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Number of results: 10
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Abstract

In this paper an active multimodal beam vibration reduction via one actuator is considered. The optimal actuator distribution is analyzed with two methods: an exact mathematical principles and the LQ problem idea. It turned out that the same mathematical expressions are derived. Thus, these methods are equivalent.
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Authors and Affiliations

Elżbieta Żołopa
Adam Brański
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Abstract

The cuboidal room acoustics field is modelled with the Fourier method. A combination of uniform, impedance boundary conditions imposed on walls is assumed, and they are expressed by absorption coefficient values. The absorption coefficient, in the full range of its values in the discrete form, is considered. With above assumptions, the formula for a rough estimation of the cuboidal room acoustics is derived. This approximate formula expresses the mean sound pressure level as a function of the absorption coefficient, frequency, and volume of the room separately. It is derived based on the least-squares approximation theory and it is a novelty in the cuboidal room acoustics. Theoretical considerations are illustrated via numerical calculations performed for the 3D acoustic problem. Quantitative results received with the help of the approximate formula may be a point of reference to the numerical calculations.
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Authors and Affiliations

Anna Kocan-Krawczyk
Adam Brański
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Abstract

The article presents the main results of research on plaster samples with different physical parameters of their structure. The basic physical parameter taken into account in the research is plaster aeration. Other physical parameters were also considered, but they play a minor part. The acoustic properties of the modified plaster were measured by the sound absorption coefficient; the results were compared with the absorption coefficient of standard plaster. The influence of other physical, mechanical and thermal properties of plaster was not analyzed. The effect of modified plasters on indoor acoustics was also determined. To this end, an acoustic problem with impedance boundary conditions was solved. The results were achieved by the Meshless Method (MLM) and compared with exact results. It was shown that the increase in plaster aeration translated into an increase in the sound absorption coefficient, followed by a slight decrease in the noise level in the room. Numerical calculations confirmed this conclusion.
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Bibliography

1. Bonfiglio P., Pompoli F. (2007), Acoustical and physical characterization of a new porous absorbing plaster, ICA, 19-th International Congress on Acoustics, Madrid, 2–7 September 2007.
2. Branski A. (2013), Numerical methods to the solution of boundary problems, classification and survey [in Polish], Rzeszow University of Technology Press, Rzeszow.
3. Branski A., Kocan-Krawczyk A., Predka E. (2017), An influence of the wall acoustic impedance on the room acoustics. The exact solution, Archives of Acoustics, 42(4): 677–687, doi: 10.1515/aoa-2017-0070.
4. Branski A., Predka E. (2018), Nonsingular meshless method in an acoustic indoor problem, Archives of Acoustics, 43(1): 75–82, doi: 10.24425/118082.
5. Branski A., Predka E., Wierzbinska M., Hordij P. (2013), Influence of the plaster physical structure on its acoustic properties, 60th Open Seminar on Acoustics, Rzeszów–Polanczyk (abstract: Archives of Acoustics, 38(3): 437–437).
6. Chen L., Zhao W., Liu C., Chen H., Marburg S. (2019), Isogeometric fast multipole boundary element method based on Burton-Miller formulation for 3D acoustic problems, Archives of Acoustics, 44(3): 475– 492, doi: 10.24425/aoa.2019.129263.
7. Chen L., Li X. (2020), An efficient meshless boundary point interpolation method for acoustic radiation and scattering, Computers & Structures, 229: 106182, doi: 10.1016/j.compstruc.2019.106182.
8. Cucharero J., Hänninen T., Lokki T. (2019), Influence of sound-absorbing material placement on room acoustical parameters, Acoustics, 1(3): 644–660; doi: 10.3390/acoustics1030038.
9. ISO 10354-2:1998 (1998), Acoustics – determination of sound absorption coefficient in impedance tube. Part 2: Transfer-function method.
10. Kulhav P., Samkov A., Petru M., Pechociakova M. (2018), Improvement of the acoustic attenuation of plaster composites by the addition of shortfibre reinforcement, Advances in Materials Science and Engineering, 2018: Article ID 7356721, 15 pages, doi: 10.1155/2018/7356721.
11. Li W., Zhang Q., Gui Q., Chai Y. (2020), A coupled FE-Meshfree triangular element for acoustic radiation problems, International Journal of Computational Methods, 18(3): 2041002, doi: 10.1142/S0219876220410029.
12. McLachlan N.W. (1955), Bessel Functions for Engineers, Clarendon Press, Oxford.
13. Meissner M. (2012), Acoustic energy density distribution and sound intensity vector field inside coupled spaces, The Journal of the Acoustical Society of America, 132(1): 228−238, doi: 10.1121/1.4726030.
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15. Meissner M. (2016), Improving acoustics of hardwalled rectangular room by ceiling treatment with absorbing material, Progress of Acoustics, Polish Acoustical Society, Warsaw Division, Warszawa, pp. 413–423.
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19. Predka E., Branski A. (2020), Analysis of the room acoustics with impedance boundary conditions in the full range of acoustic frequencies, Archives of Acoustics, 45(1): 85–92, doi: 10.24425/aoa.2020.132484.
20. Predka E., Kocan-Krawczyk A., Branski A. (2020), Selected aspects of meshless method optimization in the room acoustics with impedance boundary conditions, Archives of Acoustics, 45(4): 647–654, doi: 10.24425/aoa.2020.135252
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26. You X., Li W., Chai Y. (2020), A truly meshfree method for solving acoustic problems using local weak form and radial basis functions, Applied Mathematics and Computation, 365: 124694, doi: 10.1016/j.amc.2019.124694.
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Authors and Affiliations

