One-dimensional Wave Propagation Research Articles

Design and Validation of a Stratified Shear Model Box for Seismic Response of a Sand-Blowing Reclamation Site

The global increase in building collapses and damage on soft-soil sites due to distant significant earthquakes poses similar challenges for sand-blowing reclamation (SBR) sites on soft-soil layers. This study was initiated to capture the vibration characteristics of the SBR sites and to provide fresh insights into their seismic responses. Initially, considering the heterogeneity and layered structure of soil at SBR sites, we developed a novel stratified shearing model box. This model box enables the simulation of the complex characteristics of soil layers at SBR sites under laboratory conditions, representing a significant innovation in this field. Subsequently, an innovative jack loading system was developed to apply active vertical pressure on the soil layer model, accelerating soil consolidation. Furthermore, a new data collection and analysis system was devised to monitor and record acceleration, pore water pressure, and displacement in real time during the experiments. To verify the model box’s accuracy and innovation, and to examine the seismic response of SBR sites under varying consolidation pressures, four vibration tests were conducted across different pressure gradients to analyze the model’s predominant period evolution due to consolidation pressures. The experimental results demonstrate that the model box accurately simulates the propagation of one-dimensional shear waves in soil layers under various consolidation pressures, with notable repeatability and reliability. Our experiments demonstrated that increasing consolidation pressure results in higher shear wave speeds in both sand and soft-soil layers, and shifts the site’s predominant period towards shorter durations. Concurrently, we established the relationship between the site’s predominant period and the input waves. This study opens new paths for further research into the dynamic response properties of SBR sites under diverse conditions through shaking-table tests.

An improved algorithm for Finite Particle Method considering Lagrange-type remainder

The Finite Particle Method (FPM) is a significant improvement to the traditional Smoothed Particle Hydrodynamics method (SPH), which can greatly improve the computational accuracy of the entire computational domain. However, unstable calculation results and long computational time are still major obstacles to the development of FPM. Based on matrix decomposition, the fundamental equations of the traditional Finite Particle Method are rewritten and a Generalized Finite Particle Method (GFPM) is derived by introducing Lagrange-type remainder. By deriving and rewriting the fundamental equations, the GFPM method can be theoretically proven to be always stable. Numerical examples show that the GFPM method can utilize a smaller computational scale to achieve the same computational accuracy as the FPM method, with a corresponding reduction in computational time. Finally, the GFPM method is applied to a one-dimensional stress wave propagation problem and a one-dimensional heat conduction problem, and the computational results are compared with those of the SPH method and the FPM method, which verify that the GFPM has higher computational accuracy and stability.

Experimental Study on the Boundary Reflection Effect of Stress Wave Propagation Based on the Newly Developed Test Apparatus

There is a ubiquitous boundary reflection effect of stress wave propagation in the indoor experimental studies. It is critical to improve the validity of waveform data by optimizing boundary materials to absorb reflection waves. In the present study, a calculation method for the optimal wave impedance of boundary materials was proposed based on the transmission and reflection principle of one-dimensional stress waves at the interface of different media. By using the calculation method, the optimal wave impedance value of the boundary material was obtained. A one-dimensional stress wave propagation test apparatus was developed for exploring the improvement effect of absorbing materials on the boundary reflection effect. One-dimensional stress wave propagation experimental studies in the complete red sandstone samples were carried out by setting various boundary absorbing materials such as pine pad, rubber pad, and steel pad. The results indicated that the experimental test results were consistent with the theoretical calculation results. In the stress wave propagation tests, the optimal wave impedance value of the boundary material was 1.12 × 106 kg/m2·s. When the pine pads were used as boundary absorbing materials, the suppression effect of boundary reflection effects is relatively the best. The present study provides references for analyzing the characteristics and mechanism of stress wave propagation and attenuation.

