Energy Transmission Coefficients Research Articles

Broadband low-transmission study of ventilation metasurfaces based on Archimedean spirals

The primary objectives of acoustic material design include ensuring indoor ventilation and isolating external noise. This study introduces a ventilation metamaterial surface based on Archimedean spirals (ASVM) and calculates its energy transmission coefficient using simulation and the Transfer Matrix Method (TMM). Experimental validation confirms the accuracy of the proposed model, highlighting ASVM’s potential as an effective ventilation metamaterial surface. Subsequently, ASVM is integrated with Helmholtz resonators (HR) to create two new metasurfaces: HR-ASVM without a neck and N-HR-ASVM with a neck. The former exhibits a power transmission coefficient below 0.2 across the broadband range of 1300 Hz to 2500 Hz, while the latter demonstrates superior sound insulation performance (power transmission coefficient below 0.1) from 639 Hz to 2500 Hz, with complete transmission suppression at 710 Hz. Notably, the thickness of N-HR-ASVM at this frequency is only 1/13 of the wavelength. Simulations of the acoustic pressure field and energy flow analyze the mechanisms responsible for low transmission. Finally, the energy transmission coefficient of N-HR-ASVM is experimentally measured and found to align closely with simulation results. This study provides valuable insights into the research on spiral ventilation metamaterial surfaces.

Reflection and Transmission of Plane Waves at the Interface of Fluid and Porous Media with Seismoelectric Effect

Abstract The relationship between energy flux reflection and transmission coefficient of seismoelectric plane waves in plane layered media and incident angle and frequency is studied. Pride equations is adopted to describe the coupling phenomenon between elastic waves and electromagnetic fields in subsurface fluid-saturated porous media. The Helmholtz decomposition is used to derive the energy flux expression for seismoelectric plane waves propagating in fluid-saturated porous media. It shows that the impermeable interface conditions have a great influence on the reflection and transmission coefficient of seismoelectirc waves. The transmission coefficient of slow longitudinal waves under impermeable interface is much smaller than that of permeable interface conditions Reflection coefficient of longitudinal wave, transmission coefficients of the fast longitudinal waves and transverse waves are all larger under impermeable interface conditions than that of permeable cases. And the reflection coefficient of electromagnetic wave under impermeable interface conditions is almost one order of magnitude smaller than that permeable case.

Coupling polaritons in near-field radiative heat transfer between multilayer graphene/vacuum/α-MoO3/vacuum heterostructures.

Both materials and structures can significantly affect radiative heat transfer, which is more pronounced in the near-field regime of two-dimensional and hyperbolic materials, and has promising prospects in thermophotovoltaics, radiative cooling, and nanoscale metrology. Hence, it is important to investigate the near-field radiative heat transfer (NFRHT) in complicated heterostructures consisting of two-dimensional and hyperbolic materials. Recent studies have reported that adding vacuum layers to multilayer structures can effectively enhance the NFRHT. Take the case of multilayer graphene/α-MoO3 heterostructures: the effect of vacuum layers on these heterostructures has not been studied, and hence investigations on adding vacuum layers between graphene and α-MoO3 layers should be emphasized. In this work, we conduct an investigation of the NFRHT between multilayer graphene/vacuum/α-MoO3/vacuum heterostructures. Compared to unit graphene/α-MoO3 heterostructures without vacuum layers, it is found that NFRHT between the heterostructures with vacuum layers can be suppressed to 49.1% when the gap distance is 10 nm, and can be enhanced to 16.3% when the gap distance is 100 nm. These phenomena are thoroughly explained by the coupling of surface plasmon polaritons and hyperbolic phonon polaritons. Energy transmission coefficients and spectral heat flux are analysed during the calculations changing chemical potentials of graphene, thicknesses of vacuum layers, and α-MoO3 layers. This study is expected to provide guidance in implementing the thermal management of reasonable NFRHT devices based on graphene/α-MoO3 heterostructures.

