Transient Wave Propagation Research Articles

An origami longitudinal–torsional wave converter

Wave mode conversion has received great attention in the past few years. In this work, we propose a Kresling origami wave-mode converter which can transform the longitudinal waves of one rod to hybrid or near-pure torsional waves in the other one. Both the converted transient and steady-state wave propagation as standing waves in the proposed rod system are studied with a special focus on the frequency-dependent wave-mode contributions. With a definition of a frequency-dependent conversion ratio of longitudinal wave to torsional wave (L–T Ratio), we investigate the generation of the combined or near-pure torsional waves. The longitudinal–torsional wave conversion frequencies are tightly associated with the initial geometrical parameters of the Kresling origami. An experimental system based on optical fiber Bragg gratings (FBGs) is set up to verify the Kresling-ori wave converter. The longitudinal–torsional wave converter based on the origami engineering has potential applications in wave manipulation, wave energy distributing, or unidirectional wave transmission.

Interactions in a nonlocal thermoelastic hollow sphere with voids due to harmonically varying heat sources

The present work is devoted to discuss the transient wave propagation in an isotropic homogenous thermoelastic spherical body with voids due to harmonically varying heat sources in the context of nonlocal thermoelasticity. The constitutive relations and the governing equations are resolved by applying harmonic variations in time and transformed into coupled ordinary differential equations. The outer and the inner surfaces of the sphere are kept stress-free and free from void concentration. A harmonically varying heat source is supplied on the inner surface along the radial direction and the outer surface is assumed to be isothermal. Numerical simulations are implemented to the analytical results with the support of MATLAB software tool. Numerically, generated data are presented graphically for the field variables of interest (temperature, stresses, cubical dilation, displacement and void volume fraction field) and at the end analysis of these results are given.

Two dimensional stress wave propagation analysis of infinite 2D-FGM hollow cylinder

There are controversial findings on how projectile penetration into the human tissue can induce tissue damage. The evidence from recent experimental investigations has explained the related underlying mechanisms. To understand and simulate the exact biomechanical mechanisms of projectile penetration-induced tissue damage, we evaluated effects of two-dimensional (2D) transient stress wave propagation of 2D-functionally graded material (FGM, radial and circumferential inhomogeneity) in an infinite hollow cylinder. A periodic radial and circumferential material gradation fluctuating a constant value has been considered as the effective material properties, across the cylinder wall and the problem has been solved by implementing the graded finite element method with nonlinear Lagrangian shape functions. In contrast with other researches, the stress wave propagation for r and θ -inhomogeneity is different compared to the case in which the r or θ -inhomogeneity has been considered, separately. Moreover, this example resembles the bullet penetration in human tissue that produces stress wave propagation, resulting in unintentional trauma in human organs. For the case of 1D-FGM ( r – inhomogeneity), the responses are pulse-like and symmetric. Finally, due to shear waves, the θ -inhomogeneity has more visible effect on the stress wave propagation than r – inhomogeneity due to shear waves, especially when the pulse collapses.

Boundary element modeling of 3 T nonlinear transient magneto-thermoviscoelastic wave propagation problems in anisotropic circular cylindrical shells

The principle motivation behind this paper is to introduce boundary element modeling of three-temperature (3 T) nonlinear transient magneto-thermoviscoelastic wave propagation problems in anisotropic circular cylindrical shells under the effects of electron, ion, phonon, and total temperatures. The governing equations have solved using the boundary element method (BEM) to obtain the three-temperature, displacements and magneto-thermoviscoelastic stresses. The mathematical outcomes demonstrate that the impacts of three-temperature on the magneto-thermoviscoelastic stresses are extremely articulated. Additionally, these mathematical outcomes show the legitimacy and precision of the present mathematical strategy.