Hopkinson bar impact force measurement for application to development of an artificial bird

A test method has been published for measuring forces from bird cadavers and artificial birds to demonstrate equivalency to support the use of artificial birds in aircraft certification testing. The test method involves a large diameter Hopkinson bar as the technique for measuring and comparing forces. The method involves the assumption that a force on one end of the bar results in a one-dimensional plane wave that travels down the bar. To avoid reflected waves from the end of the bar overlapping the input pulse, and due to practical limitations on the length of the bar, strain transducers are located relatively close to the impacted face of the bar, raising questions about the validity of the assumption of one-dimensional wave propagation. In addition, the large diameter of the bar can introduce dispersion effects in the propagated pulse. These must be assessed to determine the impact on the accuracy of impact force measurements and, if significant, dispersion correction techniques must be used. In this study analytical, experimental, and computational methods are used to analyze the wave propagation characteristics for impact forces expected from realistic bird impacts. While wave dispersion and effects of non-concentric impacts are present, the resulting errors are small relative to typical test-to-test variation observed in bird impact testing. For the response we expect to see in bird impacts up to velocities of approximately 300 m/s the large diameter Hopkinson bar test appears to be an acceptable method for measuring the impact forces and comparing the response of real and proposed artificial birds.

Comparative Studies between Frequency Domain Analysis and Time Domain Analysis on Free-Field One-Dimensional Shear Wave Propagation

In Korea, the underground silo structure for low- and intermediate-level radioactive waste disposal facilities has been constructed and operated since 2014. Large-scale earthquakes occurred in 2016 and 2017, respectively, in Gyeongju and Pohang areas near the underground silo structures, and interest in the stability of the underground silo increased significantly. In this paper, one-dimensional free-field analyses have been carried out before the three-dimensional silo dynamic analyses subjected to earthquake loadings. As an additional study, a new form of the finite element equilibrium equation is derived in terms of relative motions, which is essentially the same equation expressed in terms of total motions where the base shear force is applied to the earthquake load. The accuracy of conventional finite element solutions is evaluated by directly comparing them with closed-form solutions by frequency domain analysis such as SHAKE91.

Thermodynamically extended symplectic numerical simulation of viscoelastic, thermal expansion and heat conduction phenomena in solids

AbstractSymplectic numerical schemes for reversible dynamical systems predict the solution reliably over large times as well, and are a good starting point for extension to schemes for simulating irreversible situations like viscoelastic wave propagation and heat conduction coupled via thermal expansion occuring in rocks, plastics, biological samples etc. Dissipation error (artificial nonpreservation of energies and amplitudes) of the numerical solution should be as small as possible since it should not be confused with the real dissipation occurring in the irreversible system. In addition, the other well-known numerical artefact, dispersion error (artificial oscillations emerging at sharp changes), should also be minimal to avoid confusion with the true wavy behavior. The continuum thermodynamical aspects (respect for balances with fluxes, systematic constitutive relationships between intensive quantities and fluxes, the second law of thermodynamics with positive definite entropy production, and the spacetime-based kinematic viewpoint) prove valuable for obtaining such extended schemes and for monitoring the solutions. Generalizing earlier works in this direction, here, we establish and investigate such a numerical scheme for one-dimensional viscoelastic wave propagation in the presence of heat conduction coupled via thermal expansion, demonstrating long-term reliability and the applicability of thermodynamics-based quantities in supervising the quality of the solution.

Track-bridge deformation relation and interaction of long-span railway suspension bridges subject to strike-slip faulting

During earthquakes, the long-span railway bridges crossing active faults are more vulnerable because of the combined effects of pulsed ground motions and surface dislocations. To study the track-bridge deformation and interaction of long-span railway suspension bridges crossing the strike-slip faults, the refined finite element model of a ballasted track-bridge-pile-soil coupled system was established using the nonlinear finite element software ANSYS/LS-DYNA. A detailed and systematic numerical simulation was conducted from the soil cracking and compression during the ground surface rupture, pile–soil interaction, and three-dimensional track constraints to track-bridge deformation relationships and interactions. One-dimensional wave propagation theory was employed to derive the ground motions on the bedrock according to ground surface-measured seismic records. The influences of the fault-crossing angle (FCA) and permanent ground rupture displacement (PGRD) on the seismic responses and track-bridge interaction were analysed by considering the pile–soil interaction and site response effect. A method for calculating the track curvature radius based on track deformation is presented to evaluate the running traffic conditions of the trains. Additionally, the stability of the ballast bed was estimated using the track-bridge relative displacement. The conclusions drawn can be applied in practical seismic design and train running safety assessment of long-span railway suspension bridges crossing the strike-slip faults.

