Incident Plane Shear Research Articles

Three-Dimensional Scattering of an Incident Plane Shear Horizontal Guided Wave by a Partly through-Thickness Hole in a Plate**Supported by the National Natural Science Foundation of China under Grant Nos 11474195, 11274226, 51478258 and 51405287.

We investigate the three-dimensional (3D) scattering problem of an incident plane shear horizontal wave by a partly through-thickness hole in an isotropic plate, in which the Lamb wave modes are also included due to the mode conversions by the scattering obstacle in the 3D problem. An analytical model is presented such that the wave fields are expanded in all of propagating and evanescent SH modes and Lamb modes, and the scattered far-fields of three fundamental guided wave modes are analyzed numerically for different sizes of the holes and frequencies. The numerical results are verified by comparing with those obtained by using the approximate Poisson/Mindlin plate model for small hole radius and low frequency. It is also found that the scattering patterns are different from those of the S0 wave incidence. Our work is useful for quantitative evaluation of the plate-like structure by ultrasonic guided waves.

Kinematic interaction factors of deep foundations with inclined piles

SUMMARYThe beneficial or detrimental role of battered piles on the dynamic response of piled foundations has not been yet fully elucidated. In order to shed more light on this aspect, kinematic interaction factors of deep foundations with inclined piles, are provided for single‐battered piles, as well as for 2 × 2 and 3 × 3 groups of piles subjected to vertically incident plane shear S waves. Piles are modelled as linear‐elastic Bernoulli beams, whereas soil is assumed to be a linear, isotropic, homogeneous viscoelastic half‐space. Different pile group configurations, pile‐soil stiffness ratios, and rake angles are considered. The relevance and main trends observed in the influence of the rake angle on the kinematic interaction factors of the analysed foundations are inferred from the presented results. An important dependence of the kinematic interaction factors on the rake angle is observed together with the existence of an inclination angle at which cap rotation and excitation become out of phase in the low‐to‐mid frequency range. The existence of a small batter angle that provides minimum cap rotation is also shown. Copyright © 2014 John Wiley & Sons, Ltd.

Reflection and Transmission Coefficients for an Incident Plane Shear Wave at an Interface Separating Two Dissimilar Poroelastic Solids

Using Biot’s poroelasticity theory, we derive expressions for the reflection and transmission coefficients for a plane shear wave incident on an interface separating two different poroelastic solids. The coefficients are formulated as a function of the wave incidence angle, frequency and rock properties. Specific cases calculated include the boundary between water-saturated sand and water-saturated sandstone and the gas–water interface in sand. The results show a very different interface response to that of an incident P wave. Plane SV wave incidence does not significantly excite the Biot slow P wave if the frequency of the wave is below the transition frequency. Above this frequency, an incident plane SV wave can generate a mode-converted slow Biot P wave which is actually a normal propagating wave and not highly attenuating as in the usual (diffusive) case. For an incident SV wave onto a gas–water interface, even at very high frequency, there is no significant Biot second P wave produced. For small incident angles, the gas–water interface is essentially transparent. With increasing angles, there can arise an unusual definitive angle in the reflection/transmission coefficient curves which is related to the change of fluid viscosity on both sides of the interface and provides a possible new means for underground fluid assessment.

Isolation of plane shear wave using water saturated trench barrier

The article presents a theoretical investigation of the propagation of normally and obliquely incident plane shear waves past a rectangular trench filled up with water saturated soil sandwiched between anisotropic elastic media. The motivation for this work is due to the effectiveness of the isolation of waves by the in-filled rectangular trench. Unlike the most of the previous researchers, this model considers the soil–structure interaction effects and directly determines the influence of barrier in the form of in-filled trench on the mode of wave propagation. It is of interest to determine the reflection and transmission coefficients, and the energy partition distribution of shear waves in the in-filled rectangular trench showing the influence of barrier on the propagation of waves. An extensive parametric study through numerical computation is carried out to investigate the influence of the material properties of the in-filled trench and the amplitude ratios on shear waves. The in-filled trench barrier directly declines the intensity of waves significantly in such a way that the waves do not create any hazards to the nearby structures, if exists at all.

