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PZT Asymmetrical Shape Optimization in Active Vibration Reduction of Triangular Plates

Brański Adam, Kuras Romuald

Archives of Acoustics

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2023

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Vol. 48, No. 3

425--432

EN

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.

2

Project of acoustic adaptation of the church with a long reverberation time

Brański Adam, Janas Lucjan, Prędka Edyta, Klich Rafał, Szynal Daniel

Vibrations in Physical Systems

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2022

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Vol. 33, nr 2

art. no. 2022209

EN

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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Asymmetrical PZT Applied to Active Reduction of Asymmetrically Vibrating Beam – Semi-Analytical Solution

Brański Adam, Kuras Romuald

Archives of Acoustics

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2022

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Vol. 47, No. 4

555--564

EN

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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Selected Aspects of Meshless Method Optimization in the Room Acoustics with Impedance Boundary Conditions

Prędka Edyta, Kocan-Krawczyk Anna, Brański Adam

Archives of Acoustics

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2020

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Vol. 45, No. 4

647--654

EN

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.

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Analysis of the Room Acoustic with Impedance Boundary Conditions in the Full Range of Acoustic Frequencies

Prędka Edyta, Brański Adam

Archives of Acoustics

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2020

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Vol. 45, No. 1

85--92

EN

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.