Appearing shock waves in Arruda – Boyce incompressible rod

The Arruda – Boyce incompressible hyperelastic potentials are used for analyzing one-dimensional acoustic wave propagation in a semi-infinite nonlinearly elastic rod. It has been found that during the propagation of the delta-like pulses, the following phenomena are observed, (i) the shock wave fronts arise; (ii) the pulses spread out due to physical dispersion; (iii) the mechanical energy of the considered system decreases with time, resulting in a decrease of the pulse magnitudes; and, at the same time (iv) thermal energy arises and increases with time, that is caused by formation and propagation of shock wave fronts. The analysis utilizes a combined method consisting of the explicit time integration technique coupled with the finite element method for spatial discretization.

Direct spatio-temporal stress field determination combining full-field deformation measurements and explicit finite element method: Concept verification

High strain rate loading of materials with spatially heterogeneous properties produces non-homogeneous and transient stress-strain states. Such stress-strain states are atypical of classical split Hopkinson pressure bar (SHPB) analysis that assumes homogeneous deformation and dynamic force equilibrium. To determine spatio-temporal stress fields in heterogeneous materials, a novel concept combining digital image correlation (DIC) full-field deformation measurements and explicit dynamic finite element method (EFEM) is described in this paper. The concept utilizes measured boundary forces and DIC measurements including both displacements and accelerations as input. The measured input is used to calculate internal forces, and hence the stress fields, within each continuum finite element by solving the governing equations of motion using the framework of EFEM. The DIC+EFEM concept procedure is verified using simulated synthetic data considering one-dimensional stress wave propagation in a bar. The reconstructed axial stress fields match identically with the exact EFEM solution for both homogeneous and heterogeneous materials that are elastic or elastic-plastic. The influence of DIC measurement noise on the reconstructed stresses is also studied.

Longitudinal wave propagation analysis in Entangled metallic wire materials using an improved wave and finite element method

This paper proposes a novel concept and methodology to study longitudinal wave propagation in entangled metallic wire material (EMWM), a porous structural network consisting of spatial helix wires. The numerical model of EMWM is constructed using representative volume elements (RVE) obtained through X-ray tomography and skeletonization of a standard specimen. By increasing the approximate periodic boundary, the improved wave and finite ele-ment method (WFE) is employed to model EMWM as approximately periodic structures, allowing for numerical simulations of wave propagation characteristics. Frequency bands and resonance modes of EMWM are calculated to analyze the characteristics of one-dimensional wave propagation. The numerical results show that EMWM exhibits unique frequency band characteristics compared to typical periodic porous materials. In the frequency range of 15 to n n 35 kHz, the first pass band corresponds to the tensile-compressive motion of the entire specimen, while the higher pass bands correspond to localized vibrations within the spatial wires. Additionally, the frequency bands can be adjusted across a wide range based on the relative density of EMWM specimens. The improved WFE method and obtained numerical data can facilitate the application of EMWM on high frequency vibration isolation.

