Theory Of Elastic Waves Research Articles

Compare between rotational and translational seismic response spectra

Rotational response spectra are still absent due to the substantial lack of direct measurements of rotational seismic waves. The work develops a relationship between rotational response spectra and translational ones. By the elastic wave theory, seismic rotations can be calculated form translational waves. In this paper, 113 translational waves are used to calculating rotational waves. And then the translational response spectra and rotational response spectra are calculated and compared. Factors such as the site condition and frequency are considered. The results show that from lower frequency to higher frequency, the ratio of normalized response spectra between rotational and translational waves increases. The ratios are also related to the site condition.

A micro-kinetic model of enhanced foam stability under artificial seismic wave

Abstract To get a deeper understanding on the synergistic enhancement effect of low frequency artificial seismic wave on foam stability, a micro-kinetic model of enhanced foam stability under low frequency artificial seismic wave is established based on a vertical liquid film drainage model and elastic wave theory. The model is solved by non-dimensional transformation of the high order partial differential equations and a compound solution of implicit and explicit differences and is verified to be accurate. The foam film thickness, surfactant concentration distribution and drainage velocity under the action of low frequency artificial seismic wave are quantitatively analyzed. The research shows that low-frequency vibration can reduce the difference between the maximum and minimum concentrations of surfactant in the foam liquid film at the later stage of drainage, enhance the effect of Marangoni effect, and improve the stability of the foam liquid film. When the vibration frequency is close to the natural frequency of the foam liquid film, the vibration effect is the best, and the best vibration frequency is about 50 Hz. The higher the vibration acceleration, the faster the recovery rate of surfactant concentration in the foam liquid film is. The higher the vibration acceleration, the stronger the ability of Marangoni effect to delay the drainage of foam liquid film and the better the foam stability is. It is not the higher the vibration acceleration, the better. The best vibration acceleration is about 0.5 times of gravity acceleration. Reasonable vibration parameters would greatly enhance the effect of Marangoni effect. The smaller the initial concentration of surfactant, the better the vibration works in enhancing Marangoni effect.

Torsional wave dispersion in a bi-layered hollow cylinder with inhomogeneous initial stresses caused by internal and external radial pressures

The present paper studies the influence of the inhomogeneous initial stresses in the bi-layered hollow cylinder and it is assumed that these stresses are caused by the hydrostatic pressures acting on the interior and outer free surfaces of the cylinder. The study is made by utilizing the version of the three-dimensional linearized theory of elastic waves in bodies with initial stresses for which the initial stress-strain state in bodies is determined within the scope of the classical linear theory of elasticity. For the solution to the corresponding eigenvalue problem, the discrete-analytical method is employed. Numerical results are presented and analyzed for concrete selected pairs of materials. According to these results and their analyses, it is established that, unlike homogeneous initial stresses, the influence of the inhomogeneous initial stresses on the torsional wave dispersion has not only quantitative but also qualitative character. For instance, in particular, it is established that as a result of the initial stresses caused by the hydrostatic pressure acting in the interior free surface of the cylinder, the cut-off frequency appears for the fundamental dispersive mode and the values of this frequency increase with the intensity of this pressure.

Dynamic Response of the Entrance Structure of an Elliptical Mountain Tunnel under the Action of SH Waves

Generally, the surrounding rock at the entrance of a mountain tunnel is loose, and the entrance has more slopes due to topography, which causes the tunnel entrance section to be easily destroyed under an earthquake. Based on the established slope model with a single free surface, this paper adopted the elastic wave theory to derive the analytical solution of the strain at the entrance of the mountain tunnel when the SH wave is incident perpendicularly to the bottom of the tunnel; besides, the factors affecting strain were also analyzed. The tangential strain curve at each point of the entrance section takes the centre of the elliptical tunnel as the centre of symmetry, forming symmetry between the left and right sides and mirror symmetry between the top and bottom sides. Then, large‐scale shaking table model experiments were conducted to model the actual working conditions, and the correctness of the analytical solution was verified. The research can provide a theoretical reference for the seismic design of the entrance section of the high‐speed railway tunnel and greatly improve the understanding of its seismic response.

Broad-angle refractive transmodal elastic metasurface

Achieving total mode conversion from longitudinal to shear waves for a broad incident angle has been a big scientific challenge in elastic fields, which was impossible to be achieved in classical elastic wave theory. In this paper, we propose and realize a refractive transmodal elastic metasurface that can convert an incident longitudinal wave to a shear wave for a broad incident angle. Here, the total mode conversion is achieved via a sufficiently large phase gradient, while the full transmission is achieved with the impedance-matched single-layered metasurface. Numerical and experimental investigations show that the proposed metasurface can provide almost total mode conversion for a broad incident angle from −20.4° to 22.3°. We expect that the proposed refractive transmodal metasurface can be applied in various ultrasonic systems.

