Transient Wave Propagation Research Articles

The transient dynamic wave process in unidirectional composites

The propagation of nonstationary waves in unidirectional composite material is simulated by finite-element analysis. The composite material is explicitly formulated, i.e., discrete, stiff, elastic inclusions uniformly distributed in a viscoelastic matrix are modeled. An original procedure rooted in the linear Boltzmann–Volterra equations accounts for the viscoelastic effects in the matrix behavior. The chosen approach involves finite-element simulations of the transient wave process in two indicative configurations to study the effects attributed to wave scattering by the inclusions. The transient wave propagation in the unidirectional composite material and a viscoelastic specimen without inclusions are compared. Peculiarities in the numerical results due to the finite-element algorithm employed are decoupled from the output that reveals purely mechanical phenomena. For this purpose, the transient wave propagation in a one-dimensional elastic continuum, for which the exact analytical solution is well known, is effectively obtained by finite-element analysis. Furthermore, based on the unidirectional composite a homogenized model is defined by applying the mixture rule. An additional comparison between the composite containing discrete inclusions and the analogous homogenized material provides a basis to assess the output of models obtained by implementing a self-consistent scheme in a broader context.

Analysis on transient wave propagation in the soft matter of hydrogels

The precise control and structural design of the soft matter of the hydrogel subjected to dynamic loading require an in-depth understanding of its transient wave characteristics. However, for the complex solid–liquid coupling effects of the soft matter of hydrogels, the traditional single-phase wave model is no longer applicable. In this study, a transient wave propagation model that considers the solid–liquid coupling effects and its computational method is proposed. The wave-governing equations of hydrogels are derived based on the mass conservation and dynamic equilibrium equations, where the motions of solid and liquid phases are independently described. After transforming the governing equations into the equivalent weak form, numerical solutions for transient wave propagation in one- and two-dimensional hydrogels are calculated. The accuracy of the proposed model is verified by a comparison between semi-analytical and commercial finite element method solutions. We observe that the travelling and reflection processes of the two types of compression waves, P1 and P2, with different wave speeds are captured when the dynamic coefficient of permeability kf increases. Furthermore, the influence of solid–liquid coupling effects on the transient responses of hydrogels is discussed. The results show that the hydrogels exhibit the dynamic characteristics of a single-phase medium to a certain extent when kf is sufficiently small.

Enhanced damping and bandwidth in roton-like dispersion of a beyond nearest neighbor periodic chain

This paper investigates the intriguing roton-like phenomenon occurring in systems with non-local interactions, wherein a single dispersion curve exhibits positive and negative group velocities. Previous research has predominantly concentrated on investigating the roton dispersion in undamped metamaterials through steady-state vibration and driven wave methodologies. However, exploring transient wave propagation in damped metamaterials, employing a free wave approach to study damping enhancement (metadamping), has received comparatively little attention. Addressing this research gap, the damping of the system is quantified as the rate of decay of transient vibrations. Results show a significant increase in damping and attenuation bandwidth, coinciding with the presence of the roton-like phenomenon. Unlike previous studies on metadamping, the proposed beyond nearest neighbor (BNN) chain simultaneously enhances both damping and reduction in acoustic bandwidth without sacrificing either property. Spatiotemporal domain simulation evidenced the existence of backward propagating wave packets due to a roton-like phenomenon in the specific frequency range.

Transient behavior of a plate partially immersed in the fluid subjected to impact loadings: Theoretical analysis and experimental measurements

This study aimed to investigate the transient behavior of a rectangular plate partially in contact with fluid subjected to a dynamic external force. To this purpose, a theoretical model was developed to analyze vibration characteristics and transient wave propagation. Based on superposition method, the dry mode shapes and natural frequencies of the plate under vacuum could be obtained. The dry mode shapes were treated as the fundamental function to construct the wet mode that describes the vibration behavior of the fluid-plate coupled system. The velocity potential and fluid pressure within a finite tank due to the plate deflection were derived using an equation governing the incompressible fluid. Based on the relationship between dry mode shape and wet mode shape, the fluid-plate coupled system's wet mode shape and resonant frequency could be determined from the frequency response function. Applying the normal mode method, the transient displacement of plate and fluid pressure can be obtained by solving a system of non-homogeneous differential equations. The theoretical predictions were verified by finite element method (FEM) and experimental measurements. Experiments were conducted using piezoelectric film sensors (polyvinylidene fluoride, PVDF) to measure the force history induced by a steel ball impact to quantitatively analyze the transient response. The comparison results proved that the theoretical predictions and experiments were in good agreement, including the transient responses of the displacement and in-plane strain of a plate partially submerged in the fluid. The results indicate that changes in water depth can induce resonance frequency shifts and wet mode shape distortions, which also illustrate that the vibrational properties of wet modes affect transient behavior. The proposed transient solution demonstrates an analytical approach that connects the physical significance of the dynamic behavior of the fluid-plate coupled system in time and frequency domains; it provides a connection between the transient behaviors and vibration characteristics.