Computational approach for the acoustic modelling of large aftertreatment devices with multimodal incident sound fields

The influence of multimodal incident sound fields on the acoustic behaviour of large aftertreatment devices incorporating a monolith is modelled and analysed in detail. The analytical mode matching method is applied to the compatibility conditions of the three-dimensional acoustic fields at the device geometric discontinuities, leading to the computation of the complex wave amplitudes in all the subdomains involved and the corresponding device transmission loss. To have a realistic model, three-dimensional propagation must be considered in the inlet/outlet ducts and chambers, while one-dimensional wave propagation has to be assumed along the small capillaries of the aftertreatment device monolith (such catalytic converters and particulate filters); therefore, the monolith can be replaced by a plane wave four-pole transfer matrix from an acoustical point of view. On the other hand, for large aftertreatment device inlet ducts such as those found in heavy-duty and off-road engines, the usual models with plane incident wave excitation are not accurate since the onset of higher order incident modes in the inlet duct is expected for the frequency range of interest. Therefore, a variation of the acoustic attenuation performance is likely to occur depending on these modes, similar to the results previously found in the case of large dissipative silencers. Results are presented for three different multimodal incident sound field hypotheses: equal modal amplitude, equal modal power and equal modal energy density. A relevant influence on the sound attenuation is found for the test problems considered in the current investigation.

Global method for nonlinear seismic analysis of embedded base-isolated nuclear island buildings in layered sites

Owing to the increasing scarcity of high-quality sites, the seismic analysis of base-isolated nuclear power plants (NPPs) under complex non-lithology sites has gained important engineering significance. In this study, a global method for nonlinear numerical analysis was developed for the seismic evaluation of base-isolated NPPs in complex layered sites. The seismic analysis of layered sites is realised using the equivalent linear method and one-dimensional wave propagation theory, the radiation damping of the infinite domain is modelled with a visco-elastic artificial boundary, and the nonlinear behaviour of the isolators is fully considered using a bilinear hysteretic model. Using this method, the influence of soil–structure interaction (SSI) and soil nonlinearity on the behaviour of base-isolated NPPs under the design basis earthquake and beyond design basis earthquake was analysed and compared, in terms of the floor response spectra (FRS) and inter-story displacement angle. In addition, the influence of embedment is also studied. The results show that in layered sites, the SSI significantly amplifies the response values for base-isolated NPPs, and as the ground motion input increases, the soil nonlinearity more effectively inhibits the response of base-isolated NPPs. In addition, embedding can significantly reduce the response, but it increases the FRS at some frequency domains. The isolation effect of base-isolated NPPs decreases significantly when SSI effects are considered, and the soil nonlinearity and embedment have little impact on the base isolation capacity. The method proposed in this study can be easily applied to study base-isolated NPPs in layered sites.

Compressive Split Hopkinson Pressure Bar Apparatus: Part I - Design and Development

Optimum utilization of composite materials envisages its use under static as well as dynamic loading conditions. Hence, there is a need to assess the behavior of composite materials at high strain rates. Split Hopkinson Pressure Bar (SHPB) apparatus is widely used to assess high strain rate behavior of composites. Even though SHPB apparatus is widely used, its design methodology and development technique are not readily available. Design and devel- opment details of a compressive SHPB apparatus for characterizing mechanical properties of different materials at high strain rate loading are presented. Brief theoretical background necessary for the design of SHPB apparatus is presented based on one-dimensional wave propagation theory in elastic bars. Next, brief working principle of the apparatus and schematic arrangement are presented. Different components of the compressive SHPB appa- ratus are identified. Design, development and commissioning of the apparatus are discussed. Further, different instruments used and the calibration technique used are presented.

Machine learning simulation of one-dimensional deterministic water wave propagation

Deterministic phase-resolved prediction of the evolution of surface gravity waves in water is challenging due to their complex spatio-temporal dynamics. Physics-based methods of varying complexity are available, but the conflicting objectives of numerical efficiency and accuracy impede real-time wave prediction. Data-driven methods may be able to overcome this challenge by using training data generated by complex numerical methods. This work explores the potential of a machine learning (ML) approach based on a fully convolutional encoder–decoder architecture for the efficient and accurate prediction of water waves. The high-order spectral (HOS) method forms the foundation for the generation of the training data. The HOS method is applied for different, consecutive orders of nonlinearity starting from first order up to fourth order. The JONSWAP wave energy spectrum serves as the basis for modeling the one-dimensional irregular sea states. The overall objective of this work is to evaluate whether the complex non-linear physical processes can be identified and learned by the ML approach. The trained ML flow mapper is used to perform time integration of an initial sea state. The results indicate that the proposed ML approach is able to reproduce the distinctive physical processes of the different orders of nonlinearities. It is shown that the ML approach enables fast and accurate predictions of one-dimensional waves over a time horizon that spans multiple peak periods.