The stability of poro-elastic wave equations in saturated porous media

Poro-elastic wave equations are one of the fundamental problems in seismic wave exploration and applied mathematics. In the past few decades, elastic wave theory and numerical method of porous media have developed rapidly. However, the mathematical stability of such wave equations have not been fully studied, which may lead to numerical divergence in the wave propagation simulation in complex porous media. In this paper, we focus on the stability of the wave equation derived from Tuncay’s model and volume averaging method. By analyzing the stability of the first-order hyperbolic relaxation system, the mathematical stability of the wave equation is proved for the first time. Compared with existing poro-elastic wave equations (such as Biot’s theory), the advantage of newly derived equations is that it is not necessary to assume uniform distribution of pores. Such wave equations can spontaneously incorporate complex microscale pore/fracture structures into large-scale media, which is critical for unconventional oil and gas exploration. The process of proof and numerical examples shows that the wave equations are mathematically stable. These results can be applied to numerical simulation of wave field in reservoirs with pore/fracture networks, which is of great significance for unconventional oil and gas exploration.

A one-dimensional stress wave model for analytical design and optimization of oscillation-free force measurement in high-speed tensile test specimens

In this work, the phenomenon of the oscillation-free force measurement in a new sample shape, called the Generation III (Gen. III) sample in a previous work, was first physically analyzed. Based on metal physics findings and the classical elastic stress wave theory, a simplified one-dimensional elastic stress wave model was developed. For this model, several assumptions were applied so that the Gen. III sample was modeled by five thin bar sections with different section sizes and material properties.By implementing the derived governing equations in the MATLAB software, which enables the combination with a mathematical optimization algorithm (sequential quadratic programming), both the characteristic of the current Gen. III sample and its sensitivity to the geometric parameters (such as the section sizes of the beams) and the material properties could be calculated.The developed model can not only correctly calculate the principle section design, but also make correct predictions of effects that have been overlooked until know. The model assumptions are thus reasonable. It was found that strain hardening of the sample material has an influence on the geometric parameters of the Gen. III sample. Therefore, the Gen. III sample geometry may be slightly adapted for each material.

Experimental and Theoretical Analysis of Stress Superposition in Double-Hole Blasts

Abstract Using an experimental system of digital image correlation based on a high-speed camera which can be applied for blast-induced loading, model experiments of single-hole and double-hole blasts were conducted in polycarbonate specimens, and the evolutionary processes of the full-field strain were studied during blast loading. The results showed that the strain peak at the midpoint between two blastholes in double-hole blasts was 2.4–2.7 times as large as that in single-hole blasts. The stress superposition effect of double-hole blasts was much larger than 2, which is predicted by elastic wave theory. In addition, the superposition of double-hole blast stresses was analyzed by elastic and shock wave theories. These results indicated that when examining the superposition of blast stress waves, the shock wave theory is more in line with the experimental results. Based on the experimental results, there were discussions of the definition of the elastic vibration zone in the traditional blast theory.

Analytical model for thermal boundary conductance based on elastic wave theory

Interfacial phonon-mediated heat transport plays a key role in nanoscale materials and devices. We propose a model based on elastic wave theory, that considers the mode conversion of acoustic waves transmitted across an interface and combines isotropic dispersion relations to describe the interfacial phonon thermal transfer process and estimate the thermal boundary conductance (TBC). In this model, we calculate the amplitude ratios of all reflected and transmitted acoustic waves using the frequency-dependent interfacial displacement and stress components of the continuity equation; we then determine the energy transmission coefficient of the three modes of incident waves. Consequently, our model can produce the complete angular and frequency spectra of the phonon transmission coefficients for the three acoustic modes. These results show that the specular scattering dominates the transmission of low-frequency phonons at interfaces (e.g., the transmission coefficients of the Al–Si interface are close to 1 below 4 THz, and due to different elastic properties, the phonons at frequencies below 5 THz dominate the heat transfer for Al–diamond interfaces). In addition, the TBC numerical results by our model for Al–Si and Al–diamond interfaces are consistent with those found in previous experimental works. Compared with existing theoretical models, better prediction values were obtained at temperatures higher than 100 K, which verified the model’s feasibility for phonon transmission coefficients and TBC prediction. Finally, we quantitatively analyze the differences between various theoretical models by considering the mode conversion of interfacial acoustic waves, models using acoustic mismatch simplifications, and the importance of phonon dispersion relations for TBC analysis at high temperatures.