Transient computational homogenization of heterogeneous poroelastic media with local resonances

AbstractA computational homogenization framework is proposed for solving transient wave propagation in the linear regime in heterogeneous poroelastic media that may exhibit local resonances due to microstructural heterogeneities. The microscale fluid‐structure interaction problem and the macroscale are coupled through an extended version of the Hill‐Mandel principle, leading to a variationally consistent averaging scheme of the microscale fields. The effective macroscopic constitutive relations are obtained by expressing the microscale problem with a reduced‐order model that contains the longwave basis and the so‐called local resonance basis, yielding the closed‐form expressions for the homogenized material properties. The resulting macroscopic model is an enriched porous continuum with internal variables that represent the microscale dynamics at the macroscale, whereby the Biot model is recovered as a special case. Numerical examples demonstrate the framework's validity in modeling wave transmission through a porous layer.

Thermal effect on the transient behavior of a piezomagnetic half-space subjected to dynamic anti-plane load

Considering the importance of understanding the propagation of transient waves in the piezomagnetic solids, the thermal effect on the transient behavior of a piezomagnetic half-space subjected to dynamic anti-plane load is investigated analytically in this paper. Using one-sided, two-sided Laplace transformation and Cagniard–de Hoop (CH) technique, an efficient and accurate analytical derivation for the solution of the anti-plane displacement, shear stress, magnetic potential, and induction in Laplace domain is presented. The study shows that the thermal stresses developed in x-axis and y-axis directions have significant influence on the transient response of the half-space. The magnetic induction B x increases obviously when the thermal stress is applied in x-axis direction, while it decreases when the thermal stress is applied in y-axis direction. Approaching time of magnetic induction B x and B y will become longer with higher thermal stress in x-axis direction. With the growth of the thermal stress in x-direction, contribution from the electromagnetic–elastic head (EH) wave increases, while the contribution from the shear elastic (SE) wave and the static value of shear stress decrease.

Dissipative stratified elastic metamaterials for broadband blast-wave impact mitigation

In this paper, impact attenuation and blast-wave mitigation are effectively realized by the dissipative stratified metamaterials with negative mass mechanism due to the coupling of the different resonators. To create a broad bandgap of the metamaterials, the dispersion curve and effective negative mass property are investigated. It is found that the coupling effect of different resonators produced by the relative movement of different main masses can create a broad bandgap and make the original bandgap by starting with a lower frequency, and thus impact input waves could be blocked effectively. Simulation results show that a stratified elastic metamaterial containing 25 units can reduce the amplitude of the load by two thirds under impact loading and almost completely impede its further propagation. Furthermore, the bandgap is broadened by optimization of the structure parameters and dissipative coefficient for blocking transient shock waves propagation. It is shown in numerical experiment that the wider bandgap produced by the new elastic metamaterials can effectively absorbed the energy of the blast and impact waves. Therefore, the results of this study provide a remarkably novel strategy for the design of new blast-resistant materials.

Theoretical and numerical study on transient acoustic wave propagation across ice layers in the Arctic Ocean.

The study of transient acoustic wave propagation across the Arctic Ocean ice layer provides theoretical guidance for the design of trans-ice acoustic communication systems. In this study, the Arctic Ocean was modeled as an ice-water composite structure, where the ice and water are regarded as an elastic solid and liquid, respectively. An analytical transient solution for acoustic wave propagation in this structure was derived using the eigenfunction expansion method. Further, the numerical procedures were presented and used to analyze the acoustic wave propagation characteristics across the ice layer. The results show that waveforms corresponding to the radial displacements are more severely distorted than the axial displacements. The amplitudes of the radial and axial displacements decreased rapidly with increasing propagation distance. The ice thickness had a greater impact on the radial displacement than axial displacement; the thicker the ice, the greater the distortion for both radial and axial displacements.

