Propagation Characteristics Of Elastic Waves Research Articles

Influences of gradient profile on the band gap of two-dimensional phononic crystal

Propagation characteristics of elastic waves in two-dimensional (2D) phononic crystal consisting of parallel cylinders or cylindrical shells embedded periodically in a homogeneous host are investigated. The cylinders or cylindrical shells with varying material parameters along the radial direction are considered. The influences of the gradient profile on the band gap are the main concern. First, the multiple scattering method and the Bloch theorem are used to derive the dispersive equation. Second, the transfer matrix of graded medium is derived based on the laminated cylindrical shell model. Three cases of combination are considered: (1) Solid cylinders embedded in solid host (solid-solid type). (2) Solid cylinders embedded in liquid host (solid-liquid type). (3) Hollow cylinder filled with liquid embedded in liquid host (liquid-solid-liquid type). Next, the dispersive curves and the band gaps between them are evaluated numerically in the reduced Brillouin zone. Five kinds of typical gradient profiles and two limited cases are considered. At last, the influence of the graded medium with different gradient profiles upon dispersive curves and the band gaps are discussed based on the numerical results.

Band Gaps of 2D Phononic Crystal with Graded Interphase

Propagation characteristics of elastic waves in 2D phononic crystal consisting of parallel cylinders embedded periodically in a homogeneous host medium are investigated. The multiple scattering method and the Bloch theorem are used to derive the dispersive equation. The dispersive curves and the band gaps between them are evaluated numerically in the reduced Brillouin zone. The graded interphase between the cylinders and the host are considered. The influences of the graded interphase with different gradient profiles are discussed based on the numerical results.

Study on the Characteristics of Elastic Wave Propagation in Corrugated Fiberboard

Corrugated fiberboard is considered as the world’s environmentally acceptable packaging that has a wide range of applications in packaging field. Through studying the characteristics of elastic wave propagation in the Corrugated fiberboard, this paper inferences variations of displacement and stress with time, when the corrugated fiberboard suffering the uniform load. It provides theoretical and mathematical basis for the design of cushioning package.

Coupled Flexural-Longitudinal Vibration in a Curved Periodic Pipe Conveying Fluid

A longitudinal vibration coupling with a flexural vibration in a curved fluid-filled periodic pipe is studied. The pipe is fabricated by a periodic composite material structure based on the Bragg scattering mechanism of Phononic Crystals. Using the transfer matrix method, the band structure of an infinite periodic straight pipe is calculated, and the elastic wave propagation characteristics of the periodic pipe are discussed. Furthermore, the vibrational frequency response functions of a finite curved pipe are performed and the coupled vibration is studied. Finally, the transmission properties of longitudinal vibration, flexural vibration and their coupling vibration in the curved periodic fluid-filled pipe are investigated.

Effects of viscous fluid on wave propagation in carbon nanotubes

In this Letter, the effects of the viscous fluid on the propagation characteristics of elastic waves in carbon nanotubes are studied. Based on the nonlocal continuum theory, the small scales effects are also considered. The equations of wave motion are derived and the dispersion relation is presented. Numerical simulations are performed with the consideration of different scale coefficients to discuss the influence of the viscous fluid. From the results, it can be observed that the dispersion relation can be changed by the fluid viscosity obviously. Moreover, due to the fluid viscosity, the wave frequency will be reduced to a low region and the elastic wave behaviors can be significantly influenced by the viscous fluid velocity.

Formation of longitudinal wave band structures in one-dimensional phononic crystals

Existing research on the mechanism of frequency bands in phononic crystals were without exception concerned with the band gaps (stop-bands). This paper reports, for the first time, the formation mechanism of the band structures, including both the phase constant and the attenuation constant spectra, of longitudinal waves in one-dimensional phononic crystals based on the periodic ternary rod model. Closed-form dispersion relation is obtained by our proposed method of reverberation-ray matrix. The band structures of characteristic longitudinal wave in the infinite one-dimensional phononic crystal are found to be generated from the dispersion curves of equivalent longitudinal wave in the unit cell due to zone folding effect and wave interference phenomenon. The characteristic times of longitudinal wave traversing the individual components of the unit cell as well as traversing the unit cell itself and the contrast of characteristic impedances of components are revealed to be the essential parameters determining the band structures. The deep understanding of band-structure formation provides direct scheme for adjusting frequency bands and propagation characteristics of elastic waves in one-dimensional phononic crystals. It will facilitate the design and optimization of phononic crystals to satisfy specific requirements for wave guiding/filtering and vibration control/isolation applications.

