Analytical Solutions of Heat Conduction Problems for Anisotropic Solid Body

Exact analytical solutions of heat conduction problems in anisotropic twodimensional solid bodies are presented in this study. Timedependent and steadystate problems are considered. A linear coordinate transformation is introduced which reduces the anisotropic heat conduction problem to an equivalent isotropic one. The solution of the anisotropic heat conduction problem is expressed in terms of solutions of the corresponding isotropic heat conduction problem. The connection of data of the applied linear coordinate transformation and the thermal material properties of anisotropic solid body is analysed. All result of the paper is based on the Fourier’s theory of heat conduction in solid bodies. Examples illustrate the applications of the developed method

Non-reciprocal acoustics in a viscous environment

It is demonstrated that acoustic transmission through a phononic crystal with anisotropic solid scatterers becomes non-reciprocal if the background fluid is viscous. In an ideal (inviscid) fluid, the transmission along the direction of broken P symmetry is asymmetric. This asymmetry is compatible with reciprocity since time-reversal symmetry ( T symmetry) holds. Viscous losses break T symmetry, adding a non-reciprocal contribution to the transmission coefficient. The non-reciprocal transmission spectra for a phononic crystal of metallic circular cylinders in water are experimentally obtained and analysed. The surfaces of the cylinders were specially processed in order to weakly break P symmetry and increase viscous losses through manipulation of surface features. Subsequently, the non-reciprocal part of transmission is separated from its asymmetric reciprocal part in numerically simulated transmission spectra. The level of non-reciprocity is in agreement with the measure of broken P symmetry. The reported study contradicts commonly accepted opinion that linear dissipation cannot be a reason leading to non-reciprocity. It also opens a way for engineering passive acoustic diodes exploring the natural viscosity of any fluid as a factor leading to non-reciprocity.

Multiple Rayleigh waves guided by the planar surface of a continuously twisted structurally chiral material

The Stroh formalism was adapted for Rayleigh-wave propagation guided by the planar traction-free surface of a continuously twisted structurally chiral material (CTSCM), which is an anisotropic solid that is periodically non-homogeneous in the direction normal to the planar surface. Numerical studies reveal that this surface can support either one or two Rayleigh waves at a fixed frequency, depending on the structural period and orientation of the CTSCM. In the case of two Rayleigh waves, each wave possesses a different wavenumber. The Rayleigh wave with the larger wavenumber is more localized to the surface and has a phase speed that changes less as the angular frequency varies in comparison with the Rayleigh wave with the smaller wavenumber.