Multiple surface polariton-enhanced near-field radiative heat transfer between layered graphene/porous SiC terminals

Near-field radiative heat transfer (NFRHT) between two separated terminals can enhance the heat flux determined by blackbody theory by several orders of magnitude. In this work, we study the NFRHT between two terminals made of periodic multilayered graphene/porous silicon carbide (SiC), specifically focusing on the multiple surface polariton effects. The two terminals are parallel and separated by a vacuum gap. The porous SiC-supported surface phonon polaritons (SPhPs) and hyperbolic phonon polaritons (HPhPs), and their coupling with the graphene-supported surface plasmon polaritons (SPPs) leads to apparent enhancement of the radiative heat flux between the gapped terminals. The underlying mechanism of multiple polaritons for amplifying the near-field heat flux is revealed through the energy transmission coefficients for different scenarios. Results show that the heat flux between the multilayered terminals is a combination result of the multiple surface polaritons and the medium loss. When the vacuum gap is set as d = 10 nm, the heat flux between the 50-layered terminals is 1.48 times that between the single-layered terminals. We demonstrate that the NFRHT can be dynamically controlled and optimized by appropriately engineering the number of layers, the chemical potential of graphene, and the porosity and thickness of the porous SiC sheet. This work paves an alternative controllable structure for strengthening and regulating NFRHT and thus has potential applications in micro-nanoscale thermal management.

Prediction of the Transient Local Energy by Energy Finite Element Analysis

Energy finite element analysis (EFEA) has been successfully applied to steady-state response prediction over the past three decades. Compared with other energy-based methods, such as statistical energy analysis (SEA), EFEA can consider more local structural information without increasing the computational consumption too much, which makes it attractive. Inspired by the transient local energy approach (TLEA), a general transient energy balance equation was derived by assuming that the plane wave condition is satisfied. The properties of the energy balance equation were studied, and the analytical solutions with different initial conditions were provided. Utilizing the derived transient energy balance equation, transient EFEA is proposed, which has the same advantages as EFEA. A general formula is presented for the energy transmission coefficients of any number of coupled in-plane beams. The present approach was validated using a single beam and a coupled collinear beam structure under unloading conditions. The coupled collinear beams were also investigated using constant and quasi-static input power. The validation results show that TEFEA can accurately predict the local response of the structure. All of these results were compared with those of finite element analysis (FEA), simplified TEFEA (sTEFEA), transient statistical energy analysis (TSEA), and analytical formulas.

Significant Enhancement of Near-Field Radiative Heat Transfer by Misaligned Bilayer Heterostructure of Graphene-Covered Gratings

Abstract The near-field radiative heat transfer of heterostructure consisting of SiC gratings and graphene is investigated in this work. The rigorous coupled-wave analysis is employed to calculate the spectral heat flux. Nevertheless, monolayer heterostructure and nonmisaligned bilayer heterostructure consistently suffer from a lack of spectral heat flux. In this work, we investigate the prominent effect of misaligned bilayer heterostructure in enhancing near-field radiative heat transfer by plotting energy transmission coefficients and electromagnetic fields. The results show that when the misalignment reaches half a period, the bilayer heterostructure exhibits optimal performance with a total heat flux of 3.5 × 104 W/m2. Besides the well-known coupled surface phonon polaritons supported by SiC gratings, the surface plasmon polaritons supported by graphene dominate the enhancement of heat flux from 0.01 × 1014 rad/s to 1.5 × 1014 rad/s. Due to the spatial misalignment of the upper and lower gratings, the lower layer graphene surface plasmon polaritons are intensified, compensating for the lack of spectral heat flux. Meanwhile, the graphene surface plasmon polaritons and SiC surface phonon polaritons can be hybridized to form surface plasmon-phonon polaritons. In addition, the dynamic modulation of near-field radiative heat transfer in the misalignment state is achieved by manipulating the Fermi level of graphene. We finally show that the superiority of misaligned heterostructure is robust with respect to the frequency shift in the phonon band, providing an effective way to improve the near-field radiative heat transfer in different configuration.