P-wave monitoring of hydrate-bearing sand during CH4–CO2 replacement

The replacement of methane for carbon dioxide in natural gas hydrate-bearing sediments is a promising technology in view of a more sustainable use of fossil fuels. While previous studies have shown successful CH4–CO2 replacement in hydrates, the mechanical response of hydrate-bearing sediments during CO2 injection, CH4–CO2 replacement, and CH4 production needs to be adequately understood in order to avert production problems such as borehole instability, sand production, and buckling of the casing. We take advantage of the characteristics of elastic mechanical wave propagation in sediments to monitor CH4 hydrate-bearing sands before, during, and after CO2 injection. Results show that CH4–CO2 replacement occurs without a loss of stiffness in the granular medium. This implies that CO2-flooded sandy reservoirs can remain mechanically stable during and after CH4 gas production. On the other hand, dry CO2 dissolves hydrate, and continued sediment flushing with dry CO2 reduces the degree of hydrate saturation in the pore space, opens the pore throats, and weakens the granular skeleton. This phenomenon may cause a significant loss of strength near the injection points and regions subjected to high liquid CO2 flow rate. The results of complimentary analyses show a decrease in bulk stiffness as water is displaced by liquid CO2, a stiffening of the granular skeleton during hydrate formation at contacts (diffusion limited), and the implications of water solubility in liquid CO2.

Exact and numerical elastodynamic solutions for thick-walled functionally graded cylinders subjected to pressure shocks

In the present paper, analytical and numerical elastodynamic solutions are developed for long thick-walled functionally graded cylinders subjected to arbitrary dynamic and shock pressures. Both transient dynamic response and elastic wave propagation characteristics are studied in these non-homogeneous structures. Variations of the material properties across the thickness are described according to both polynomial and power law functions. A numerically consistent transfinite element formulation is presented for both functions whereas the exact solution is presented for the power law function. The FGM cylinder is not divided into isotropic sub-cylinders. An approach associated with dividing the dynamic radial displacement expression into quasi-static and dynamic parts and expansion of the transient wave functions in terms of a series of the eigenfunctions is employed to propose the exact solution. Results are obtained for various exponents of the functions of the material properties distributions, various radius ratios, and various dynamic and shock loads.

PC道路橋のプレストレス評価に関する研究

A study on applicability of non-destructive inspection methods to evaluate degree of soundness of PC bridges was conducted. An experiment for radio propagation characteristics of ultrasonic waves and impact elastic waves was conducted. First, for PC structures consisting of PC steels, reinforcing bars, and concrete, a study on a possibility of grasping the pre-stressing rate from the radio propagation characteristics was conducted. Also, experiments using model and real PC girders to study on the applicability to the real structures were conducted. As a result, a possibility to apply the non-destructive inspection methods was indicated.

Application of optical and acoustic methods for estimation of fatigue damage

The results of the investigation of variations in the parameters of elastic wave propagation and microplastic characteristics of steels 12 (12GS) and (08Kh18N10T) during their fatigue damage are given. The characteristics of microplastic deformations (density of microzones subjected to plastic deformations and average value of microplastic deformations) are determined using an optical method with a help of a portable SPECTR-MET metallograpic complex. Attenuation and propagation velocities of bulk transverse and longitudinal elastic waves are shown to be sensitive to structural variations at an earlier stage of alloy damage. The degree of damage to the analyzed materials before formation of a macrocrack is estimated using a combination of an acoustic and an optical method of nondestructive testing.

Exact and numerical elastodynamic solutions for spherically symmetric problems of functionally graded thick-walled spheres subjected to pressure shocks

In the present paper, analytical and numerical elastodynamic solutions are developed for spherically symmetric problems of functionally graded thick-walled spheres subjected to arbitrary dynamic and shock loads. Both transient dynamic response and elastic wave propagation characteristics are studied in the mentioned nonhomogeneous structures. Variations of the material properties across the thickness are described according to both polynomial and power law functions. The numerical consistent transfinite element formulation is presented for both functions whereas the exact solution is presented for the power law function. The functionally graded material sphere is not divided into isotropic sub-spheres. An approach associated with dividing the dynamic radial displacement expression into quasi-static and dynamic parts and expansion of the transient wave functions in terms of a series of eigenfunctions is employed to propose the exact solution. Results are obtained for various exponents of the functions of the material properties distributions, various radius ratios, and variety of dynamic and shock loads.

