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Indoors sound field distribution is important to Room Acoustics, but the field suffers numerous problems, for example, multipath propagation and scattering owing to sound absorption by furniture and other aspects of décor. Generally, an ideal interior space must have a sound field with clear quality. This provides both the speaker and the listener with a pleasant conversational environment. This investigation uses the Finite Element Method to assess the acoustic distribution based on the indoor space and chamber volume. In this situation, a fixed sound source at different frequencies is used to simulate the acoustic characteristics of the indoor space. This method considers the furniture and decoration sound absorbing material and thus different sound absorption coefficients and configurations. The preliminary numerical simulation provides a method that can forecast the distribution of sound in an indoor room in complex situations. Consequently, it is possible to arrange interior furnishings and appliances to optimize acoustic distribution and environmental friendliness. Additionally, the analytical results can also be used to calculate the Reverberation Time and speech intelligibility for specified indoor space.

Economic development in human society has been more demanding in terms of quality of life, particularly in relation to noise issues. Noise is defined as undesirable sound or sound with inappropriate timing and location. Noise thus includes sound that interferes with talking and listening and may include sound with a potential to damage hearing. In modern living environments, noise is ubiquitous and includes pile driving and hammering on construction sites, vehicle engines and horns, and mechanical sounds associated with printing, underground factories, or other industrial activities. Noise quality of vehicles and electric appliances causes stress, and noise problems associated with public construction, which can affect a citizen’s health and damage quality of life, are also emphasized. This makes it necessary to understand noise characteristics and then select a favorable engineering control to protect people against noise. Current domestic research on the evaluation of interior sound fields rarely considers the evaluation of environmental noise, and distinct approaches are applied to test and evaluate different noise sources. Noise evaluation indices and sound field simulation are commonly employed for interior sound field analyses. In a residential study, Huang and Lai [

Among various methods used in discussions of simulation, the Finite Element Method is commonly utilized in research analyses. It tends to obtain solutions by simplifying complex problems, such as those involving complex and irregular boundary conditions and loads. Huang and Yang [

This study analyzes the characteristics of interior sound fields with fixed capacity and sound sources. The effects of shape, absorption property, and room boundary on sound delivery are analyzed to determine the improvement of interior noise. The research results can be used in the predesign of interior architecture to improve interior noise, decrease construction costs, and improve living quality.

Sound comprises pressure change that resulted from the vibration of objects or molecules (the sound source), which, transmitted through water, air, or other media (communication path), becomes mechanical energy detected by human ears (the sound body). The waveform of sound comprises the mathematical and physical characteristics of sine waves, including frequency, wavelength, time lapse, and phase angle. Sound volume is normally represented using the physical quantity of sound pressure, with the unit of measurement being decibels (dB), and is related to an object’s vibration. Volume is the subjective perception of human ears of the amplitude, which differs from the definition in physics.

The sound discrimination ability of human ears exhibits nonlinear characteristics and is sensitive to distinct frequency. The general auditory frequency of human ears appears at 20-20 kHz. Sound pressure and sound intensity are normally used to measure sound as the perception of loudness changes with frequency. In this case, noise level meters are generally equipped with different weighted noise levels, A, B, and C, where weighted noise level A most closely resembles the human ear.

W. C. Sabine spent five years seeking to improve acoustics in university lecture halls and developed the famous Reverberation Theory, which defined Reverberation Time (RT) to present reflection time for a direct sound to decay 60 dB. He further explained the relations between the shape, size, and decoration of a room, which could improve the quality of interior listening environment, as well as Reverberation Time, which became the determinant of Room Acoustics [

Three sound waves are transmitted in interior sound environments. Direct sound indicates that the sound source is directly transmitted to the receiving point without influence from interior interfaces [

When analyzing indoor acoustic simulation, the coupling of fluid and a structure is generally taken into account [

This study establishes the Finite Element Method as the model used for interior sound field analysis. With the development of CAE during recent decades, the Finite Element Method (FEM), Boundary Element Method (BEM), and Finite Differential Method (FDM) have been developed for different applications. Finite Element Analysis (FEA), being widely utilized, was based on Hamilton’s Variation Principle, which was defined as the total energy required to achieve extreme values in neighboring areas. Based on this definition, analyses can be performed to calculate the sum energy, and the Euler-Lagrange differential equation can be derived using differential calculus. The governing equation is a simultaneous multivariate partial differential equation where an accurate solution can be obtained by given simple shape, boundary condition, and material property of the domain. Nevertheless, this approach only yields approximate solutions when applied in the real world.