Experimental and Numerical Study of the Nonlinear Evolution of Regular Waves over a Permeable Submerged Breakwater

The permeable submerged breakwater has gained popularity in recent days due to its merits of reducing incident wave energy without negatively impacting the aesthetics of the ocean view and allowing for water exchange. However, the effect of porosity on wave nonlinearity and turbulence motion close to the water/structure interface is not well resolved in the literature. This paper presents an experimental and numerical study of regular wave propagation over a permeable submerged breakwater with a wide top width. The laboratory experiments were conducted in a wave flume and included 45 test cases. The numerical simulations were performed utilizing validated olaFoam. The results show that the nonlinearity of the waves on the permeable submerged breakwater is weak, which can effectively suppress and reduce the second harmonic waves. A large amount of turbulent kinetic energy exists at the interface between the permeable submerged breakwater and the water body, which helps to dissipate wave energy. For the wider permeable submerged breakwater in this paper, the wave dissipation capacity is greatest when the porosity is between 0.2 and 0.3, and as the length of the breakwater increases, the energy transmission coefficient decreases, and the energy dissipation coefficient increases. Better wave attenuation is achieved when the permeable submerged breakwater has a certain porosity and a large width.

Phonon Focusing Effect in an Atomic Level Triangular Structure

The rise of artificial microstructures has made it possible to modulate propagation of various kinds of waves, such as light, sound and heat. Among them, the focusing effect is a modulation function of particular interest. We propose an atomic level triangular structure to realize the phonon focusing effect in single-layer graphene. In the positive incident direction, our phonon wave packet simulation results confirm that multiple features related to the phonon focusing effect can be controlled by adjusting the height of the triangular structure. More interestingly, a completed different focusing pattern and an enhanced energy transmission coefficient are found in the reverse incident direction. The detailed mode conversion physics is discussed based on the Fourier transform analysis on the spatial distribution of the phonon wave packet. Our study provides physical insights to achieving phonon focusing effect by designing atomic level microstructures.

Investigation on near-field radiative heat transfer between two SiC films with different substrates

Near-field radiative heat transfer (NFRHT) has drawn significant attention in the past years due to potential applications in energy harvesting, and information storage. In practical applications, the substrate is necessary to make the structure more stable. However, the investigation of substrate influence on the NFRHT in previous works is rarely carried out. In this work, the influence of the substrate on the NFRHT between two SiC films is investigated. For lossless substrates, the NFRHT is enhanced in thick films (h = 7 nm and h = 20 nm), while suppressed in thin films (h = 1 nm). For lossy substrates, the loss of the substrate can effectively promote the NFRHT. The substrates of real materials are also considered. We find the NFRHT between two SiC films is suppressed, when the substrates are Au and SiO2. The underlying physics mechanism can be explained by the antisymmetric and symmetric mode of surface phonon polaritons (SPhPs) in SiC films, which are analyzed by the energy transmission coefficients (ETCs) as a function of angular frequency and wavevector. In addition, we find that the dispersion relations and ETCs exhibit a good agreement. We believe this work is helpful in understanding the effect of substrates on SPhPs and designing near-field radiation devices.

