Theory Of Elastic Waves Research Articles

The influence of the initial stresses on Lamb wave dispersion in pre-stressed PZT/Metal/PZT sandwich plates

Within the scope of the plane-strain state, by utilizing the three-dimensional linearized theory of elastic waves in initially stressed piezoelectric and elastic materials, Lamb wave propagation and the influence of the initial stresses on this propagation in a sandwich plate with pre-stressed piezoelectric face and pre-stressed metal elastic core layers are investigated. Dispersion equations are derived for the extensional and flexural Lamb waves and, as a result of numerical solution to these equations, the corresponding dispersion curves for the first (fundamental) and second modes are constructed. Concrete numerical results are obtained for the cases where the face layers' materials are PZT-2 or PZT-6B, but the material of the middle layer is Steel (St) or Aluminum (Al). Sandwich plates PZT-2/St/PZT-2, PZT-2/Al/PZT-2, PZT-6B/St/PZT-6B and PZT-6B/Al/PZT-6B are examined and the influence of the problem parameters such as piezoelectric and dielectric constants, layer thickness ratios and third order elastic constants of the St and Al on the effects of the initial stresses on the wave propagation velocity is studied.

Elastic wave theory for propagation of Rayleigh waves at surface of unsaturated semi-infinite media

Elastic wave theory for propagation of Rayleigh waves at surface of unsaturated semi-infinite media

Elastic rocking vibration of an offshore Gravity Base Foundation

Gravity Base Foundation is one of the main foundations in offshore wind turbine structure, and the foundation rocking stiffness mostly controls the structure fatigue life. This study models the rocking vibration of a rigid disc foundation on a poro-elastic seabed, covered by a compressible inviscid seawater half-space. The coupled rocking problem is solved using the 3-dimensional elastic wave theory. The behavior of seawater and soil are depicted with the Euler equations and the Biot's theory, respectively. The contact surface of the disc foundation with the soil and the water is assumed to be smooth. The solutions are expressed in Fredholm integral equations of the second kind and solved numerically. The obtained dynamic impedances are used to study the dynamic behavior of Gravity Base Foundations of offshore wind turbines, which are very sensitive to dynamic moments. It is found that foundation with a permeable surface has much smaller dynamic amplitudes, compared to the one with an impermeable surface. The existence of seawater half-space will also alleviate the dynamic amplitudes, but decreasing the natural frequency of the foundation.

The Button Head Bullet Effects on the Incident Pulse of Split Hopkinson Press Bar

In order to make the specimen deformed under a constant strain rate and the stress in the specimen kept homogeneous, the wave shaper technology was adopted to modify the incidence waves of the normal Split Hopkinson Press Bar. A method of changing the shape of the bullet was suggested to be applied on the SHPB. Bullets with different length and different curvature have been researched in this paper. And the effection of the button head bullet about incidence pulse was simulated with Lagrange method by ANSYS/LS-DYNA. It is shown in the results that changing the curvature of the bullet impact the rising edge of incidence waves, and the peak stress increase with the speed of the bullet increase, the peak stress and length of incidence waves increased with the length of the button head bullet, when the peak stress reached a certain strength, increasing the bullet length could make the stress peak value lasted longer. Due to the reason that the button head bullet was based on the elastic wave theory, the wave length and the max stress of the shaped wave would be controlled conveniently and avoid the shortcoming that the analogue specimens could not be recycled in the normal pulse shaper technology.

Identification of co-seismic ground motion due to fracturing and impact of the Tsaoling landslide, Taiwan

Earthquakes can generate seismic disturbances that propagate vast distances and trigger landslides that can achieve high-speeds. It remains difficult to identify the co-seismic ground motion of these landslides and their triggering earthquakes. In this paper, we report on the analysis of co-seismic ground motions generated by the initiating fracture and deposition impact of the Tsaoling landslide. The landslide, with a source volume of 125×106m3, was triggered by the 1999 Chi-Chi earthquake in Taiwan. The ground motion was recorded by a strong ground motion station, CHY080, near the scar area. The polarization of the seismic waves indicates that the peak acceleration was parallel to the dip direction. Modified ensemble empirical mode decomposition (EEMD), with additional clustering analysis, was applied to decompose the seismic signals. Two instances were found in the seismic records of a series of peculiar wave packets, with the first being associated with the landslide initiation and the second the landslide impact on the deposit valley. To confirm the first landslide breakage, the decomposed signals were compared with the predictions of the analytic elastic wave model and Newmark analysis. The landslide impact was verified with a computational fluid dynamic simulation. Comparison between the EEMD decomposed signals, elastic wave theory, Newmark rigid body analysis, and numerical simulation demonstrates the claimed landslide motion.

