Biomedical subjects

Michal Bednarik

Publications and source records attributed to Michal Bednarik.

4 recordsLinked to original sources

PubMed2006

Nonlinear interactions in elastic resonators.

This work is dedicated to nonlinear interactions in elastic resonators. It is supposed that a resonator wall yields locally to the inner pressure. The elastic wall of the resonator induces strong dispersion and dissipation of acoustic energy. The dispersion can significantly influence studied nonlinear interactions which are ineffective because the synchronous conditions are not satisfied and hence a coherence length is too short. In the frame of this work conditions for generation of subharmonics are studied on the basis of topological and numerical analyze. For this reason the method of local stability is applied. For description of nonlinear standing wave is derived modified inhomogeneous Burgers equation and the inhomogeneous Korteweg-de Vries-Burgers equation. These equations take into account thermo-viscous losses of supposed fluids, boundary layer losses, wall losses and dispersion effects caused by both the resonator wall and the acoustic boundary layer. Number of numerical solutions of these model equations is shown and unsteady solitary waves are investigated.

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PubMed2006

Nonlinear standing waves in 2-D acoustic resonators.

This paper deals with 2-D simulation of finite-amplitude standing waves behavior in rectangular acoustic resonators. Set of three partial differential equations in third approximation formulated in conservative form is derived from fundamental equations of gas dynamics. These equations form a closed set for two components of acoustic velocity vector and density, the equations account for external driving force, gas dynamic nonlinearities and thermoviscous dissipation. Pressure is obtained from solution of the set by means of an analytical formula. The equations are formulated in the Cartesian coordinate system. The model equations set is solved numerically in time domain using a central semi-discrete difference scheme developed for integration of sets of convection-diffusion equations with two or more spatial coordinates. Numerical results show various patterns of acoustic field in resonators driven using vibrating piston with spatial distribution of velocity. Excitation of lateral shock-wave mode is observed when resonant conditions are fulfilled for longitudinal as well as for transversal direction along the resonator cavity.

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PubMed2004

Asymptotic solutions of the inhomogeneous Burgers equation.

The method of the active second harmonic suppression in resonators is investigated in this paper both analytically and numerically. The resonator is driven by a piston which vibrates with two frequencies. The first one agrees with an eigenfrequency and the second one is equal to the two times higher eigenfrequency. The phase shift of the second piston motion is 180 deg. It is known that for this case it is possible to describe generation of the higher harmonics by means of the inhomogeneous Burgers equation. This model equation was solved for stationary state analytically by a number of authors but only for ideal fluids. Unlike their solutions, new asymptotic solutions are presented here which take into account dissipative effects. The asymptotic solutions are compared with numerical ones. For study of generation higher harmonics the solutions are developed in a spectral form.

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PubMed2002

Propagation of quasiplane nonlinear waves in tubes and the approximate solutions of the generalized Burgers equation.

This paper deals with using the generalized Burgers equation for description of nonlinear waves in circular ducts. Two new approximate solutions of the generalized Burgers equation (GBE) are presented. These solutions take into account the boundary layer effects. The first solution is valid for the preshock region and gives more precise results than the Fubini solution, whereas the second one is valid for the postshock (sawtooth) region and provides better results than the Fay solution. The approximate solutions are compared with numerical results of the GBE. Furthermore, the limits of validity of the used model equation are discussed with respect to boundary conditions and radius of a circular duct.

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