Near-field radiative heat transfer between multilayer structures composed of different hyperbolic materials

Near-field radiative heat transfer (NFRHT) has drawn significant interest in the recent years, including thermal management and energy harvesting. The NFRHT between single hyperbolic materials (HMs) has been thoroughly investigated. However, the research on the NFRHT between periodic multilayer structures composed of different HMs is rarely discussed. Moreover, the coupling effect of hyperbolic phonon polaritons (HPPs) supported by different HMs is still unclear. In this work, we investigated the NFRHT between multilayer structures composed of hexagonal boron nitride (hBN) and α-phase molybdenum trioxide (α-MoO3), separated by vacuum layers. The influence of the gap distance, the unit-cell number, the thickness of the HMs and thickness of the vacuum layer on the NFRHT are discussed. The numerical results show that the maximal total heat flux (THF) between six-cell multilayer structures is 19 times compared to the THF between hBN films at the gap distance of 50 nm and is 1.46 times compared to the THF between α-MoO3 films at the gap distance of 30 nm. Such enhancement can also be found at other similar gap distances. The vacuum layer promotes the coupling of HPPs supported by different HMs, which can be elucidated by the energy transmission coefficients. This work could benefit the application of near-field thermal radiative devices based on HMs.

Effect of substrate on the near-field radiative heat transfer between α-MoO3 films

Near-field radiative heat transfer (NFRHT) has promising prospects in modern nanotechnology, such as near-field thermal microscopy, nanoscale non-contact thermal management, and information processing. Experimentally, supported substrates are crucial in ensuring structural stability, especially in ultrathin structures. However, the effect of the substrate on the NFRHT has seldom been explored. Here, the NFRHT between α-MoO3 films with different permittivities of substrate is studied. For lossless substrates, the NFRHT is suppressed as the permittivity of the substrate increases when the heat transfer is along the [010] and [100] crystal directions of α-MoO3. When the NFRHT is along the [001] crystal direction of α-MoO3, high-permittivity substrates suppress the NFRHT when the film is thin (< 10 nm), while enhancing the NFRHT in thicker films (> 10 nm). Moreover, we find that the effect of the substrate on the NFRHT highly relies on film thickness. The effect of lossy substrate on NFRHT is also discussed. We find that the loss of the substrate is more significant for the enhancement of heat flux at a small gap distance (20 nm). However, when the gap distance is large (100 nm), the excessive loss suppresses the NFRHT. Hyperbolic polaritons (HPs) can effectively explain the above phenomenon, as confirmed by energy transmission coefficients distribution and dispersion relation in wavevector space. In particular, the volume-confined hyperbolic polaritons play a dominant role in the flux variation between the thin films (1 nm and 10 nm). For the 100-nm film, surface-confined hyperbolic polaritons are more important. This study sheds light on the effect of substrate on HPs and provides theoretical guidance for designing near-field thermal radiation devices.

Polariton hybridization phenomena on near-field radiative heat transfer in periodic graphene/α-MoO3 cells

Abstract Coupling of surface plasmon polaritons (SPPs) supported by graphene and hyperbolic phonon polaritons (HPPs) supported by hyperbolic materials (HMs) could effectively promote photon tunneling, and hence the radiative heat transfer. In this work, we investigate the polariton hybridization phenomena on near-field radiative heat transfer (NFRHT) in multilayer heterostructures, which consist of periodic graphene/α-MoO3 cells. Numerical results show that increasing the graphene/α-MoO3 cells can effectively enhance the NFRHT when the vacuum gap is less than 50 nm, but suppresses the enhanced performance with larger gap distance. This depends on the coupling of SPPs and HPPs in the periodic structure, which is analyzed by the energy transmission coefficients distributed in the wavevector space. The influence of the thickness of the α-MoO3 film and the chemical potential of graphene on the NFRHT is investigated. The findings in this work may guide designing high-performance near-field energy transfer and conversion devices based on coupling polaritons.

