Modeliranje akustike prostora z naprednimi žarkovnimi metodami

Prislan, Rok (author), Svenšek, Daniel (mentor)

Razvil sem geometrijsko metodo semiklasičnega sledenja žarku (RTS), s katero modeliramo zvočno polje v prostorih. Metoda temelji na konstrukciji Greenove funkcije amplitudne enačbe s semiklasičnim propagatorjem. RTS sodi med fazne geometrijske metode, kar jo ločuje od komercialnih geometrijskih metod, ki so energijske in zato uporabne izključno v višjefrekvenčnem območju. RTS temelji na propagaciji/sledenju zvočnim žarkom, ki se iz točkastega izvira širijo v naključno smer in zrcalno odbijejo na mejnih površinah. Žarke detektiramo v opazovanem območju in z njimi konstruiramo frekvenčni odziv, ki daje celovit vpogled v akustične lastnosti prostora. Prednost metode RTS je modeliranje interferenčnih pojavov, zaradi česar je metoda uporabna tudi v območju nizkih frekvenc, na katerega sem se tudi osredotočil pri raziskovanju. Frekvenčni odziv v pravokotnem prostoru sem primerjal z analitično rešitvijo, ki sem jo kot perturbacijo razvil za primer šibkega dušenja na mejnih površinah. S tem sem izvedel rigorozen test metode RTS, ki je pokazal, da se frekvenčni odziv dobro ujema z analitičnim. Testiral sem tudi delovanje metode RTS v primeru kompleksnejših robnih pogojev (resonator, porozni material) in frekvenčni odziv ter odmevni čas v terčnih pasovih primerjal z metodo končnih elementov. Sistematično ujemanje rezultatov za širši nabor robnih pogojev kaže na uporabnost RTS tudi v bolj realističnem okolju. Rezultate metode RTS sem primerjal tudi z meritvami v prostoru, izvedenimi z večmikrofonsko merilno metodo, ki sem jo razvil v ta namen. Z obema metodama lahko dobro prepoznamo prostorske resonance in vizualiziramo tlačne načine prostora. Geometrijske metode po definiciji ne zajemajo uklona, zato sem metodo poskušal direktno razširiti na lomljene trajektorije, s katerimi dosežemo tudi točke v geometrijski senci. Za primer neskončnega roba sem odzive primerjal z metodo končnih elementov, kjer sem dobil le kvalitativno ujemanje. Dodatno sem teoretično pregledal konstrukcijo Greenove funkcije s seštevanjem po neklasičnih trajektorijah, kjer kot numerično ugodno možnost predlagam lomljene odsekoma ravne trajektorije. V njihovi okolici sem pregledal variacijo akcije in nakazal možnosti numerične implementacije.

• Language: Slovenian
• Keywords: akustično modeliranje, geometrijsko modeliranje, fazna geometrijska metoda, semiklasični propagator, Greenova funkcija, modalne oblike v prostoru
• Work type: Doctoral dissertation
• Typology: 2.08 - Doctoral Dissertation
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2018
• PID: 20.500.12556/RUL-103581
• COBISS.SI-ID: 3238756
• Publication date in RUL: 20.09.2018

Secondary language

• Language: English
• Title: Room acoustic modelling with advanced ray-based methods

Abstract

A ray-tracing semiclassical (RTS) geometrical method was developed to model the sound field in a room. The method relies on the construction of the Green's function of the amplitude equation by employing the semiclassical propagator. Available commercial applications of geometrical methods in room acoustics are restricted to energy methods and therefore limited to higher frequencies. RTS is classified as a phased geometrical method capable of modeling interference effects, and can be thus used also in the lower frequency range which was as well the goal of this study. In RTS, sound rays are emitted from a point source in random directions. They reflect specularly on the boundaries and are detected in a spherical region. In this way the frequency response is constructed, giving a complete insight into the acoustic properties of a room. The frequency response in a rectangular room has been compared to the analytical solution derived as a perturbation for the case of weak damping. This presented a rigorous test of the method which provided good results. The RTS method was tested also for a set of more complex boundary conditions (resonator, porous material) for which the frequency response and 1/3 octave band reverberation time were compared to the finite element method. A systematic agreement is observed. Furthermore, the RTS results were compared to measurements performed by the specially developed multi-microphone measurement technique. Both methods can correctly identify room resonances and visualize modal shapes. In geometrical methods diffraction is excluded by definition, therefore I attempted to directly extend the RTS method to trajectories in the form of broken straight lines, which can propagate in the geometric shadow. For the infinite edge case the frequency response was compared to the finite element method and qualitative agreement was observed. Moreover, I theoretically reviewed the possibility of constructing the Green's function with the summation over non-classical trajectories. From this viewpoint, I again suggested the use of broken trajectories. In their proximity the variation of the action was examined and important aspects of the numerical implementation were introduced.

• Keywords: acoustic modeling, geometrical modeling, phased geometrical methods, semiclassical propagator, Green's function, room modal shapes