Edyta Prędka
1
Adam Brański
1
ORCID: ORCID
Małgorzata Wierzbińska
2

  1. Department of Electrical and Computer Engineering Fundamentals, Technical University of Rzeszow, Rzeszów, Poland
  2. Department of Materials Science, Technical University of Rzeszow, Rzeszów, Poland
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Abstract

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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Authors and Affiliations

Edyta Prędka
Adam Brański
ORCID: ORCID
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Abstract

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.

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Authors and Affiliations

Edyta Prędka
Anna Kocan-Krawczyk
Adam Jan Brański
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Abstract

The article presents the new 2D asymmetrical PZT (a-PZT) and its effectiveness in the active reduction of triangular plate vibrations. The isosceles right triangular plate with simply supported edges was chosen as the research object. To determine the a-PZT asymmetry and its distribution on the plate, a maximum bending moment criterion for the beam was used. First of all, this criterion points out exact center location of the a-PZT. It was at the point, at which the plate bending moment has reached its maximum value. Next, at this point, it was assumed that the piezoelectric consists of active fibers located radially from the center. Each fiber acted on the plate as a separate actuator. Next, at each direction, the actuator asymmetry was found mathematically by minimizing the amplitude of the vibrations. By connecting the outer edges of individual fibers, the 2D a-PZT was obtained. It was quantitatively confirmed that the effectiveness of the new a-PZT was the best compared with the effectiveness of the standard square and the circular PZTs, adding the same exciting energy to the PZTs.
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Authors and Affiliations

Adam Brański
1
ORCID: ORCID
Romuald Kuras
1
ORCID: ORCID

  1. Department of Electrical and Computer Engineering Fundamentals, Rzeszow University of Technology, Rzeszow, Poland
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Abstract

The article extended the idea of active vibration reduction of beams with symmetric modes to beams with asymmetric modes. In the case of symmetric modes, the symmetric PZT (s-PZT) was used, and the optimization of the problem led to the location of the s-PZT centre at the point with the greatest beam curvature. In the latter case, the asymmetric modes that occur due to the addition of the point mass cause an asymmetric distribution of the bending moment and transversal displacement of a beam. In this case, the optimal approach to the active vibration reduction requires both new asymmetric PZT (a-PZT) and its new particular distribution on the beam. It has been mathematically determined that the a-PZT asymmetry point (a-point), ought to be placed at the point of maximum beam bending moment. The a-PZT asymmetry was found mathematically by minimizing the amplitude of the vibrations. As a result, it was possible to formulate the criterion of the maximum bending moment of the beam. The numerical calculations confirmed theoretical considerations. So, it was shown that in the case of asymmetric vibrations, the a-PZTs reduced vibrations more efficiently than the s-PZT.
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Authors and Affiliations

Adam Brański
1
ORCID: ORCID
Romuald Kuras
1
ORCID: ORCID

  1. Laboratory of Acoustics, Department of Electrical and Computer Engineering Fundamentals, Rzeszow University of Technology, Rzeszow, Poland

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