Interpretation of petrographic anisotropy in ornamental granites based on P wave velocity measurements

The existence of a possible anisotropy, determined by the orientation of any mineral or by micro­crack network in granite rock, isn´t easily detected by the naked eye. Five granitic rocks from Galicia (Spain), namely Albero, Gris Alba, Gris Mondariz, Rosa Porriño and Traspielas, were characterized petrographically by means of textural and mineralogical studies, using optical polarizing microscopy, and fractographic studies were carried out under scanning electron microscopy. Longitudinal wave propagation velocity was measured in three orthogonal directions on cubic samples, oriented according to rift surface (known in quarry works like the preferential partition surface visible in the blocks). Vp was measured on dry and water saturated samples. All the dry samples showed an anisotropic behaviour of Vp. Models of microcrack network distribution and possible mineral grain orientation were developed based on the obtained data.

Longitudinal Wave in a Thermally Conducting Elastic Medium

The longitudinal wave propagation in a thermally conducting elastic medium has been investigated. Considering the equations of motions of longitudinal wave in displacement and temperature field, the frequency equation has been derived. The dispersion and damping equations have been derived for the propagation of longitudinal wave in four materials i.e Copper, Steel, Aluminum, and Lead. Effect of Phase velocity and damping coefficient are shown graphically. It is found that the increase in wave number results the decrease in Phase velocity and increase in damping coefficient.

Longitudinal wave propagation in a one-dimensional quasi-periodic waveguide

The paper deals with the analysis of wave propagation in a general one-dimensional (1D) non-uniform waveguide featuring multiple modulations of parameters with different, arbitrarily related, spatial periods. The considered quasi-periodic waveguide, in particular, can be viewed as a model of pure periodic structures with imperfections. Effects of such imperfections on the waveguide frequency bandgaps are revealed and described by means of the method of varying amplitudes and the method of direct separation of motions. It is shown that imperfections cannot considerably degrade wave attenuation properties of 1D periodic structures, e.g. reduce widths of their frequency bandgaps. Attenuation levels and frequency bandgaps featured by the quasi-periodic waveguide are studied without imposing any restrictions on the periods of the modulations, e.g. for their ratio to be rational. For the waveguide featuring relatively small modulations with periods that are not close to each other, each of the frequency bandgaps, to the leading order of smallness, is controlled only by one of the modulations. It is shown that introducing additional spatial modulations to a pure periodic structure can enhance its wave attenuation properties, e.g. a relatively low-frequency bandgap can be induced providing vibration attenuation in frequency ranges where damping is less effective.

Inverse boundary-value problem for the equation of longitudinal wave propagation with non-self-adjoint boundary conditions

We study the inverse coefficient problem for the equation of longitudinal wave propagation with non-self-adjoint boundary conditions. The main purpose of this paper is to prove the existence and uniqueness of the classical solutions of an inverse boundary-value problem. To investigate the solvability of the inverse problem, we carried out a transformation from the original problem to some equivalent auxiliary problem with trivial boundary conditions. Applying the Fourier method and contraction mappings principle, the solvability of the appropriate auxiliary inverse problem is proved. Furthermore, using the equivalency, the existence and uniqueness of the classical solution of the original problem are shown.