Differential and finite-difference problems of active shielding

Ryaben’kii, Victor S.; Utyuzhnikov, Sergey

doi:10.1016/j.apnum.2006.05.002

Cited by 20 publications

(13 citation statements)

References 12 publications

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“…Thus, if m < 0, the additional termĝ + 0 δ 0 in (26) provides the field coinciding with the solution without the effect of external noise (22). It is important to note that the result does not depend on the value ofĝ + 0 .…”

Section: Discrete Solution Of As Problem With Terminationmentioning

confidence: 85%

“…In our case, in order to substitute the measurement values, we are able to obtain them from exact solution (22), (23):…”

Section: Discrete Solution Of As Problem With Terminationmentioning

confidence: 99%

“…A comprehensive analysis of continuous and finite-difference surface potentials mostly appropriate for the Helmholtz-type equation is carried out by Tsynkov in [24]. In [22] the solution of the linear AS problem is obtained in the continuous space for the acoustic equation with constant and variable coefficients. Whereas optimization of AS sources is studied in detail in the papers cited above, not much attention has been paid to the wave analysis of AS process itself.…”

Section: Introductionmentioning

confidence: 99%

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On the application of difference potential theory to active noise control

Ryaben’kii

Utyuzhnikov

Turan

2008

Advances in Applied Mathematics

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The application of the theory of difference potentials to the problem of active shielding and noise control is considered. Difference potential theory allows us to obtain the general solution of the problem in a finitedifference formulation. The solution is valid for arbitrary space domains, medium and boundary conditions. It only requires the information on the total sound (both "friendly" and "adverse") at the perimeter of the domain to be shielded. In contrast to the previous publications, in the current paper the mechanism of active shielding solution based on the difference potential theory is analysed. The theory of difference potentials is applied to the system of acoustic equations. The correspondence between the finite-difference solution and the continuous solution based on Green's function is shown for the case of a uniform medium. Different possible representations of the active shielding source terms are analysed. A clear physical interpretation of the optimal space step in the finite-difference solution is provided. The results can be important for both understanding the solution of the active shielding problem and practical applications.

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Section: Discrete Solution Of As Problem With Terminationmentioning

confidence: 85%

“…In our case, in order to substitute the measurement values, we are able to obtain them from exact solution (22), (23):…”

Section: Discrete Solution Of As Problem With Terminationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the application of difference potential theory to active noise control

Ryaben’kii

Utyuzhnikov

Turan

2008

Advances in Applied Mathematics

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“…It is to be noted that surface controls have the same fundamental properties as volumetric controls. A universal framework for both volumetric and surface controls is built by Ryaben'kii and Utyuzhnikov in the recent paper [22]; it treats the governing equation for the field in an operator form. We should also emphasize that the continuous formulation is not practical for implementation.…”

Section: Introductionmentioning

confidence: 99%

“…This will lead to a discretization of the problem on a grid. Discrete active shielding problems were analyzed, and the corresponding solutions obtained in [14,15,16,25], as well as more recently in [22]. The finite-difference analysis of [14,15,16,22,25] uses the constructs developed previously in the works by Ryaben'kii [18] and by Veizman and Ryaben'kii [27,28].…”

Section: Introductionmentioning

confidence: 99%

Active Control of Sound for Composite Regions

Peterson¹,

Tsynkov²

2007

SIAM J. Appl. Math.

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We present a methodology for the active control of time-harmonic wave fields, e.g., acoustic disturbances, in composite regions. This methodology extends our previous approach developed for the case of arcwise connected regions. The overall objective is to eliminate the effect of all outside field sources on a given domain of interest, i.e., to shield this domain. In this context, active shielding means introducing additional field sources, called active controls, that generate the annihilating signal and cancel out the unwanted component of the field. As such, the problem of active shielding can be interpreted as a special inverse source problem for the governing differential equation or system. For a composite domain, not only do the controls prevent interference from all exterior sources, but they can also enforce a predetermined communication pattern between the individual subdomains (as many as desired). In other words, they either allow the subdomains to communicate freely with one another or otherwise have them shielded from their peers. In the paper, we obtain a general solution for the composite active shielding problem and show that it reduces to solving a collection of auxiliary problems for arcwise connected domains. The general solution is constructed in two stages. Namely, if a particular subdomain is not allowed to hear another subdomain, then the supplementary controls are employed first. They communicate the required data prior to building the final set of controls. The general solution can be obtained with only the knowledge of the acoustic signals propagating through the boundaries of the subdomains. No knowledge of the field sources is required, nor is any knowledge of the properties of the medium needed.

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Linear and nonlinear problems of active sound control

Utyuzhnikov

Ryaben’kii

Turan

2007

Proc Appl Math and Mech

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The problem of active shielding of some domain from the effect of the field generated in another domain is considered. The active shielding is implemented via the placement of additional sources in such a way that the total contribution of all sources leads to the desirable effect. The obtained solution does not require either the knowledge of the particular Green's function or any other information on source distribution and the surrounding medium. It is also important that along with undesirable field to be shielded, a desirable field can be admitted in the analysis. The solution of the problem requires only knowledge of the total field on the perimeter of the shielded domain. The active shielding sources are obtained for both the linear and nonlinear formulations of the problem.

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Differential and finite-difference problems of active shielding

Cited by 20 publications

References 12 publications

On the application of difference potential theory to active noise control

On the application of difference potential theory to active noise control

Active Control of Sound for Composite Regions

Linear and nonlinear problems of active sound control

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