An Influence of the Wall Acoustic Impedance on the Room Acoustics. The Exact Solution

2018

An efficiency of the nonsingular meshless method is analyzed in an acoustic indoor problem. The solution is assumed in the form of the series of radial bases functions. The Hardy's multiquadratic functions, as the bases, are taken into account. The room acoustic field with uniform, impedance walls is considered. The representative, rectangular cross section of the room is chosen. Practical combinations of acoustic boundary conditions, expressed through absorption coefficient values, are considered. The classical formulation of the boundary problem is used. It is established any coefficient in the multiquadratic functions depend on the number of influence points, the frequency and the absorption coefficient. All approximate results are calculated in relation to the exact ones. This way, it is proved that the meshless method based on the multiquadratic functions is simple and efficient method in the description of the complicated acoustic boundary problems for the low and medium ranges of frequency.

Section: Numerical Calculations Results Conclusionmentioning

confidence: 99%

“…For this reason, recently researches are concerned on meshless methods (MLM), sometimes called meshfree method (MFM) (Atluri, 2004;Chen et al, 2013;Brański, Prędka, 2014;Prędka, 2015).…”

Section: Introductionmentioning

confidence: 99%

Archives of Acoustics

2018

“…The intensity of the source A is chosen, so that the L m (Eq. ( 9)) takes the same value for different values of the absorption coefficient α and frequencies f (Brański et al, 2017).…”

Section: Formulation Of the Boundary Acoustic Problemmentioning

confidence: 99%

Archives of Acoustics

Kocan-Krawczyk

2020

Two optimization aspects of the meshless method (MLM) based on nonsingular radial basis functions (RBFs) are considered in an acoustic indoor problem. The former is based on the minimization of the mean value of the relative error of the solution in the domain. The letter is based on the minimization of the relative error of the solution at the selected points in the domain. In both cases the optimization leads to the finding relations between physical parameters and the approximate solution parameters. The room acoustic field with uniform, impedance walls is considered.As results, the most effective Hardy's Radial Basis Function (H-RBF) is pointed out and the number of elements in the series solution as a function of frequency is indicated. Next, for H-RBF and fixed n, distributions of appropriate acoustic fields in the domain are compared. It is shown that both aspects of optimization improve the description of the acoustic field in the domain in a strictly defined sense.

“…In general, WBM is used for low frequencies, ISM for the early part of the room response for middle and high frequencies and AEM for the rest of the response for middle and high frequencies. Each method has advantages and disadvantages; some of them are enumerated in (Brański, Prędka, 2018). These different groups of methods have some links among them (Rindel, 2010) and in some frequency ranges they can be applied interchangeably.…”

Section: Introductionmentioning

confidence: 99%

“…Such a method ought to be searched among WBM; other two methods, i.e. ISM and AEM, are not suitable for describing the field in full acoustic frequencies, (Brański, Prędka, 2018) and references cited therein. The finite element method (FEM) (Fish, Belytschko, 2007 To avoid this problem, researchers are currently focusing on MLM (Atluri, 2004 The purpose of this study is to apply MLM and analyze its effectiveness to solve the internal acoustic problem with impedance boundary conditions imposed on walls and in full range of acoustic frequencies.…”

Section: Introductionmentioning

confidence: 99%

Archives of Acoustics

2020

An efficiency of the nonsingular meshless method (MLM) was analyzed in an acoustic indoor problem. The solution was assumed in the form of the series of radial bases functions (RBFs). Three representative kinds of RBF were chosen: the Hardy's multiquadratic, inverse multiquadratic, Duchon's functions. The room acoustic field with uniform, impedance walls was considered. To achieve the goal, relationships among physical parameters of the problem and parameters of the approximate solution were first found. Physical parameters constitute the sound absorption coefficient of the boundary and the frequency of acoustic vibrations. In turn, parameters of the solution are the kind of RBFs, the number of elements in the series of the solution and the number and distribution of influence points. Next, it was shown that the approximate acoustic field can be calculated using MLM with a priori error assumed. All approximate results, averaged over representative rectangular section of the room, were calculated and then compared to the corresponding accurate results. This way, it was proved that the MLM, based on RBFs, is efficient method in description of acoustic boundary problems with impedance boundary conditions and in all acoustic frequencies.