Effect of Imperfect Contact on the Dispersion of Generalized Rayleigh Waves in a System Consisting of a Prestressed Layer and a Prestressed Half-Plane

The effect of shear-spring + normal-spring-type imperfect contact conditions on the dispersion of generalized Rayleigh waves in a system consisting of a two-axially prestressed covering layer and a two-axially prestressed half-plane is investigated. A three-dimensional linearized theory of elastic waves in initially stressed bodies is utilized, and a plane strain state is considered. The elasticity relations for materials of the constituents are described by the Murnaghan potential. Numerical results obtained for the effect of the parameters entering in the imperfect contact conditions on wave dispersion curves are presented and discussed.

Suppression of phonon transport in multiple Si/PtSi heterostructures

Using a Green function method based on an atomic vibration model, herein we report the results from our investigation of phonon transport through multiple Si/PtSi layered structures. In contrast with values predicted using elastic wave theory and an impedance mismatch method, we find that a detailed atomic-vibration approach exhibits significantly suppressed phonon transport and leads to a 30-times reduction of the thermal conductance, compared to that of Si bulk. We attribute the origin of the suppression to the lack of PtSi phonon modes in the energy range of 20–30 meV, and to the effects of interface scattering between Si and PtSi layers.

不同岩性条件下孔壁爆炸载荷及透射波比能量计算

为研究不同激发岩性对孔壁爆炸载荷及透射波比能量的影响，基于经典的冲击波理论，建立了岩石介质中柱状装药爆炸时孔壁的初始冲击载荷计算模型，该模型将爆轰波简化为含化学反应的强间断面，弥补了弹性波理论认为孔壁周围岩石内直接产生应力波的不足，成功解释了爆轰波参数的基本关系式；建立了不同激发岩性时柱状装药爆炸的孔壁质点速度和压力随时间变化的计算模型，编程计算得到其随时间变化的函数关系式和透射波比能量的解析解。 To study the impact of explosion load and transmission wave specific energy under the different excitation lithology, based on the classical shock wave theory, the calculation model of initial ex-plosive loading parameters of blasting hole was established, when blasting in columnar charge. The detonation waves were simplified to discontinuous surfaces which contain chemical reactions in the calculation model. It made up the weakness of the elastic wave theory which thought stress wave was produced directly in the wall of blast hole. The basic relationship of the detonation wave parameters was explained successfully. Based on the elastic wave theory, the calculation methods of the velocity and press of blasting hole particle when columnar charge blasting was established for different excitation lithology. The functional relationships and the analytical solutions of the transmitted wave specific energy were got by program.

Seismic Stability Time-Frequency Analysis Method of Reinforced Retaining Wall

The first-order differential equation of the seismic active earth pressure is established by horizontal slices analysis method, based on the elastic wave theory, with the summarized dynamic analysis model of the reinforced retaining wall and the plane of fracture assumed as linear type. And then this paper proposes a time-frequency analysis method for the internal antiseismic stability analysis on the retaining wall. The reasonability of this method is verified by the results from other methods, for example, rule. The internal frictional angle of filling earth, the seismic intensity, and the frequency of the input earthquake wave have a predominant effect on the needed total tensile force of the lacing wires, which shows that (1) the needed total tensile force of the lacing wires goes up with the increase of the PGA and the internal frictional angle; (2) the needed total tensile force of the expandability lacing wires is bigger than that of the nonexpandability lacing wires; (3) the needed total tensile force of lacing wires is saddle distributed and the force achieves maximum value when the frequency of input wave equals the natural frequency of reinforced retaining wall. Besides, if the reinforced retaining wall is designed in compliance with the rules, the emergency capacity of reinforced retaining wall is reduced. At last, this paper not only takes into account the effect of three factors of the seismic wave (PGA, frequency, and duration) on the internal antiseismic stability analysis of reinforced retaining wall but also provides some valuable references for the time-frequency seismic design of other retaining structures.

