Calculations of longitudinal and transverse velocity structure functions using a vortex model of isotropic turbulence

The longitudinal structure function (LSF) and the transverse structure function (TSF) in isotropic turbulence are calculated using a vortex model. The vortex model is composed of the Rankine and Burgers vortices which have the exponential distributions in the vortex Reynolds number and vortex radii. This model exhibits a power law in the inertial range and satisfies the minimal condition of isotropy that the second-order exponent of the LSF in the inertial range is equal to that of the TSF. Also observed are differences between longitudinal and transverse structure functions caused by intermittency. These differences are related to their scaling differences which have been previously observed in experiments and numerical simulations.

Governing Equations and Numerical Solutions of Tension Leg Platform with Finite Amplitude Motion

It is demonstrated that when tension leg platform (TLP) moves with finite amplitude in waves, the inertia force, the drag force and the buoyancy acting on the platform are nonlinear functions of the response of TLP. The tensions of the tethers are also nonlinear functions of the displacement of TLP. Then the displacement, the velocity and the acceleration of TLP should be taken into account when loads are calculated. In addition, equations of motions should be set up on the instantaneous position. A theoretical model for analyzing the nonlinear behavior of a TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e., finite displacement, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. Based on the theoretical model, the comprehensive nonlinear differential equations are deduced. Then the nonlinear dynamic analysis of ISSC TLP in regular waves is performed in the time domain. The degenerative linear solution of the proposed nonlinear model is verified with existing published one. Furthermore, numerical results are presented, which illustrate that nonlinearities exert a significant influence on the dynamic responses of the TLP.

Interactions of Penny-Shaped Cracks in Three-Dimensional Solids

The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is developed in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.

Anisotropic, gradient and metal-like mechanical behaviors of teeth and their implications on tooth functions

The anisotropy and gradient of the elastic modulus and the hardness of teeth were investigated by means of instrumented indentation method. Such properties are attributed to the unique microstructures of teeth based on scanning electron microscopic analysis. By comparing the relationship between the ratio of hardness to the reduced elastic modulus and the ratio of elastic unloading work to the total work of teeth in course of indentation to those of other materials, we found that the material behaviors of teeth display metal-like characteristics rather than ceramics as considered traditionally. These material behaviors and relevant functions are discussed briefly.

Wave propagation and the frequency domain Green's functions in viscoelastic Biot/squirt (BISQ) media

In this paper, we examine the characteristics of elastic wave propagation in viscoelastic porous media, which contain simultaneously both the Biot-flow and the squirt-flow mechanisms (BISQ). The frequency-domain Green's functions for viscoelastic BISQ media are then derived based on the classic potential function methods. Our numerical results show that S-waves are only affected by viscoelasticity, but not by squirt-flows. However, the phase velocity and attenuation of fast P-waves are seriously influenced by both viscoelasticity and squirt-flows; and there exist two peaks in the attenuation-frequency variations of fast P-waves. In the low-frequency range, the squirt-flow characteristic length, not viscoelasticity, affects the phase velocity of slow P-waves, whereas it is opposite in the high-frequency range. As to the contribution of potential functions of two types of compressional waves to the Green's function, the squirt-flow length has a small effect, and the effects of viscoelastic parameter are mainly in the higher frequency range. Crown Copyright (C) 2006 Published by Elsevier Ltd. All rights reserved.