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The paper studies the influence of the initial inhomogeneous thermal stresses on the dispersion of the axisymmetric longitudinal waves propagating in the bi-layered hollow cylinder within the scope of the 3D linearized theory of elastic waves in initially stressed bodies. The initial static thermal stresses are determined within the scope of the uncoupled classical linear theory of thermo-elasticity and it is assumed that the temperature change in the cylinder is caused by the heating or cooling of the inner and outer surfaces of the cylinder. The discrete analytical solution method is employed for the solution to the corresponding equations of the wave propagation. Concrete numerical results are obtained for the cylinder, the materials of the layers of which are steel and aluminum, as well for the cylinder made of steel only. Numerical results on the influence of the initial inhomogeneous thermal stresses on the dispersion curves related to the first, second and third modes are presented and discussed. In particular, it is established that the cooling or the heating of the outer and inner surfaces of the bi-layered hollow cylinder influences the dispersion curves not only in the quantitative sense, but also in the qualitative sense. [ABSTRACT FROM AUTHOR]

In situ stress is an important feature of underground rock masses. This paper extends the time-domain recursive method to the study of S-wave propagation through in situ stressed rock masses containing parallel joints. A linear elastic model and hyperbolic nonlinear slip model (HNSM) are first used to establish equations for wave propagation across jointed rock masses under a combination of gravitational and tectonic stress. Then, a comparison is made of the waveforms generated using the HNSM and Mohr–Coulomb slip model. Their differences are investigated and the wave propagation equation verified. Finally, parametric studies are conducted to investigate the effect of joint angle, joint number, in situ stress, and lateral pressure coefficient. The results show that the HNSM can describe the dynamic changes in the stress and their effect on the deformation behavior of the joint during the propagation of the S-wave. The effect of in situ stress on wave propagation is related to the joint angle and lateral pressure coefficient, which determine the initial stress state and contact state of the joint. [ABSTRACT FROM AUTHOR]

Rock joints with unequal close-open behavior have significant influences on stress wave propagation across them. A stress wave of sufficiently large amplitude does not only mobilize the nonlinear deformation of joints, but also force the joints to close and open. In the present study, the Bandis-Barton model and the Coulomb-slip model are adopted to describe the normal and tangential behavior, respectively, of the closed joints. However, when the joints are open, both sides of the joints behave as two free surfaces. The improved time-domain recursive method is employed to derive wave propagation equations for three cases, i.e. the joint is closed but does not slide, the joint is closed and slides, and the joint is open. Then, the normal and tangential relative displacements of joints, as well as the energy attenuation coefficient, are calculated. A comparison of transmitted waves based on different methods is conducted to verify the validity of the present approach. Eventually, parametrical studies show that the higher in-situ stress causes the smaller energy attenuation coefficient, and the wave energy attenuation is also dependent on the frequency and amplitude of the incident wave, the incident angle, the joint spacing and the joint number. [ABSTRACT FROM AUTHOR]

Rock joints, usually with nonlinear deformation, widely exist in many natural rock masses, which greatly affect stress wave propagation. In practical engineering, the generated stress wave is taken as a cylindrical wave when an explosion with cylindrical charge or a tunneling explosion occurs. The cylindrical wave propagation in jointed rock mass is a great concern of underground structure safety. In this paper, the time-domain recursive method (TDRM) is extended to investigate cylindrical stress wave propagation through a rock joint with nonlinear normal deformation. Based on the conservation of momentum at the wave fronts and the displacement discontinuity method, a quantitative analysis for the interaction between wave and the joint is carried out and the wave propagation equation is accordingly deduced by considering the attenuation. Verification of the TDRM-based results is conducted by comparison with the simulated results from UDEC code. Finally, parametric studies are carried out, which include the influences of joint stiffness, the maximum allowable closure of joint and the frequency of the incident wave on the transmission and reflection coefficients. [ABSTRACT FROM AUTHOR]

This paper investigates the impact of corrugated boundary surfaces, reinforcement on the propagation of Love-type wave in prestressed corrugated heterogeneous fiber-reinforced layer resting over a void pores half-space. The heterogeneity in the upper corrugated layer is caused due to exponential variation in the elastic constants with respect to the space variable pointing positively downwards. The dispersion equation in the complex form has been derived using method of separation of variables. The real and imaginary parts of the complex dispersion equation were separated and found in well agreement with the classical Love wave equation. Also, the attenuation of the Love waves has been discussed. The study reveals that such a medium transmits two fronts of Love waves. The first front depends upon the change in volume fraction of the pores and the second front depends upon the modulus of rigidity of the elastic matrix of the medium. The substantial influence of corrugation parameters, reinforcement, undulatory parameter, initial stress, heterogeneity parameter and position parameter on the phase velocity, and attenuation of Love-type wave have been observed and depicted by means of graph. It has been observed that the phase velocity decreases with the increase in initial stress parameters, heterogeneity, and reinforcement in upper layer. [ABSTRACT FROM PUBLISHER]

The secular equation of Rayleigh propagating in an orthotropic half-space coated by an orthotropic layer has been obtained by Sotiropolous [Sotiropolous, D. A. (1999), The e®ect of anisotropy on guided elastic waves in a layered half-space, Mechanics of Materials 31, 215–233] and by Sotiropolous & Tougelidis [Sotiropolous, D. A. and Tougelidis, G. (1998), Guided elastic waves in orthotropic surface layer, Ultrasonics 36, 371–374]. However, it is not totally explicit and some misprints have occurred in this secular equation in both papers. This secular equation was derived by expanding directly a six-order determinant originated from the traction-free conditions at the top surface of the layer and the continuity of displacements and stresses through the interface between the layer and the half-space. Since the expansion of this six-order determinant was not shown in both two papers, it has been difficult to readers to recognize these misprints. This paper presents a technique that provides a totally explicit secular equation of the wave. The technique makes clear the way from the traction-free and continuity conditions to the secular equation and enables us to recognize the misprints appearing in the reported secular equation. The technique can be employed to obtain explicit secular equations of Rayleigh waves for many other cases. Moreover, the paper introduces a transfer matrix in explicit form for an orthotropic layer that is much simpler in form than the one obtained previously. [ABSTRACT FROM AUTHOR]

The method of small perturbations has been developed for the wave equation of the most general type, and applied for studying the propagation, scattering and transformation of scalar and vector waves in weakly inhomogeneous dispersive media. Both periodic and random inhomogeneities have been considered. [ABSTRACT FROM AUTHOR]

The propagation of a transient electromagnetic pulse over irregular terrain is considered. We model the wave propagation using the parabolic wave equation, which is valid for near-horizontal propagation. We model the effect of scattering from the rough terrain by introducing a surface-flattening coordinate transform. This coordinate transform simplifies the boundary condition of our problem, and introduces an effective refractive index into our wave equation. As a result, the problem of propagation over an irregular surface becomes equivalent to the problem of propagation through random media. The parabolic equation is solved analytically using the path integral method. Both vertically polarized and horizontally polarized signals are treated. Cumulant expansion is introduced to obtain an approximate expression for the two-frequency mutual coherence function. From the mutual coherence function, spatial and temporal dependence of the propagating signal can be determined. It can be shown that scattering from the irregular surface can cause broadening of the transient signal. This can have a significant impact on the performance of radio communication systems. [ABSTRACT FROM AUTHOR]