Substrate effects on the near-field radiative heat transfer between two hBN films

Near-field radiative heat transfer (NFRHT) could surpass the blackbody limit defined by Stefan-Bolzmann’s law by several orders of magnitude, which has potential applications in thermal switching, thermal management, and photovoltaics. To further develop the NFRHT from theory to application, the substrate, which could enhance the stability of the structure, is a critical factor not to be ignored. However, the substrate effect on the NFRHT is still rarely discussed. In this work, we investigate the NFRHT between hexagonal boron nitride (hBN) films with different permittivities of the substrate. Results demonstrate that when the thickness of the film is 1 nm, increasing the permittivity of the substrate will suppress the NFRHT. In contrast, when the thickness of the film is larger (&amp;gt;2 nm), the high-permittivity substrate could enhance the NFRHT. The spectral heat flux (SHF) corresponding to substrates with different permittivities was investigated. The SHF in Type I hyperbolic band of hBN increases with the increase in the permittivity of the substrate, while that in Type II hyperbolic band is completely opposite. This competitive relationship leads to the above-mentioned phenomenon of NFRHT. The underlying physics mechanism can also be explained by the hyperbolic phonon polaritons (HPPs), which are analyzed by the energy transmission coefficients and dispersion relations. The findings in this work will deepen the understanding of the substrate on HPPs and pave a novel way for near-field radiation devices based on hyperbolic materials.

Debonding Detection in Aluminum/Rigid Polyurethane Foam Composite Plates Using A0 Mode LAMB Wave EMATs

Aluminum/rigid polyurethane foam composite plates (ARCPs) are widely used for thermal insulation. The interface debonding generated during manufacturing degrades the thermal insulation performance of an ARCP. In this study, the debonding of an ARCP, a composite plate with a porous and damped layer of rigid polyurethane foam (RPUF), was detected using A0 mode Lamb wave electromagnetic acoustic transducers (EMATs). The low energy transmission coefficient at the interface caused by the large acoustic impedance difference between aluminum and RPUF made the detection difficult. Based on these structural characteristics, an A0 mode Lamb wave with large out-of-plane displacement was used to detect the debonding. EMATs are preferred for generating A0 mode Lamb waves due to their advantages of being noncontact, not requiring a coupling agent, and providing convenient detection. A finite element simulation model considering the damping of the RPUF layer, the damping of the PU film at the interface, and the bonding stiffness of the interface was established. The simulation results indicated that the Lamb wave energy in the aluminum plate transmits into the RPUF layer in small amounts. However, the transmitted energy rapidly attenuated and was not reflected into the aluminum plate, as the RPUF layer was thick and highly damped. Therefore, energy attenuation was evident and could be used to characterize the debonding. An approximately linear relationship between the amplitude of the received signals and the debonding length was obtained. Experiments were performed on an ARCP using EMATs, and the experimental results were in good agreement with the simulation results.

Impact of interfacial compositional diffusion on interfacial phonon scattering and transmission in GaN/AlN heterostructure

Compositional diffusion at interfaces often occurs during the synthesis of heterostructures, which poses a significant challenge to the reliability and performance of heterostructure-based electronic devices. In this study, the effect of interfacial compositional diffusion on the interfacial phonon transport in GaN/AlN heterostructures has been explored using molecular dynamics and phonon dynamics simulations. It is found the compositional diffusion results in a remarkable reduction in the interfacial thermal conductance (ITC) of the heterostructures, which can be modulated by tuning the compositional diffusion thickness. Phonon wave packet simulations further revealed that the energy transmission coefficient across the interface is strongly phonon frequency-dependent and interfacial morphology-dependent, which is consistent well with the calculated ITC of the structures. The phonon mode conversion and phonon localization are observed at the region of interfaces. Furthermore, it is found that the longitudinal acoustic phonons are more sensitive to the compositional diffusion interface than transverse-acoustic phonons do. However, it is interesting to find that the energy transmission coefficients of transverse-acoustic phonons with a high frequency (above 3.6 THz) across the compositional interface are abnormally higher than those across the sharp interface due to the stronger phonon mode conversion in the compositional diffusion region, which provides additional pathways for energy transmission. Our findings provide a deeper insight into the interfacial phonon scattering and transmission under the coupling effect of interfacial morphology and compositional diffusion.