Collimation and enhancement of elastic transverse waves in two-dimensional solid phononic crystals

In this Letter, we numerically investigate the propagation characteristics of elastic transverse waves emitted by line sources embedded inside two-dimensional (2D) solid phononic crystals (PCs). The results show that collimation and enhancement of elastic transverse waves can be achieved at the band edge frequencies. We find that the collimation effect originates from the flat equifrequency contours (EFCs) at the band edge of appropriately designed 2D solid PCs. It is shown that, in addition to geometric symmetry, appropriate constituent material combination is essential to obtain flat EFCs at the band edge. A highly directional and enhanced elastic transverse wave source with a half power angular width of only 5.6° and an enhancement factor of 530 is realized simply by utilizing a finite-size 2D solid PC structure.

Size-dependent effective dynamic properties of unidirectional nanocomposites with interface energy effects

This article studies the size effect on wave propagation characteristics of plane longitudinal and transverse elastic waves in a two-phase nanocomposite consisting of transversely isotropic and unidirectionally oriented identical cylindrical nanofibers embedded in a transversely isotropic homogeneous matrix. The surface elasticity theory is employed to incorporate the interfacial stress effects. The effect of random distribution of nanofibers in the composite medium is taken into account via a generalized self-consistent multiple scattering model. The phase velocities and attenuations of longitudinal and shear waves along with the associated dynamic effective elastic constants are calculated for a wide range of frequencies and fiber concentrations. The numerical results reveal that interface elasticity at nanometer length scales can significantly alter the overall dynamic mechanical properties of nanofiber-reinforced composites. Limiting cases are considered and excellent agreements with solutions available in the literature have been obtained.

An investigation into the propagation characteristics of AE signals in PE/PE composite laminates

Theoretical and experimental methods were presented to study the propagation characteristics of elastic waves in PE/PE composite laminates. Approximate plate theories were explored to predict the dispersion of flexural mode of the elastic waves. Arrival times of the waves at different frequency were determined on the base of Gabor wavelet transform. A pencil lead break generated the elastic waves in orthotropy and quasi-isotropy PE/PE composite laminates. Experimental results illustrated more serious attenuation of the waves. The comparison between the experimental measurements and predictions showed good agreement.

A Signal Processing Approach for Elastic Wave-Based Structural Health Monitoring Using Active Piezoelectrics

A series of digital frequency filters (DFFs) were designed to screen diverse noises and the spectrographic analysis was conducted to isolate complex boundary reflection, which obscures the damage-induced signals. The scale-averaged wavelet power (SAP) technique was applied to enhance the measurement accuracy of Time of Flight (TOF). As an example, the propagation characteristics of elastic wave in a structural beam of square cross-section were analyzed using such an approach and verified experimentally and numerically, with the consideration of the complicated wave scatter caused by the non-ignorable section dimensions.