Some inverse problems arising from elastic scattering by rigid obstacles

In the first part of this paper, it is proved that a C2-regular rigid scatterer in can be uniquely identified by the shear part (i.e. S-part) of the far-field pattern corresponding to all incident shear waves at any fixed frequency. The proof is short and it is based on a kind of decoupling of the S-part of scattered wave from its pressure part (i.e. P-part) on the boundary of the scatterer. Moreover, uniqueness using the S-part of the far-field pattern corresponding to only one incident plane shear wave holds for a ball or a convex Lipschitz polyhedron. In the second part, we adapt the factorization method to recover the shape of a rigid body from the scattered S-waves (resp. P-waves) corresponding to all incident plane shear (resp. pressure) waves. Numerical examples illustrate the accuracy of our reconstruction in . In particular, the factorization method also leads to some uniqueness results for all frequencies excluding possibly a discrete set.

Scattering of obliquely incident shear waves from a cylindrical cavity

Prior work has proposed the use of ultrasonic angle-beam shear wave techniques to detect cracks of varying angular location around fastener sites by generating and detecting creeping waves. To better understand the nature of the scattering problem and quantify the role of creeping waves in fastener site inspections, a 3D analytical model was developed for the propagation and scattering of an obliquely incident plane shear wave from a cylindrical cavity with arbitrary shear wave polarization. The generation and decay of the spiral creeping waves was found to be dependent on both the angle of incidence and polarization of the plane shear wave. A difference between the angle of displacement in 3D and the direction of propagation for the spiral creeping wave was observed and attributed to differences in the curvature of the cavity surface for the tangential and vertical (z) directions. Using the model, practical insight was presented on measuring the displacement response in the far-field from the hole. Both analytical and experimental results highlighted the value of the diffracted and leaky spiral creeping wave signals for nondestructive evaluation of a crack located on the cavity. Last, array and signal processing methods are discussed to improve the resolution of the weaker creeping wave signals in the presence of noise.

Non-axisymmetric dynamic response of imperfectly bonded buried liquidfilled orthotropic thin cylindrical shell due to incident shear wave (SH wave)

The main aim of this paper is to assess the effects of the liquid presence and the bond imperfection while evaluating the nonaxisymmetric dynamic response of an imperfectly bonded liquid filled buried orthotropic thin cylindrical pipeline excited by shear horizontal wave (SH-wave) due to seismic excitation. Using thin shell theory, the effect of shear deformation and rotary inertia is not considered. The pipeline is modeled as an infinite thin cylindrical shell imperfectly bonded to surrounding. A thin layer is assumed between the shell and the surrounding medium (soil) such that this layer possesses the properties of stiffness and damping both. The degree of imperfection of the bond is varied by changing the stiffness and the damping parameters of this layer. For the wave propagation in the liquid inside the pipe, linear acoustic equation is used. The effects of the liquid presence on the shell displacement are studied for different soil condition and at various angles of incidence of the shear wave. The effect of the bond imperfection on the shell response is compared with the effects realized due to the presence of liquid inside the pipeline. It is found that magnitude of the response of liquid filled pipeline can become even more than that of an empty pipeline, and hence, it cannot be assumed that a liquid filled pipeline will always furnish safe and conservative response. Numerical results are presented for the case of an incident plane shear horizontal wave (SH- wave) only. Such studies are critical for design considerations for providing utility services through underground pipelines made of orthotropic material in seismic zones.

Characterization of seismic hazard and structural response by energy flux

Seismic safety of structures depends on the structure's ability to absorb the seismic energy that is transmitted from ground to structure. One parameter that can be used to characterize seismic energy is the energy flux. Energy flux is defined as the amount of energy transmitted per unit time through a cross-section of a medium, and is equal to kinetic energy multiplied by the propagation velocity of seismic waves. The peak or the integral of energy flux can be used to characterize ground motions. By definition, energy flux automatically accounts for site amplification. Energy flux in a structure can be studied by formulating the problem as a wave propagation problem. For buildings founded on layered soil media and subjected to vertically incident plane shear waves, energy flux equations are derived by modeling the building as an extension of the layered soil medium, and considering each story as another layer. The propagation of energy flux in the layers is described in terms of the upgoing and downgoing energy flux in each layer, and the energy reflection and transmission coefficients at each interface. The formulation results in a pair of simple finite-difference equations for each layer, which can be solved recursively starting from the bedrock. The upgoing and downgoing energy flux in the layers allows calculation of the energy demand and energy dissipation in each layer. The methodology is applicable to linear, as well as nonlinear structures.