Mathematical Modeling of Dynamical Stress Field Problem for a Pre-stressed Bi-layered Plate-Strip

According to the principle of the three-dimensional linearized theory of elastic waves in initially stressed bodies, a dynamical stress field in a pre-stressed bi-layered plate-strip under the action of an arbitrary inclined force resting on a rigid foundation is studied. It is assumed that the force applied to upper free surface of the plate-strip is time-harmonic and the materials used are linearly elastic, homogenous, and isotropic. By employing finite element method, the governing system of partial differential equations of motion is approximately solved. The different dependencies of the problem such as the ratio of height of plates and initial stress of the materials are numerically investigated. Particularly the effect of arbitrary inclined force is analyzed. It is observed that the numerical results obtained according to various angles converge to the ones in the previous studies.

Transition edge sensors with few-mode ballistic thermal isolation

We have fabricated Transition Edge Sensors (TESs) whose thermal characteristics are completely characterised by few-mode ballistic phonon exchange with the heat bath. These TESs have exceptionally small amorphous SiNx support legs: 0.2 μm thick, 0.7–1.0 μm wide, and 1.0 to 4.0 μm long. We show, using classical elastic wave theory, that it is only necessary to know the geometry and bulk elastic constants of the material to calculate the thermal conductance and fluctuation noise. Our devices operate in the few-mode regime, between 5 and 7 modes per leg, and have noise equivalent powers (NEPs) of 1.2 aW Hz−1∕2. The NEP is dominated by the thermal fluctuation noise in the legs, which itself is dominated by phonon shot-noise. Thus, TESs have been demonstrated whose thermal characteristics are fully accounted for by an elastic noise-wave model. Our current devices, and second-generation devices based on patterned phononic filters, can be used to produce optically compact, mechanically robust, highly sensitive TES imaging arrays, circumventing many of the problems inherent in conventional long-legged designs.

ON ELASTIC STRESS WAVES IN AN IMPACTED PLATE

Elastic stress wave theory is developed and the stress waves in the impacted plate are examined in the paper. Generalized linear elasticity is adopted where the couple stress and curvature tensor are both deviatoric tensors and they meet a linear constitutive relation. It is found that there exist volumetric, rotational, and deviatoric waves in the generalized elastic solids. However, for macro-scale elastic solids only two wave modes, namely a volumetric wave and a deviatoric wave should be taken into account. Wave motion in plate impact tests is studied that a volumetric wave and a deviatoric wave are proposed. A set of exact solutions is attained for elastic stress waves in an impact plate. Excitation of stress waves at impact surface and reflection at free surface are formulated. Propagation of stress waves in the plate is analyzed in the waveforms. The predicted stress history in a ceramic plate under impact is agreed very well with the experiment measurement.

Numerical Simulation of Seismic Wave Propagation in Different Media

Theory of elastic waves layered homogeneous medium or even medium for the study can not meet the actual demand for seismic exploration, especially for fine rock to construct reservoirs for the study, had to consider small-scale heterogeneity of seismic wave propagation effects. In this thesis, multi-scale model of a complex medium, in ensuring the premise to further improve simulation accuracy simulation efficiency issue, the introduction of a variable grid numerical simulation techniques, and were analyzed for different types of grid difference, establish a different media model simulation results verify the validity of simulation and analyzes its efficiency and accuracy problems.

Numerical Study on the Characteristics of Multipole Acoustic Logging While Drilling in Cracked Porous Medium

AbstractCracks and pores universally exist in earth formation rocks, significantly affecting logging while drilling (LWD) acoustic waves. Using a cracked porous medium elastic wave theory, we derive the LWD acoustic wave field for a fluid‐filled borehole containing a drill collar and study the velocity dispersion, attenuation, and sensitivity of multipole wave modes (e.g. Stoneley, flexural and quadrupole waves) as a function of crack density and gas saturation. Increasing crack concentration and gas saturation can produce significant velocity change and attenuation. Relatively speaking, the velocity is more sensitive to crack density, while the attenuation is more sensitive to gas saturation. The dispersive LWD dipole and quadrupole waves characterized by a “Airy Phase” are strongly attenuated by gas saturation. This phenomenon can be used to detect the presence of gas in tight formations. The modeling and analysis results of this study are in agreement with analysis of field LWD data.