On the development of a constitutive model for steel subjected to fire and explosion

The behavior of steel under thermal and mechanical loading including high transient temperatures and strain rates (e.g., fire, creep or explosion) is extremely complex. To study this behavior, we propose a constitutive model accordance with the laws of thermodynamic, the principle of virtual power and experimental results. The thermodynamic framework considers the Clausius-Duhem inequality and maximum dissipation rate principle, as well as the theory of finite deformations, linear isotropic viscoelasticity, nonlinear isotropic and kinematic hardening, local and non-local viscoplasticity, local and non-local anisotropic viscodamage and parameters associated to material behavior dependent on loadings. The components of the thermodynamic conjugate forces are defined from the Helmholtz free energy function and the rate of energy dissipation, which are postulated considering the creep phenomenon, thermal-mechanical transient phenomenon, cyclic phenomenon and plastic wave propagation phenomenon. The balance of microforces is defined based on the principle of virtual power. A novel rule of non-associated thermo-viscoplastic flow of the Perzyna type and a novel rate dependent local and non-local damage evolution law are introduced from constitutive model. The verification of the model was carried out in two benchmark studies composed of fire tests. The predictions of the model have shown in according with the results of the experiments. A sensitivity study was also performed with a view to analysis the influence of the parameters in achieved results. From this study a simplified constitutive model is presented. Benchmark studies composed of explosion tests are part of future work.

On the Application of Fractional Derivative Operator Theory to the Electromagnetic Modeling of Frequency Dispersive Media

Fractional derivative operators are finding applications in a wide variety of fields with their ability to better model certain phenomena exhibiting spatial and temporal nonlocality. One area in which these operators are applicable is in the field of electromagnetism, thereby modelling transient wave propagation in complex media. To apply fractional derivative operators to electromagnetic problems, the operator must adhere to certain principles, like the trigonometric functions invariance property. The Grünwald–Letnikov and Marchaud fractional derivative operators comply with these principles and therefore could be applied. The fractional derivative arises when modelling frequency-dispersive dielectric media. The time-domain convolution integral in the relation between the electric displacement and the polarisation density, containing an empirical extension of the Debye model, is approximated directly. A common approach is to recursively update the convolution integral by approximating the time series by a truncated sum of decaying exponentials, with the coefficients found through means of optimisation or fitting. The finite-difference time-domain schemes using this approach have shown to be more computationally efficient compared to other approaches using auxiliary differential equation methods.

Lost circulation detection method based on cepstrum analysis of transient pressure waves

Encountering natural fractures or unbalanced formation pressure during oil drilling can result in economic loss and environmental pollution due to well leakage. Existing detection methods encounter challenges such as high costs, complex downhole environments, and difficult data acquisition. To address these issues, we propose a well leakage detection method using cepstrum for analyzing transient pressure waves. Cepstrum is a signal Fourier transform after logarithmic operation and then Fourier inverse spectrum obtained. By studying the propagation of transient pressure waves in the wellbore, we identify drilling fluid leakage location and amount based on time-dependent and amplitude changes of pressure wave signal characteristic peaks. To handle noise in the pressure wave signal, we employ adaptive noise-complete ensemble empirical modal decomposition (CEEMDAN) and wavelet threshold (WT) joint denoising. Correlation coefficient (CCF) with the Hilbert joint spectrum (HJS) is used to extract main frequency components, achieving denoising. Experimental results confirm: ① Noise interference in transient pressure waves is effectively suppressed using the CEEMDAN-WT-CCF-HJS denoising method. ② Cepstrum analysis of the pressure wave signal during wellbore annulus system leakage reveals distinct reflected wave characteristic peaks, aiding in locating different leakage points, with the amplitude of these peaks reflecting the size of the leakage. ③ This method efficiently utilizes time-frequency information from the excitation pressure wave signal, offering advantages over traditional time-domain and frequency-domain analysis. Experiments covering various leakage scenarios, amounts, and borehole sizes yielded controlled experimental errors (2.25%–9.10%), within a reasonable range. The method's validity and reliability were confirmed, providing theoretical support and technical guidance for well leakage detection in oil drilling.