On soliton solutions of the modified equal width equation

PurposeThe soliton solutions are obtained by using extended rational sin/cos and sinh-cosh method. The methods are powerful and have ease of use. Applying wave transformation to the nonlinear partial differential equations (NLPDEs) and the considered equation turns into a nonlinear differential equation (NODE). According to the methods, the solution sets of the NODE are supposed to the form of the rational terms as sinh/cosh and sin/cos and the trial solutions are substituted into the NODE. Collecting the same power of the trigonometric functions, a set of algebraic equations is derived.Design/methodology/approachThe main purpose of this paper is to obtain soliton solutions of the modified equal width (MEW) equation. MEW is a form of regularized-long-wave (RLW) equation that represents one-dimensional wave propagation in nonlinear media with dispersion processes. This is also used to simulate the undular bore in a long shallow water canal.FindingsThus, the solution of the main PDE is reduced to the solution of a set of algebraic equations. In this paper, the kink, singular and singular periodic solitons have been successfully obtained.Originality/valueIllustrative plots of the solutions have been presented for physical interpretation of the obtained solutions. The methods are powerful and might be used to solve a broad class of differential equations in real-life problems.

Exploring the dynamics of soliton waves: A comparative analysis of analytical and numerical methods for the modified Equal-Width equation

The modified Equal-Width (MEW) equation is a fundamental model in the realm of partial differential equations that is used to simulate one-dimensional wave propagation in nonlinear media, incorporating dispersion processes. In this study, we have employed two contemporary analytical and numerical methods to obtain exact traveling wave solutions for this model. The derived solutions have been evaluated using a numerical technique, demonstrating excellent accuracy. Various graphical representations, including a contour plot, a two-dimensional graph, and a three-dimensional graph, have been utilized to illustrate and analyze the results. Our study offers significant contributions to the field by providing new insights into the dynamics of solitary wave solutions of the MEW model. Furthermore, our method proves to be a valuable and effective mathematical tool that can be utilized to solve various nonlinear wave problems, making it highly applicable in a range of physical and mathematical studies. By showcasing the properties of the investigated model and the primary advantages of the employed techniques, our study highlights the potential for further developments and advancements in this field.

Experimental study on dynamic compression behavior characteristics and stress wave propagation law of rigid-flexible combinations under cyclic bi-directional impact loading

To explore the dynamic compression behavior and damage evolution characteristics of “rigid-flexible coupling” surrounding rock supporting structure. Split Hopkinson pressure bar (SHPB) was used to carry out constant amplitude cyclic bi-directional impact compression tests on the combination specimens of “rigid-rigid: rock (sandstone)-like material (RLM) - normal cement mortar (NCM)", “rigid-flexible: RLM - rubber cement mortar (RCM)" and “flexible-rigid: RCM - high-performance supporting concrete (HPSC)". The characteristics of stress-strain curve evolution, stress attenuation, strain growth, energy transformation, damage evolution characteristics, and damage state were compared and analyzed. The results show that compared with RLM-NCM, RLM-RCM and RCM-HPSC had remarkable dynamic yield ductility and excellent impact resistance. RCM and HPSC can work together to hinder the dynamic damage development of “rigid-flexible coupling” supporting structure and surrounding rock. Based on the one-dimensional stress wave propagation theory, the stress wave propagation models of rigid-flexible combination specimens under SHPB cyclic bi-directional impact were established, and the corresponding stress wave propagation equations were derived, which profoundly revealed the propagation law and attenuation mechanism of stress waves in SHPB impact rigid-flexible combination tests. Finally, based on the energy drive theory and residual energy theory, the impact instability energy criteria of surrounding rock under the rigid component combined support system and “rigid-flexible coupling” component combined support system were analyzed and discussed.