Axionic and nonaxionic electrodynamics in plane and circular geometry

Various aspects of axion electrodynamics in the presence of a homogeneous and isotropic dielectric medium are discussed. First, we consider the ``antenna-like'' property of a planar dielectric surface in axion electrodynamics, elaborating on the treatment given earlier on this topic by Millar et al. [J. Cosmol. Astropart. Phys. 01 (2017) 061.]. We calculate the electromagnetic energy transmission coefficient for a dielectric plate, and compare with the conventional expression in ordinary electrodynamics. Second, we consider the situation where the medium exterior to the plate, assumed elastic, is ``bent back'' and glued together, so that we obtain a circular dielectric string in which the waves can propagate clockwise or counterclockwise. As will be shown, a stationary wave pattern is permitted by the formalism, and we show how the amplitudes for the two counterpropagating waves can be found. Third, as a special case, by omitting axions for a moment, we analyze the Casimir effect for the string, showing its similarity as well as its difference from the Casimir effect of a scalar field for a piecewise uniform string [I. Brevik and H. B. Nielsen, Phys. Rev. D 41, 1185 (1990).]. Finally, including axions again we analyze the enhancement of the surface-generated electromagnetic radiation near the center of a cylindrical haloscope, where the interior region is a vacuum and the exterior region a high refractive index medium. This enhancement is caused by the curvature of the boundary, and is mathematically a consequence of the behavior of the Hankel function of the second kind for small arguments. A simple estimate shows that enhancement may be quite significant, and can therefore be of experimental interest. The presence of an absorber in the center and the possibility of adopting it to search for axions with mass in the THz region, and possibly the GHz region too, is also discussed. This proposal is suggested as an alternative to the reflector arrangement in a similar arrangement recently discussed by Liu et al. [, Phys. Rev. Lett. 128, 131801 (2022).].

Reflection and transmission of plane waves in stressed media with an imperfectly bonded interface

SUMMARY The reflection and transmission of elastic waves are of great significance for predicting reservoir physical properties, interpreting seismic data and detecting crustal structures. Most studies only consider the initial vertical stress state when studying the reflection and transmission of elastic waves at imperfectly bonded interfaces, but few studies consider the influence of initial stress on boundary conditions. Moreover, the effect of initial stress on the energy distribution of elastic waves at imperfectly bonded interfaces has rarely been investigated. We propose a unified method to calculate the energy reflection and transmission coefficients for different incident waves at welded or imperfectly bonded interfaces in stressed media. The effects of initial stress on the equation of motion, the elastic properties of the medium and the boundary conditions at the interface are considered. The elastic properties of rocks under initial stress are described by acoustoelasticity theory. In addition, we define a new stress tensor to modify the linear-slip model for describing boundary conditions at the imperfectly bonded interface in the presence of initial stress. Numerical results show that the energy reflection and transmission coefficients at the non-welded interface in stressed media depend on the elastic properties of the incident and transmitted media, the initial stress, the type and magnitude of the interfacial compliance and the frequency and propagation direction of the incident wave. The initial vertical and horizontal stresses dominate the reflection and transmission coefficients at small and large angles, respectively. The discontinuity in displacement across the imperfectly bonded boundary results in the frequency dependence of the reflection and transmission coefficients. Imperfect bonding enhances P-wave and SV-wave energy reflection and weakens P-wave energy transmission. However, imperfect bonding can enhance the energy transmission of the SV wave for the imperfectly bonded interface with high contrast between tangential and normal compliance and a resonance peak appears at a specific frequency. We also notice that imperfectly bonded interfaces with interfacial compliance less than $1.0 \times {10}^{ - 11}$ m Pa−1 can be regarded as welded interfaces in the seismic frequency band (lower than 100 Hz). In addition, the initial stress greatly influences the reflection coefficients at high frequencies and the transmission coefficients at low frequencies. The initial vertical stress can reduce the energy transmission of SV waves at imperfectly bonded interfaces. In contrast, the initial horizontal stress can significantly increase the energy transmission of low-frequency SV waves and may lead to the disappearance of the resonant peak in the transmission coefficients.