Combined Data-Driven and Model-Driven Location of Lightning Strikes: Application to Meshed HVDC Grids

This paper addresses the low-delay location of faults due to lightning strikes using single-ended measurements in HVDC grids. A combined data-driven and model-driven approach is used to estimate the fault location iteratively. No prior knowledge of the voltage evolution at the fault location is required. Once the first wavefront due to a fault is detected at some observation location of the HVDC grid, the measurements are fed to a model of the propagation of transient waves along the lines. The model is parameterized by the estimated fault location. As a result, a model of the waveform samples starting from the second wavefront is obtained. The measured and modeled waveform samples are then compared to update the estimate of the fault location. The performance of the proposed approach is evaluated via simulations, including field measurements of lightning currents. Typical location accuracy of 300 m is obtained by considering observations performed at 1 MHz over an observation time interval of less than 1.5 ms.

Inverse transient analysis based calibration of surrogate pipeline model for fault simulation of axial piston pumps

Axial piston pumps are the key component in power hydraulic systems. Flow and pressure ripple signals, which can reflect the flow dynamics of the axial piston pump, are important information sources for condition monitoring. Therefore, the characteristics of flow and pressure ripple signals should be investigated for further condition monitoring and fault analysis. However, measuring high-frequency flow ripple directly can be difficult, and the pressure ripple is not only affected by pump dynamics but also affected by the transient pressure wave propagation. However, in practical applications, the hydraulic pipeline system is complex due to the space constraint of the equipment, and the influence of the pipeline system cannot be ignored when modeling pressure ripple. This paper proposes a novel two-stage method for fault simulation of the pumps that considers the influence of the pipeline system on the pressure ripple. Firstly, the surrogate pipeline model with free parameters is calibrated using ITA to capture the characteristics of the complex practical pipeline system. Secondly, the calibrated model is applied to the fault simulation of axial piston pumps. A detailed 3D CFD model of the pump is built up, and the flow ripple at the pump outlet from the numerical model is used as an approximation of the real flow ripple of the pump, which serves as one of the boundary conditions of the surrogate pipeline model. After calibrating the model, the CFD model of the pump is used to simulate internal failures in the pump. Two failure cases are studied: a faulty slipper and a faulty cylinder. The simulated signal of the proposed model matches the experimental signal well under the healthy and faulty conditions, which confirms the effectiveness of the proposed method.

A new technique to measure the dynamic fracture toughness of solids

We propose and assess a new experimental technique to measure the fracture toughness of engineering materials and its sensitivity to strain rate. The proposed method is based on a ring expansion technique and it overcomes the limitations of current dynamic fracture tests, as it is not affected by transient stress wave propagation during loading and it results in spatially uniform remote stress and strain fields prior to fracture; the method is also suitable to achieve remote strain rates well in excess of 1000 s−1. We demonstrate the technique by measuring the plane-stress Mode I fracture toughness of PMMA specimens at remote strain rates ranging from 10−3 s−1 to 102 s−1. The experiments show an increase of the toughness of the material with increasing strain rate.

Performance of the quadrilateral overlapping elements combined with implicit time integration method in solving the transient wave propagations

In the analyses of transient wave propagations, a numerical method with the monotonic convergence property is favored by analysts. However, the classic finite element method does not possess this attractive property due to pronounced numerical dispersions and can generate severe spurious oscillations by using a small time step. In this work, the novel quadrilateral overlapping element is extended into the investigation of transient wave propagations by using the standard implicit Bathe time integration method. Since the local field approximation in overlapping elements can be a function, the performances of different basis functions in transient wave propagation problems are studied. Detailed analyses regarding the numerical dispersion error caused by spatial and temporal discretization are conducted. Then several numerical experiments with different types of excitation loading are investigated to show the performance of the quadrilateral overlapping elements. It is shown that the overlapping element with the trigonometric functions and the bilinear Lagrange polynomials has the monotonic convergence property and can perform well in handling various transient wave propagation problems.

