prof. Dr. Ing. Michal Bednařík

The topic is to deal with investigation of acoustic waves propagating through nonlocal dispersion zones using non-uniform profiles of the density and elastic properties of materials, which enables us to control reflection and transmission of the waves in the specified spectral range. As nonlocal dispersion zones, it is supposed to use spatially confined regions with functionally graded material properties. To control transmission and reflection coefficients it is further possible to employ locally periodic/quasi-periodic structures based on nonlocal dispersion zones because even a relatively small number of repeating nonlocal dispersion zones evinces acoustic energy frequency band gaps.

The topic is focused on investigation of nonlinear acoustic fields which interact with mechanical structures. Mechanical structures can affect the acoustic field due to their frequency-dependent response, which often leads to a significant influence on the resulting spectrum of nonlinear acoustic waves. Further information can be obtained from supervisor.

The topic is focused on exploring and comparison of various mechanisms and their combinations that affect the generation of harmonics of nonlinear acoustic waves. Among those mechanisms we can include appropriate impedance termination of acoustic resonators, resonant macrosonic synthesis, temperature gradient, selective attenuation, etc. Further information can be obtained from supervisor.

In this work, it is recommended to address inhomogeneities that can be explicitly expressed by spatial dependencies of some of the characteristic parameters of the studied structure, which in certain cases can lead to analytical solutions of the corresponding model equations. In particular, model equations, that can be transformed into the shape of Heun's differential equation or some of their confluent forms, play an important role. Heun's differential equations are increasingly encountered in various fields of physics, which is given by their general character. Specifically, it may be parameters related to geometrical arrangements of structures or material parameters that can be encountered in functionally graded materials. The corresponding inhomogeneity can also be realized by a local periodic structure which represents a sonic or phononic crystal.

The topic is focused on description, modeling and analysis of progressive and standing acoustic waves of finite amplitudes when dissipative and dispersive effects are considered. The results of this study are to lead to better understanding of the nonlinear wave processes in the case that there is a competition between nonlinear, dissipative and dispersive effects. Further information can be obtained from supervisor.