Performance improvement of three-body radiative diodes driven by graphene surface plasmon polaritons.

As an analogue to an electrical diode, a radiative thermal diode allows radiation to transfer more efficiently in one direction than in the opposite direction by operating in a contactless mode. In this study, we demonstrated that within the framework of three-body photon thermal tunneling, the rectification performance of a three-body radiative diode can be greatly improved by bringing graphene into the system. The system is composed of three parallel slabs, with the hot and cold terminals of the diode coated with graphene films and the intermediate body made of vanadium dioxide (VO2). The rectification factor of the proposed radiative thermal diode reaches 300% with a 350 nm separation distance between the hot and cold terminals of the diode. With the help of graphene, the rectification performance of the radiative thermal diode can be improved by over 11 times. By analyzing the spectral heat flux and energy transmission coefficients, it was found that the improved performance is primarily attributed to the surface plasmon polaritons (SPPs) of graphene. They excite the modes of insulating VO2 in the forward-biased scenario by forming strongly coupled modes between graphene and VO2 and thus dramatically enhance the heat flux. However, for the reverse-biased scenario, the VO2 is at its metallic state, and thus, graphene SPPs cannot work by three-body photon thermal tunneling. Furthermore, the improvement was also investigated for different chemical potentials of graphene and geometric parameters of the three-body system. Our findings demonstrate the feasibility of using thermal-photon-based logical circuits, creating radiation-based communication technology and implementing thermal management approaches at the nanoscale.

Interaction between medium-long period waves and smoothed mound breakwater: Physical model tests and SPH simulations

Medium-long period waves have attracted increasing attention. Laboratory and numerical investigations on the interaction between medium-long period waves and a smoothed mound breakwater were conducted. A two-dimensional numerical wave flume based on smoothed particle hydrodynamics was established. A good agreement between experimental and numerical results was observed.Wave force on the slope is positively correlated with the wave period. It is found that Neelamani's method is slightly overestimated wave force on the slope. By comparing with other overtopping methods, a new formula considering the wave period was proposed to predict the overtopping of the smoothed mound breakwater. The energy transmission coefficient was used to evaluate the protective effect of the breakwater. The results show that the smooth mound breakwater provides significant protection against longer-period waves. As the wave period increases, the number of peaks (Np) in the wave spectrum behind the breakwater increases. A formula was presented to describe the relationship between Np and wave period.

Effect of unloading behavior on stress wave transmission in a double-scale discontinuous rock mass

Stress wave propagation through double-scale discontinuous rock masses considering unloading behavior was investigated. The piecewise linear loading and unloading models of macrojoint were proposed, which were combined with a split three-characteristics mothed to investigate the stress wave transmission properties. The effects of the waveform, frequency, amplitude and propagation distance on the energy and amplitude transmission coefficients were discussed. The results of the present study were compared with the traditional study that considered single-scale discontinuities. The results show that the present study can effectively analyze the effect of the waveform, frequency, amplitude and propagation distance on the energy and amplitude transmission coefficients. The energy and amplitude transmission coefficients for rectangular wave are the largest, while those for triangular wave are the smallest. The energy and amplitude transmission coefficients decrease as frequency and propagation distance increase. The energy and amplitude transmission coefficients increase as the amplitude increase. The results also show that the effect of macrojoint unloading effect and microdefect on wave transmission can be considered comprehensively in the present study. The unloading effect of macrojoint causes the smaller energy transmission coefficient, while it does not affect the amplitude transmission coefficient. The microdefects cause smaller energy and amplitude transmission coefficients. Highlights The effect of unloading behavior on wave propagation in rock mass was studied. The piecewise linear loading and unloading models of macrojoint were proposed. Macrojoint and microdefect in rock mass were considered in a framework. Energy and amplitude transmission coefficients were studied in present study.