A 3D Creep Model considering Disturbance Damage and Creep Damage and Its Application in Tunnel Engineering

Based on the Kachanov damage theory and elastic wave theory, considering the long-term creep damage from time dimension and instantaneous disturbance damage from space dimension, we presented a 3D damage creep model and converted it to difference expressions in order to write into the finite difference software FLAC3D. Then, according to the results of creep tests, we conducted parameter inversion of our damage creep model with the help of the particle swarm optimization (PSO) method. Finally, the damage creep model was applied in a railway tunnel project in Yunnan to simulate the tunnel deformation. Compared with the Burgers model and the model considering only creep damage, our model which considers both creep damage and disturbance damage yielded more reasonable results.

Elastic Wave Scattering and Dynamic Stress Concentrations around Double Holes in Piezoelectric Media

In this paper, on the basis of Liu’s complex function and conformal mapping methods, supplemented by local coordinate system method, e-type piezoelectric material and elastic wave scattering and dynamic stress concentrations problems with double holes question are studied, and an analytical solution is given to the problems. On the basis of multiple scattering of elastic wave theory, put forward the study about microscopic dynamics model to dynamic stress in the structure of piezoelectric composites as well as dynamic playing field. As an example, the numerical results of the dynamic stress distribution around the hole in case double equal diameter holes are given in the paper, and the influence of incident wave number and hole-spacing parameters on the dynamic stress concentration factor is analyzed.

Influence of prestress on the natural frequency of a fluid-filled FGM sphere

This paper deals with the study of the influence of the inhomogeneous prestresses (initial stresses) in a hollow sphere made of a functionally graded material (FGM) filled with an inviscid compressible fluid on the natural vibration of this sphere. For this study, the three-dimensional exact field equations of the linearized theory of elastic waves in bodies with initial stresses are employed. The motion of the fluid is described by the linearized Navier–Stokes equations for inviscid barotropic compressible fluids. The discrete-analytical solution method proposed by the first author is employed for the solution to the corresponding mathematical problems. Numerical results related to the natural vibration of the mentioned sphere and the influence of the problem parameters on these frequencies are presented and discussed. In particular, it is established that the existence of the fluid leads to a decrease in the natural vibration frequencies. However, a change in the FGM properties of the sphere’s material can lead to an increase in these frequencies.

Dynamic response of a bi-axially pre-stressed bi-layered plate resting on a rigid foundation under a harmonic force

This study aims to investigate the forced vibrations caused by a time-harmonic force from a pre-stressed bi-layered plate resting on a rigid foundation under the action of a time-harmonic pointwise loading. Our investigation was conducted according to a piecewise homogeneous body model utilizing the three-dimensional linearized theory of elastic waves in initially stressed bodies. Throughout this study, we assumed that there is complete contact between the plate and the rigid foundation. The purpose of this study is threefold: the development of a mathematical model to investigate the dynamic response of the pre-stressed bi-layered plate, the analysis of the frequency response of the plate under consideration, and finally, demonstrating the relationship between the initial stress and the dimensionless frequency of the plate. We solved the mathematical model by employing the finite element method. We present our numerical results on the dynamic behavior of the plate. In particular, we have shown that an increase in the values of the aspect ratio of a plate under fixed thickness leads to a decrease in the normal stress resonance values.

Torsional wave frequency in heterogeneous earth crust lying over dry sandy semi-infinite substratum

The present study is carried out to investigate the transference of torsional surface waves in a heterogeneous anisotropic crust lying over a dry sandy half-space. The rigidities and densities as well as the initial stress are assumed varying as a function of depth in both the media. These variations are the product of the polynomial function of depth in degree n (n ∈ ℝ) and the exponential function of depth. Following the theory of elastic waves, the mathematical model is established. Separation of variables is used to obtain the displacement in the layer and the half-space. Intrinsic boundary conditions are imposed to derive the dispersion equation. The inhomogeneity parameters associated with the rigidity, the density, and the initial stress of the medium are found to have substantial influence on the phase velocity of the torsional surface wave. The graphical presentations are drawn to exhibit the findings. The results thus obtained are significant for the investigation and characterization of torsional surface wave in the heterogeneous anisotropic layer.

Forced vibration of a bi-axially pre-stressed plate subjected to a harmonic point force and resting on a rigid foundation

This paper models the harmonically forced vibration of a bi-axially pre-stressed plate resting on a rigid foundation using the three-dimensional linearized theory of elastic waves in initially stressed bodies. This model assumes that the material is linearly elastic, homogenous, and isotropic. The model of this system is numerically evaluated using the finite element method simulations. The numerical results illustrate the influence of several system parameters on the dynamic responses of the stresses acting at the interface between the plate and its rigid foundation. The simulations show that the aspect ratio of the plate determines how the initial stress influences the behavior of the system.