Forced Vibration Analysis of Prestretched Plates with Twin Circular Inclusions

AbstractThe influence of the initial stretching of a simply supported plate containing two neighboring circular inclusions on the forced vibration analysis of the plate caused by the time-harmonic bending forces on the upper face plane is studied in the plane-strain state. The corresponding boundary-value problem is formulated using the three-dimensional linearized theory of elastic waves in initially stressed bodies and is solved numerically by the FEM. The materials of each component of the plate (i.e., the circular inclusions and the matrix) are selected to be isotropic. Numerical results on the dynamic stress concentrations around the inclusions and the influence of the initial stretching on those concentrations are presented and compared with the corresponding numerical values of plates with two neighboring circular holes and a plate without holes.

Measurement of the response of an elastomer at pressures up to 9 GPa and shear-rates of 105 – 106s−1

Pressure-shear plate impact (PSPI) experiments have been conducted to study the mechanical response of an elastomer at high pressures and high strain rates. The previously determined isentrope has been extended to 9 GPa. At this pressure, the high-strain-rate shearing resistance of polyurea is approximately 500 MPa – comparable to, or greater than, that of high strength steels and at much lower density. A new symmetric pressure-shear plate impact (SPSPI) configuration has been developed in order to enable the direct measurement of the thickness-averaged nominal strain rates of the sample – as well as the tractions on both of its interfaces with linear elastic plates. This enhancement is made possible by using a symmetric configuration for which the velocity of the mid-plane of the sample is known from symmetry to be one-half of the impact velocity. One dimensional elastic wave theory is used to obtain tractions and particle velocities at the sample/anvil interface from the measured rear-surface velocities. In this way, nominal strain-rate histories are obtained for both longitudinal and shear strains.

Improvement of pseudo-static method for slope stability analysis

In this paper, two drawbacks of the traditional pseudo-static method (vertical slice method) in the slope stability evaluation have been studied. First, the sliding mass is divided into vertical slices according to this method, which is irrational to some extent in the seismic design of slope. Second, only peak ground acceleration (PGA) is considered, and the effects of shaking frequency and duration on slope stability are neglected. And then, based on the theory of elastic wave and the summarized geological model, this paper put forwards an improved method of pseudo-method by using the theory of elastic wave and Hilbert-Huang transform. The improved pseudo-static method gives reasonable considerations to the time-frequency effects of seismic wave and its rationality has been verified by the shaking table test. This method can evaluate the safety of a slope, the happening time and the scale of landslides. At the same time, this method also can improve the high accuracy of the evaluation of the safety of the slope.

Study on Measurement Method of Dynamic Linearity for High G Micro Accelerometer

Linearity, dynamic linearity particularly, is an important parameter in measuring the performance of an accelerometer. The Hopkinson bar has been widely used in calibration of high g accelerometer and other high overloading conditions. Based on one-dimension stress wave theory and superposition theory of elastic waves, designed a Dual Warhead Hopkinson bar to demarcate the dynamic linear parameters of high g micro accelerometer accurately. A finite element model for Hopkinson bar calibration system was created, ANSYS/LS-DYNA was employed to simulate the operation process of Hopkinson bar, and the effects of the projectile's materials, adjustment pads materials and thickness on the acceleration waveform were found.

3D dynamics of a prestressed stratified half-space under the action of an oscillating moving load

This paper investigates the three-dimensional (3D) dynamical response to a time-harmonic oscillating moving load of a system comprising a prestressed covering layer and a prestressed half-space, by utilizing the three-dimensional linearized theory of elastic waves in initially stressed bodies (TDLTEWISB).The materials of the covering layer and half-space are assumed to be homogeneous and isotropic. It is also assumed that perfect contact conditions between the constituents of the system under consideration are satisfied. The analytical solution method, employing double exponential Fourier integral transformation with respect to the space coordinates, and the algorithm for obtaining the numerical results for the originals of the sought values are developed and employed. Numerical results for the critical velocity and for the stress distribution on the interface plane are presented and discussed. In particular, it is established that the minimal value of the critical velocity obtained for the 3D problem coincides with the critical velocity obtained for the corresponding 2D (plane-strain state) problem.

A whole-space transform formula of cylindrical wave functions for scattering problems

The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion, and the wave function expansion technique has been widely used in many subjects. To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters, a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study. The transforms of wave functions in cylindrical coordinates can be classified into two basic types: interior transform and exterior transform, and the existing Graf’s addition theorem is only suitable for the former. By performing a new replacement between the two coordinates, the exterior transform formula is first deduced. It is then combined with Graf’s addition theorem to establish a whole-space transform formula. By using the whole-space transform formula, the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application. The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method. The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space. In addition, its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.