The edge-based smoothed FEM with [formula omitted]-Bathe implicit temporal discretization scheme for the analyses of underwater wave propagation problems

The underwater acoustic wave propagation problem is an important issue in ocean engineering field. The classical finite element approach with edge-based smoothed gradient smoothing technique is incorporated into the novel ρ∞-Bathe implicit direct time integration scheme in this paper for solving underwater transient acoustic wave propagation problems. This edge-based smoothed FEM (ES-FEM) and ρ∞-Bathe method are employed to perform the space and time domain discretization, respectively. Due to the appropriate softening effects from the ES-FEM, the space discretization errors can be markedly reduced. Meanwhile, the possible numerical error related to the temporal discretization also can be significantly suppressed by the novel ρ∞-Bathe method which possesses the controllable numerical damping effects. Through detailed analysis of the total dispersion error, we find that the numerical results from the proposed scheme can converge monotonically to the exact solutions when employing the decreasing temporal discretization intervals and the possible numerical anisotropy effects are also effectively suppressed. These excellent numerical performance clearly distinguish the present method from the conventional approaches and make it to be particularly suitable for complicated acoustic wave propagation analysis. Finally, various typical numerical experiments are performed to illustrate the capacities of the proposed scheme in tackling underwater transient acoustic wave propagation problems.

Signature and kinetics of stochastic branching of light in disordered active photonic lattices

Branched flow is a form of transient wave propagation event that occurs in extreme circumstances. We demonstrate branched propagation of light in a silica-based active disordered photonic lattices. The test-bed proposed here can be completely tailored thus providing us ample scope to study various aspects of the branched flow and explore a better insight of the formation of branches. It is observed that by applying gain above a threshold level, the branches are formed which travel through the lattice resulting in an intense collimated beam that might lead to the development of a new type of nano-laser in the near future.

An energy preserving time scheme based on the mortar element method for effective transmission conditions between fluid and solid domains in transient wave propagation problems

AbstractWe are interested in providing an efficient numerical scheme to represent wave propagation in time domain for configurations where a fluid domain and a solid domain are separated by a thin coating layer. Various computational challenges and bottlenecks occur in this context: incorporating fluid–solid coupling, enabling non‐conform space discretization when wavelengths greatly differ from the fluid and the solid domain, and rendering robust time discretization w.r.t. the thin layer thickness. In order to address these issues, the proposed approach combines the mortar element method with so‐called effective transmission conditions, where the effect of the coating layer is incorporated through spring—mass coefficients at the interface between the fluid and solid domain. Using discrete energy arguments, we are able to prove that the associated fully discrete scheme is stable upon a stability condition independent of the thin coating layer. Moreover, we provide an efficient time marching algorithm leading to significantly improved performances, illustrated in 2D and 3D configurations linked to ultrasonic testing experiments modeling.

A Hybrid 3-D-ADI-TDPE/DGTD Method for Multiscale Target Echo Simulation in Large-Scale Complex Environments

In this article, we propose a novel hybrid method for multiscale target echo simulation in large-scale complex environments. The three-dimensional-alternating direction implicit-time domain parabolic equation (3-D-ADI-TDPE) method with refractive index terms and the discontinuous Galerkin time-domain (DGTD) method are combined to solve the propagation of transient electromagnetic waves in large-scale regions and backscattering in multiscale target regions, respectively. At the same time, to realize the connection of two regions and the prediction of target echo, the transfer functions of wave propagation and target backscattering are obtained by the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Z$ </tex-math></inline-formula> transform (ZT). In addition, the target echo process is transformed into a cascade of transfer functions to realize simulation modularization and parallel processing. We also discuss the performance of the proposed method in terms of accuracy, memory consumption, and CPU processing time. Results indicate that the processing time required by the 3-D-ADI-TDPE/DGTD hybrid method is more than 11 times less than that of DGTD alone. Moreover, the ZT improves the flexibility of the hybrid method and provides a new concept for the simulation technology of radio wave propagation.

Molecular Kinetic Simulations of Transient and Steady Wave Propagation into a Planet’s Exosphere

The vertical propagation of wave energy into a planet’s exosphere, a process that affects atmospheric evolution, is calculated here using 1D molecular kinetic simulations. Effects sensitive to molecular interactions are examined by comparing simulation results to solutions of linear fluid models for steady wave activity using parameters associated with Mars’ upper atmosphere. In addition to correctly describing the wave behavior in the exobase region, these simulations directly yield nonlinear effects such as atmospheric heating. They also readily include the transient behavior due to the onset and decay of waves propagating into the rarefied region of a planet’s atmosphere. This is a first step in understanding the effects of variable wave activity in the region where the atmosphere evolves from collisional to collisionless.