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EN
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.
EN
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.
EN
The Fourier method is applied to the description of the room acoustics field with the combination of uniform impedance boundary conditions imposed on some walls. These acoustic boundary conditions are expressed by absorption coefficient values In this problem, the Fourier method is derived as the combination of three one-dimensional Sturm-Liouville (S-L) problems with Robin-Robin boundary conditions at the first and second dimension and Robin-Neumann ones at the third dimension. The Fourier method requires an evaluation of eigenvalues and eigenfunctions of the Helmholtz equation, via the solution of the eigenvalue equation, in all directions. The graphic-analytical method is adopted to solve it It is assumed that the acoustic force constitutes a monopole source and finally the forced acoustic field is calculated. As a novelty, it is demonstrated that the Fourier method provides a useful and efficient approach for a room acoustics with different values of wall impedances. Theoretical considerations are illustrated for rectangular cross-section of the room with particular ratio. Results obtained in the paper will be a point of reference to the numerical calculations.
4
EN
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.
EN
An active reduction of transverse vibration of the triangular plate with P-F-F boundary conditions is considered. The cracked plate is idealized research model as partially clamped on one edge with varying clamped length. The active reduction is realised with PZTs. In the paper, assuming the detached base clamped length, the influence of PZTs distribution on the bending moment and the shearing force at the clamped edge is investigated. To realize the purpose two cases are considered. At the former the PZTs are attached at points in which the curvatures of the surface locally take their maximum (MC sub-areas or quasi-optimal ones). At the latter, the PZTs are somewhat shifted. The plate is excited with harmonic plane acoustic wave. The second mode is considered only. The active vibration reduction study with a finite element method (FEM) is carried out. The numerical calculations show that better results are obtained for MC distribution of the PZTs.
6
Improvement of effectiveness in active triangular plate vibration reduction
EN
In the paper, a new method of the effectiveness increase of the active asymmetrical structure vibration reduction via PZTs is proposed. The new method is based on adding successive PZTs to quasi-optimal sub-areas (QO) in the determined order. A triangular plate with the C-F-F boundary conditions is chosen for this purpose. Only the second mode of the plate is taken into consideration in this study. To realise the aim, first the QO are determined. To each QO, PZTs are bonded from one to seven according to the following rule; namely, the consecutive PZT takes up free surface with locally maximal curvature on the QO. The effectiveness of the vibration reduction is measured in particular sense. Numerical experiments are performed to confirm the validity of this idea.
7
On practical aspects of optimal modelling in boundary element method
EN
The paper is concerned with application of the BEM in the environmental noise problems. The main step of the BEM is the discretization of the boundary into elements. Using too many elements is not efficient. To eliminate this drawback, in this paper two ideas are proposed. First of them is the optimal discretization, and the second one is the solution of the modelling problem in rotated coordinates. Since the optimal discretization theory derived for the function of one variable, then only the 2D problem is considered. The commercial code SYSNOISE is used to solve the numerical examples. The results confirm the utility of the proposed ideas.
EN
A new hybrid method (HM) solution to the radiation problem is presented. The HM is based on the separation of variables method and the boundary element method. An idea of the HM consists in the modelling of acoustic variables only by the boundary element method using their discrete values. The geometry of the problem is described exactly. The HM enables to solve boundary acoustic problem in an orthogonal curvilinear system of coordinates. In the paper the method is applied to acoustic radiation by axially vibrating cup or ring set on the sphere. The hybrid radiation solution is compared to the well known analytical one.
9
Problem of an optimal discretization in acoustic modelling
EN
In this paper two new models of an acoustic source in BEM are proposed. For simplicity a plane axisymmetric source is modelled. Up to now, the models consist of elements of the same dimension. Furthermore, the nodes are equi-spaced on each element. In contrast to these models, the first new one is composed of optimal elements on which the nodes are equi-spaced. The second new model is composed of optimal elements too but the nodes on each element are optimal (Tchebicheff nodes). Numerical calculations pointed out that the quality of the new models is better than the known ones.
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