Finite Element Method is composed of nodes and elements and replaces the original engineering systems. Additionally, a complete FEM contains the boundary conditions of constraints and external loads of an engineering system. This study uses ANSYS to simulate the sound field distribution under fixed noise sources in an interior space, where sound sources can be indoor fan or air-conditioner noise, and the floor, surroundings, and air can be the media that consider the absorption characteristics. The simulation results can be used to clarify the changes in sound field characteristics, such as frequency, location, and intensity of sound sources in distinct interior space and boundary reflections.

The strong form governing equation will be converted to weak form for obtaining the discrete algebraic equation. Multiplying (

Equation (

The internal approximate values of the elements could be calculated with (

Working environment is the main influence on human productivity and health that improves interior environments to reduce personnel costs through simulations that minimize loss. The Finite Element Method transforms the engineering system into the Finite Element System for the simulation and analyses. Among the acoustic parameters, the absorption coefficient is one of the main factors and is used to quantify the absorption competence for the reference and the application of soundproofing engineers interested in calculating attenuated volume. The absorption coefficient is the competence indicator of absorption materials. When the sound is transmitted to absorption materials, the sound is partially reflected and partially absorbed, as the commonly used porous absorption materials present a loose structure that allows easy sound penetration. Furthermore, absorption materials are generally fitted on thick structures like walls and metal plates that sound does not easily penetrate but from which is easily reflected. Small

Finite Element Analysis precedes the simulation in the environment with existing room arrangement, room capacity, and fixed sound sources and discusses the effects of room boundary on Reverberation Time of interior language under distinct frequency. In the analysis, the room shape and materials influence the reflection, diffraction, and scattering of sound and allow organization of the transmission in the space and the acquisition of interior data such as room size and absorption materials used on walls. The software is utilized to obtain the sound pressure distribution and Reverberation Time indoors. The results can be compared with the measured value of interior sound pressure to improve interior noise. The research results can also be used in preanalyses to improve the interior noise. Such measures not only can effectively reduce construction costs, but also can improve living quality. Table

Input parameters for this research analysis.

Properties | Air | Wall |
---|---|---|

Length (m) | 2.13 | 2.74 |

Width (m) | 0.31 | 0.31 |

Height (m) | 2.44 | 3.05 |

Density (kg/m^{3}) |
1.29 | 2600 |

Velocity (m/sec) | 335.28 | 3100 |

Absorption coefficient | ~0. | 0.04–0.70 |

Finite Element Analysis is applied to analyze the interior sound field with fixed capacity and sound sources. The effects of room shape, absorption characteristics, and boundary are also analyzed. Table

In this case, the analysis is unsuitable for the corners at the length direction. Figure ^{−6} sec, where the sound pressure is distributed in tiny sections and the instant sound pressure diffusion is observable.

Delivery of pulse sound pressure at the 0.001 sec.

Figure ^{−6} sec for the elements in the middle of the analysis. Figure

Stereo diagram of sound field before the diffusion at 1 × 10^{−6} sec.

Sound field distribution after 1 × 10^{−5} sec.

Boundary reflection with the delivery time 0.0044 sec.

Stable state of sound pressure after several reflections.

Sound decay phenomena along the perpendicular direction of the sound source.

When an indoor space existing a fluid machine, such as pump, fan, or air condition, the induced sound source for different frequency should be considered. For an electric fan and motor, the sound pressure of several frequencies is listed in Table

Sound pressure levels of an electric fan and motor.

Frequency (Hz) | Fan (dB) | Motor (dB) |
---|---|---|

63 | 84.6 | 49.0 |

125 | 81.6 | 53.0 |

250 | 83.6 | 57.0 |

500 | 84.6 | 61.0 |

1000 | 82.6 | 61.0 |

2000 | 79.6 | 57.0 |

4000 | 77.6 | 53.0 |

8000 | 67.6 | 49.0 |

Sound pressure distribution of the fan noise for propagating to the ground.

Sound pressure distributions for different frequencies at time 0.02567 sec.

63 Hz

125 Hz

250 Hz

500 Hz

1000 Hz

2000 Hz

4000 Hz

8000 Hz

The analysis data can be applied to evaluate the relevant physical parameters of the loudness component, including the interior sound quality analysis of the Reverberation Time required for the sound pressure at the fixed location attenuating to 60 dB, with (

Using the frequency 1 kHz and the induced time of five complete cycles of the pulse wave, this study analyzes the interior wave propagation. ANSYS analysis considers the boundary reflection, coupling, and the absorption characteristics of materials. The simulation results demonstrate the characteristics of interior wave propagation, as well as the superposition characteristics following boundary contact. The fluid machine sound source is also examined for obtaining the sound distribution of various amplitudes and frequencies. It can be further applied to the predesign analysis of interior architecture to improve interior noise and effectively reduce the construction costs and increase quality of life.