A new mechanism of energy dissipation in nanomechanical resonators due to the Casimir force

In this study, we report a new energy dissipation mechanism of nanomechanical resonators due to the Casimir effect originating from quantum fluctuation of the vacuum electromagnetic field at the nanoscale. An analytical study on the evaluation of the Casimir effect-induced energy loss in nanobeam resonators undergoing in-plane flexural vibration is presented. Two-dimensional elastic wave theory is employed to determine the energy transmission from the vibrating resonator to the substrate. Fourier transform and Green's function technique are adopted to solve the problem of wave motions on the surface of the substrate excited by the Casimir force. Analytical expressions of the Casimir effect-induced energy loss in terms of the quality factor, taking into account both pressure wave propagation in the noncontact substrate and shear wave propagation in the supporting substrate, as well as linear and nonlinear terms of time-varying Casimir force, have been derived. Effects of beam geometry, initial separation gap, and structural boundary conditions on energy loss are examined. Results of the present study demonstrate that the Casimir effect-induced energy loss plays an important role in the dissipation of the nanobeam resonators, in which the influence of shear wave propagation is remarkable. Also, as reflected by our results, the influence of nonlinear terms of time-varying Casimir force on the energy dissipation cannot be neglected for large-amplitude vibration, which is obviously a feature of nonlinear damping. Furthermore, we propose a possible way to experimentally measure the Casimir force by using the energy dissipation mechanism due to the Casimir force.

Axisymmetric longitudinal wave dispersion in a bi-layered circular cylinder with inhomogeneous initial stresses

The paper studies the axisymmetric longitudinal wave propagation in a bi-layered hollow cylinder with inhomogeneous initial stresses by utilizing the 3D linearized theory of elastic waves in initially stressed bodies. It is assumed that the initial stresses in the cylinder are caused by the internal and external hydrostatic pressures. Assuming that the materials of the layers of the cylinder are sufficiently stiff, these initial stresses are determined within the scope of the classical linear theory of elasticity. The discrete analytical method is employed for the solution to the corresponding 3D linearized equations of motion. The dispersion equation is obtained which is solved numerically for various values of the problem parameters. As a result of this solution, the dispersion curves are constructed and, according to these curves, the character of the influence of the inhomogeneous initial stresses on the dispersion curves obtained for the lowest first and second modes is established. Analysis of the results shows that the inhomogeneous initial stresses not only quantitatively but also qualitatively act on the character of the dispersion curves.

3J2-1 Resonance theory of elastic waves scattered from an elastic cylinder with a spring interface

3J2-1 Resonance theory of elastic waves scattered from an elastic cylinder with a spring interface

Three-Dimensional Wave-Field Characteristics of Earth-Rock Dams with Different Hidden Hazards

The three-dimensional wave-field characteristics of dangerous earth-rock dams are the premise and foundation to identify the hidden hazards of the earth-rock dams via wave test method. Based on the equivalent elastic wave theory in isotropic mediums, the three-dimensional wave field of earth-rock dams with different defects was calculated using the finite element numerical simulation method. The characteristic and regularity of the three-dimensional wave field was explored. The result of the analysis shows that the size and position of the defects are closely related with the wave-field information received on the dam surface. The elasticity modulus and density of the defects have great effect on the wave field, and alternately, Poisson’s ratio of the defects has little effect on the wave field. The greater the difference between the wave velocity of the hazardous materials and the dam body is, the stronger the energy of the scattered wave will be, which in turn will produce clearer lineups of the scattered wave on the time-history profile. For a single wave movement signal, the dominant frequency amplitude is exponentially correlated with the longitudinal wave velocity of the hazardous materials. Therefore, in the process of wave detection for earth-rock dam hazards, the effect of the elasticity modulus, density, and wave velocity on the test signal should be taken into account. The dominant frequency amplitude can serve as one of the control parameters for interpretation of dam hazards by the analysis of the wave test signal.

Back Analysis and Calculation of Dynamic Mechanical Parameters of Rock Mass with Measured Blasting Vibration Signals

How to obtain dynamic parameters of rock masses quickly and precisely is a popular and difficult problem, which plays a very important part in engineering design or construction. Currently, the methods used to obtain these parameters are in situ testing method, empirical formula, and so on. However, these methods have some shortcomings, such as large investment and long construction period, which cannot obtain the dynamic parameters precisely and quickly in the engineering scale. In this study, a new method of estimating the rock parameters based on the measured field blasting vibration signals is proposed according to theory of elastic stress wave. In addition, an improved method for S-wave identification used in engineering scale was proposed and then the numerical simulation is given to verify the feasibility. Comparison of the numerical identification results and theoretical results clearly show that the improved method is available in S-wave identification with errors less than 2%. By identifying the arrival times of P and S waves, the propagation velocities of P and S waves are calculated and the parameters of rock mass can be obtained at last. Through analyzing the measured field blasting vibration signals in Fengning pumped-storage power station, the dynamic elastic modulus of rock mass inversed by vibration signals is about 2.2~2.9 times of its static elastic modulus, while the inversed dynamic Poisson's ratio is 0.9~0.975 times of the static.