Axial gravitational waves in Bianchi I universe

In this paper, we have studied the propagation of axial gravitational waves in Bianchi I universe using the Regge–Wheeler gauge. In this gauge, there are only two nonzero components of [Formula: see text] in the case of axial waves: [Formula: see text] and [Formula: see text]. The field equations in absence of matter have been derived both for the unperturbed as well as axially perturbed metric. These field equations are solved simultaneously by assuming the expansion scalar [Formula: see text] to be proportional to the shear scalar [Formula: see text] (so that [Formula: see text], where [Formula: see text], [Formula: see text] are the metric coefficients and [Formula: see text] is an arbitrary constant), and the wave equation for the perturbation parameter [Formula: see text] has been derived. We used the method of separation of variables to solve for this parameter, and have subsequently determined [Formula: see text]. We then discuss a few special cases to interpret the results. We find that the anisotropy of the background spacetime is responsible for the damping of the gravitational waves as they propagate through this spacetime. The perturbations depend on the values of the angular momentum [Formula: see text]. The field equations in the presence of matter reveal that the axially perturbed spacetime leads to perturbations only in the azimuthal velocity of the fluid leaving the matter field undisturbed.

A vortex interaction mechanism for generating energy and enstrophy fluctuations in high-symmetric turbulence

Turbulent vortex dynamics is investigated in triply periodic turbulent flow with Kida’s high symmetry (Kida, J. Phys. Soc. Japan, vol. 54, 1985, pp. 2132–2136) by means of unstable periodic motion representing both the statistical and dynamical properties of turbulence (van Veen et al., Fluid Dyn. Res., vol. 38, 2006, pp. 19–46). In the periodic motion, the large-scale columnar vortices, the smaller-scale vortices and the large-amplitude axial waves on the large-scale columnar vortices are detected. In terms of mutual dynamical interaction between the large-scale columnar vortices and smaller-scale vortices, we demonstrate a cyclic process of excitation of the axial waves, which leads to large-amplitude fluctuations of the total kinetic energy and enstrophy. This cyclic process is characterised by three distinct phases and is therefore reminiscent of the regeneration cycle of near-wall turbulence structures (Hamilton et al., J. Fluid Mech., vol. 287, 1995, pp. 317–348). Notably, such oscillatory behaviour is observed even in freely decaying turbulence as a consequence of the instantaneous energy transfer from smaller to larger scales.

FORCED WAVES PROPAGATION IN GREAT LIVING ARTERIES TISSUES

Starting from experimental data, this work exploit the similarity of pressure and axial wave’s propagation of both pressure and axial waves in large vessel (e.g., aorta) with the solution of a mathematical model developed to describe the motion of acoustic waves in solid. In particular, we show how the motion parameters derived by fitting the experimental data measured in living dog arteries are related to mechanical properties of the vessel tissue using the same theoretical model. Furthermore, we briefly discuss the consequence on the predicted forced wave motion of inferring from experimental data a phase velocity depending from frequency.

Axial Wave Reflection and Transmission in Stepped Nanorods Using Doublet Mechanics Theory

A numerical investigation of the reflection and transmission of axial waves at stepped nanorods is presented. The scale dependent doublet mechanics theory is used in the analysis. The main difference of the doublet mechanics from other scale dependent models (stress gradient, strain gradient and couple stress theories) is its direct dependence to the micro/nano structure of the solid. Scale parameter is directly related to atomic structure of the material in doublet mechanics theory and it is assumed as carbon-carbon bond length in the present study. However, identification of scale parameters in other scale dependent theories is difficult compared to doublet mechanics theory. Governing equations of stepped nanorods are derived in the framework of doublet mechanics using the Hamilton Principle. The numerical results predicted by doublet mechanics are shown and compared with the classical elasticity.

Dynamic Buckling of Elastic Cylindrical Shells under Axial Step Load

Considering the effect of stress wave, the dynamic buckling of circular cylindrical shells under an axial step load is discussed using the classical shell theories and the state-space technique in the paper. Based on the Hamilton’s principle, the dynamic buckling governing equations of shells are derived and solved with the Rayleigh-Ritz method. If the linear homogeneous equations have a non-trivial solution, the determinant of the coefficient matrix must be equal to zero, so the expression of the critical load on the dynamic buckling is got. The relationship between the critical load and length is obtained by using MATLAB software. The influences of boundary conditions, thickness, the number of circumferential waves and the number of axial waves on the dynamic buckling loads are discussed based on numerical computation.

Coupled Vibration Analysis of a Fluid-Filled Pipe by Wavenumber Prediction

The stability and vibration of fluid-filled pipes are important in many engineering situations and have been extensively studied. In this paper, coupled fluid–structure analysis is carried on by wavenumber prediction. Pipe equations for axisymmetric wave motion are derived, and two kind of axial waves are studied analytically at low frequencies, i.e., , which is a predominantly fluid-borne wave, and , is predominantly a shell wave. Numerical results are subsequently given to show the definitely influence of the pipe and the fluid.