후쿠오카 지역에서 발생한 12개 지진의 지진원 밑 지진파 감쇠값에 관한 연구

본 연구는20005년 3월부터 약2개월에 걸쳐 후쿠오카 지역에서 짧은 기간에 발생한 12개의 지진으로부터 관측된 154개의 지반진동 자료를 이용하여 지진원 및 지진파 감쇠와 관련된 값들을 분석하였다. 본 연구에서는 구하고자 하는 모든 값을 동시에 비선형적으로 분석하기 위해 LM(Levenberg-Marquardt) 역산방법을 적용하였고 전단파 에너지를 이용하였다. 분석결과 12개 지진의 응력강하값의 평균은 약 79.2-bar이고 부지 하부 지진파 감쇠값 <TEX>$\kappa$</TEX>의 평균값은 0.043으로 분석되었다. 또한 광역적인 지진파 감쇠를 나타내는 Qo 와 <TEX>${\eta}$</TEX>값은 각각 248.1 및 0.558로 분석되었다. Qo 과 <TEX>${\eta}$</TEX>값은 지진파의 경로중 일부가 동해를 거치기 한반도 남동부의 지진파 전파의 특성뿐만 아니라 일본과 한반도 사이의 지체구조의 차이로 인한 불균질 특성도 포함하고 있는 것으로 판단된다. 특히 관측소부지 하부의 지진파 감쇠값 K의 평균값은 미국 동부지역 대표값 보다 훨씬 크고 미국 서부지역 대표값보다 거의 유사한 값을 보여 주었으며 각각 관측소 부지 고유의 증폭에 대한 정확한 정보가 있으면 보다 의미있는 결과를 얻을 수 있다고 판단된다. Parameters including the seismic sources and the elastic wave propagation characteristics were analysed using the observed ground motions from 12 Fukuoka region earthquakes. The Levenberg-Marquardt algorithm was applied to invert all the variables non-linearly and simultaneously with S wave energy in fiequency domain. Average stress drop of 12 events and local attenuation parameter <TEX>$\kappa$</TEX> under seismic stations were estimated to about 79.2-bar and 0.043 respectively. Regional attenuation parameter, Qo and <TEX>${\eta}$</TEX>, were also estimated to be about 248.1 and 0.558 respectively. Low value of Qo seems to caused by inhomogeneous tectonic characteristics between Japan island and southern Korean peninsula. <TEX>$\kappa$</TEX> values are much higher than that characterizing EUS (Eastern United States) region, and nearly similar to that of WUS (Western Waited States) region. If the informations on site specific amplification of all the seismic stations are known, <TEX>$\kappa$</TEX> values can be estimated more precisely. All the values including the seismic sources and the site and crustal scale propagation characteristics can be used as seismic design parameters.

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.

The directional propagation characteristics of elastic wave in two-dimensional thin plate phononic crystals

Abstract The directional propagation characteristics of elastic wave during pass bands in two-dimensional thin plate phononic crystals are analyzed by using the lumped-mass method to yield the phase constant surface. The directions and regions of wave propagation in phononic crystals for certain frequencies during pass bands are predicted with the iso-frequency contour lines of the phase constant surface, which are then validated with the harmonic responses of a finite two-dimensional thin plate phononic crystals with 16 × 16 unit cells. These results are useful for controlling the wave propagation in the pass bands of phononic crystals.

The Effect of Joint Conditions on the Longitudinal and Flexural Wave Velocities of a Rock Mass

The behavior of a jointed rock is different from that of an intact rock, and the characteristics of elastic wave propagation in a jointed rock are different from those of an intact rock. In this study, a rock resonant column testing device is designed to measure the longitudinal and flexural wave velocities of jointed rocks under different states of stress. A column of more than 12 rock discs is stacked on a steel base, which acts as a free-fixed system. This configuration ensures that waves propagate under an equivalent continuum condition, thereby rendering a constant and unique velocity. The effect of joint conditions on the wave velocities is investigated through rock resonant column testings. The results show that velocities are sensitive to the state of stress and increase nonlinearly with stress. The velocities are also affected by joint conditions such as roughness, spacing, and filling. The results are useful for rock mass classification based on near-surface geophysical characterization.

Non-linear seismic wave propagation in anisotropic media using the flux-corrected transport technique

Both anisotropy and non-linearity of rocks are important properties related to the elastic wave propagation in the Earth. However, in the literature, there has been a continuous increase in the interest of anisotropy, but very few studies of non-linearity are reported. In this paper, we aim to tackle this imbalance by examining propagation characteristics of non-linear elastic waves in anisotropic media. As analytic solutions to anisotropic wave equation in non-linear media (or non-linear wave equation in anisotropic media) are not readily available, we use a numerical-based approach. However, we realize that numerical modelling of non-linear seismic waves suffers from problems such as steep gradients, shocks and unphysical oscillations. Accordingly, some special treatments have been presented in the literature to reduce these problems. In this paper, we present a second-order central finite difference scheme based on the modified flux-corrected transport (FCT) technique, and we also present the stability criterion for the FCT. Our modelling results show that the product of strength of non-linearity and the initial amplitudes of the seismic source is the main factor influencing propagation characteristics accumulated with traveltimes. Moreover, the effects of non-linear elastic wave propagation can be distorted by the initial frequency of the seismic source and become enhanced by the presence of anisotropy. Similarly, the effects induced by anisotropy are enhanced in non-linear media. Both in isotropic and vertical symmetry axis media, the non-linear effects, such as the waveform aberration (or waveform distortion), the resonant peak shift and the generation of harmonics, can be clearly seen, and the interaction between anisotropy and non-linearity is also obvious. In conclusion, both the anisotropy and the non-linearity should be considered to investigate characteristics of elastic wave propagation in solid media, especially when the source is strong (e.g. in source regions).