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.
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This paper presents the results of unconfined compressive strength tests carried out on samples of two different fine grained soils mixed with anthropogenic materials produced in Poland, showing binding properties - cement kiln dust and fly ash obtained from combustion of brown coal in a pulverized boiler. The tests were performed on cylindrical samples in a testing machine for compression tests after various curing time ranging from 1 to 8 weeks. The conducted work constitutes the first stage of research devoted to the recognition of the effects of calcareous fly ash and cement kiln dust addition into the fine grained soils.
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 numer 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.
Long reverberation times are a problem in modern churches. General methods of solving the problem are given in the literature. The basic approach is to increase the acoustic absorption of the church, and this can be achieved by placing sound-absorbing materials on the walls. Due to the price, materials with a high absorption coefficient are not used. They are replaced with sound-absorbing plasters. For the known coefficient of sound absorption by plaster, the problem is to calculate the surface of the plaster coverage and its distribution on the surface. This problem was solved for the Academic Church in Rzeszow, the Roman Catholic Parish of St. Jadwiga Queen. The reverberation time before adaptation is equal to 6.78 s, while the predicted time after adaptation is 1.98 s.
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