Thermal inertia effect of reactive sources on one-dimensional discrete combustion wave propagation

In the present work, the discrete flame model developed by Shoshin et al. (Doklady Akademii Nauk SSSR, 1986) and further scrutinized by Tang et al. (Combustion Theory and Modelling, 2009) is augmented by introducing the thermal inertia of particles in the preheating zone. The effect of particle thermal inertia on the speeds, propagation limits, and near-limits dynamics of one-dimensional discrete combustion waves is studied using the new model. It is found that, with the increase of particle thermal inertia, the propagation velocity of the discrete flame decreases due to the smaller heating rate of the particles. Besides, particle thermal inertia extends the propagation limits compared to the prediction of the old model. Furthermore, it is mathematically proven that the nonphysical branch of the solutions for the discrete flame speeds, found using the old discrete model, is a set of solutions for the propagation limits of steady-state discrete flames with particle thermal inertia included. The flame speed predicted using the new model is also compared with that determined analytically using a continuum model considering the thermal inertia of the condensed phase, attributed to Goroshin et al. (Combustion and Flame, 1996). We find that the discrete flame speeds predicted by the both models become closer to each other with increasing particle thermal inertia. Finally, the two models converge regardless of the discrete nature of the heat sources when particle thermal inertia is large enough so that can limit the flame propagation. The particle thermal inertia controlled flames could be regarded as a new kind of combustion regime.

Phonon transmission through a nonlocal metamaterial slab

Previous theory and experiment has shown that introducing strong (nonlocal) beyond-nearest-neighbor interactions in addition to (local) nearest-neighbor interactions into rationally designed periodic lattices called metamaterials can lead to unusual wave dispersion relations of the lowest band. For roton-like dispersions, this especially includes the possibility of multiple solutions for the wavenumber at a given frequency. Here, we study the one-dimensional frequency-dependent acoustical phonon transmission of a slab of such nonlocal metamaterial in a local surrounding. In addition to the usual Fabry-Perot resonances, we find a series of bound states in the continuum. In their vicinity, sharp Fano-type transmission resonances occur, with sharp zero-transmission minima next to sharp transmission maxima. Our theoretical discussion starts with a discrete mass-and-spring model. We compare these results with solutions of a generalized wave equation for heterogeneous nonlocal effective media. We validate our findings by numerical calculations on three-dimensional metamaterial microstructures for one-dimensional acoustical wave propagation.

Strong motion estimation in Costa Rica at non-record sites using spectral inversion method

We performed the spectral inversion to separate the source, path, and site effects using strong ground motion records from essential facilities such as powerhouses and hydroelectric dams, distributed all over Costa Rica. The spectral inversion technique was adapted to a sparsely observed strong motion data set. We used the results to estimate strong ground motions at sites where there were no observation records in and around the intensity anomaly that appeared during the 2012 Sámara earthquake of Mw 7.6. To ensure the quality, we incorporated a broadband station to estimate levels of acceleration source spectra for six events 5.3 ≤ Mw ≤ 6.5, using them as the reference events for the spectral inversion. In this paper, we introduced two consistency checks: confirmation of the correctness of the input data, and verification of the output using synthetic spectra. We used them as an iterative implementation of sequences of elimination of suspicious data and inversions. We regulated the source spectra of the reference events for the final inversion, considering the estimate of site effect for one-dimensional SH wave propagation at the site of the lowest site amplification. We obtained the frequency-dependent quality factor Q = 179f0.5598 for the northern and central parts of Costa Rica. From the output of the spectral inversion, we reproduced the acceleration spectra of earthquakes in the sites where the event was not recorded. We applied this formulation using the earthquake mentioned above. The resulting synthetic spectra are consistent with the anomalous intensity distribution reported at that time.