensions. Multiple repetition of mode frequencies make coloration phenomenon in the room. The rooms create different sound pressure levels according to their room ratio.
The modal characteristics and diffusion of sound is not good in the room, which is the integer multiplication between the dimensions. The 1:1:1 cube room has been worst results in terms of mode. The 1:0.57:1.28 room has been best results in terms of mode. Material information (reflection, absorption and diffusion datum) is not assigned on the surfaces in the both stages of the study. The study aims to investigate the effect of shape and size properties on the acoustic quality in the room. When the first phase of the architectural design the material decisions are not made.
Schroeder frequency, volume and ringing time are at the same value as they are kept constant in all room rates. It has been observed that modes with the same frequency in volumes are supported by different surfaces of the volume. This is especially the case when there is an integer relationship and a common divisor between the ratios of 1: 1: 1, 1: 2: 3, 1: 0.75: 1.5 and 1: 0.4: 0.6 ratios. These overlapping modes do not meet the Bonello and Gilford criteria. The coincident mode was not observed in volumes with 1: 0.57: 1.28 and 1: 1.26: 1.6 ratios which has not numerical common divisor relationship between ratios. The frequency response curve (frequency-decibel graph) of the volumes are different each other.
The modal characteristic of the cube room how was affected by the shape interventions on the corners and surfaces of the volume has been investigated as the second stage of the study. To the corners and surfaces of the volume, respectively; placement of square corner elements which is continuing along the height of the room, chamfering the corners, placing convex quarter cylinders, applying the vertical slats, applying the grill system which is consisting of vertical and horizontal slats on the surfaces of the room, and the splaying of the room surface for break parallelism were applied. Placement of square corner elements and chamfering corners give similar results. The vertical slats and the grid system also give similar results.
Adding a rectangular prism to the corners (1st volume); frequency values do not differ from the cubic volume, which is the control unit. It has been observed that the position and shape characteristics of the low frequency modes do not change. Adding a convex elements to the corners (3rd volume); frequency values are similar to the cubic volume. It is observed that the convex corner form has diffuser effect. For this reason, there are shifts in the zero pressure lines. Adding a vertical laths to the surfaces (4th volume); this application did not show diffuser effect at low frequency modes as expected.
As a result of the study, it is seen that the corner and surface applications of the room have an effect in relation to the wavelength of the mode. The most effective acoustic solution can be seen in the example where splaying surfaces and break parallelism. Breaking of parallelism gives positive results on the modal characteristic of the room.
The material properties (reflection, absorption and diffusion) are one of the most important criterion which is affected the acoustic properties of the volume. In this study investigates what is the effect geometric ratio of the dimensions and shape properties of the room when in the first architectural design and planning phase where the material decisions are not made and the space is designed geometrically.