NaV1.5 knockout in iPSCs: a novel approach to study NaV1.5 variants in a human cardiomyocyte environment

Cardiomyocytes derived from patient-specific induced pluripotent stem cells (iPSC-CMs) successfully reproduce the mechanisms of several channelopathies. However, this approach involve cell reprogramming from somatic tissue biopsies or genomic editing in healthy iPSCs for every mutation found and to be investigated. We aim to knockout (KO) NaV1.5, the cardiac sodium channel, in a healthy human iPSC line, characterize the model and then, use it to express variants of NaV1.5. We develop a homozygous NaV1.5 KO iPSC line able to differentiate into cardiomyocytes with CRISPR/Cas9 tool. The NaV1.5 KO iPSC-CMs exhibited an organized contractile apparatus, spontaneous contractile activity, and electrophysiological recordings confirmed the major reduction in total Na+ currents. The action potentials (APs) exhibited a reduction in their amplitude and in their maximal rate of rise. Voltage optical mapping recordings revealed that the conduction velocity Ca2+ transient waves propagation velocities were slow. A wild-type (WT) NaV1.5 channel expressed by transient transfection in the KO iPSC-CMs restored Na+ channel expression and AP properties. The expression of NaV1.5/delQKP, a long QT type 3 (LQT3) variant, in the NaV1.5 KO iPSC-CMs showed that dysfunctional Na+ channels exhibited a persistent Na+ current and caused prolonged AP duration that led to arrhythmic events, characteristics of LQT3.

Analysis of transient wave propagation dynamics using the enriched finite element method with interpolation cover functions

To improve the performance of the low-order linear triangular element for solving transient wave propagation problems, this paper presents a novel enriched finite element method (EFEM) for wave analysis. The original linear nodal shape functions are enriched by using the additional interpolation cover functions over patches of elements. To effectively solve the wave problems, the used interpolation cover function is constructed by using the Lagrangian functions plus the harmonic trigonometric functions. The present approach can be regarded as a combination of the classical finite elements and the spectral techniques, but individual strengths of the two methods are synergized, so more accurate results can be obtained compared to the standard finite elements. In this work the root of the linear dependence (LD) issue in the present EFEM is investigated detailedly, and then an effective approach is proposed to completely eliminate the LD problem. By performing the dispersion analysis, it is found that the present EFEM possesses the attractive monotonic convergence property for transient wave propagations, that is the obtained numerical solutions will monotonically converge to the exact solutions with the decreasing time steps for time integration as long as the reasonably fine meshes are used. Several typical numerical examples are solved to illustrate the capacities of the present method.

Analysis of Propagation and Distribution Characteristics of Leakage Acoustic Waves in Water Supply Pipelines.

Leakage detection methods based on the analysis of leakage acoustic signals provide an effective technical approach for detecting small leaks in water supply pipelines. From a technical perspective, the study of the propagation characteristics of acoustic waves generated by the leakage in the water supply pipeline is necessary for detecting the leak location on the basis of acoustic signals. In this study, a 3D transient leakage acoustic wave propagation equation was derived by combining the principles of fluid dynamics and Lighthill acoustic analogy theory. The propagation of the leakage-induced noise in water supply pipeline was modelled theoretically. We simulated the propagation of a leakage acoustic wave under different conditions for different target scenarios encountered in actual pipeline inspections. Specifically, we analysed the effect of different factors, such as the pipe size and acoustic source characteristics, on acoustic propagation. Finally, the simulated experiments were practically performed using a self-designed simulated water supply pipeline and self-developed spherical water supply pipeline detector to validate the simulation analysis. The results of this study provide a theoretical guidance and basis for the analysis of characteristics of leakage acoustic wave signals and the recognition of leakage conditions in water supply pipelines.

The propagation of transient waves in two-dimensional square lattices

The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices in both plane and antiplane problems. The main idea of this article is that analytical solutions to problems of mechanics of discrete periodic media can be obtained by a method of asymptotic inversion of the Laplace and Fourier transforms in the vicinity of the quasi-front of infinitely long waves; moreover, in this method it is possible to take into account the contribution of short waves. Using this method, we obtain asymptotics of perturbations in lattices in plane and antiplane formulations under a local transient load. Besides, we show that equations describing 2D plane motion of a square lattice can be represented in the form of two linearly independent wave equations, each of which contains one unknown function only. By analogy with the theory of elasticity, one equation describes the propagation of shear waves in the lattice, while the other equation describes the propagation of longitudinal waves. As a result, it is shown that, in a homogeneous infinite lattice, a load can be specified in such a manner that either predominantly longitudinal or predominantly shear waves are formed. The problems under study are also solved by a finite difference method. The qualitative and quantitative correspondence of asymptotic and numerical solutions is shown.

Reflection and transmission of transient ultrasonic wave in fractal porous material: Application of fractional calculus

This paper provides a time domain model for the propagation of transient ultrasonic waves in a self-similar porous material having a rigid frame. This model is based on the formalism of Stillinger–Palmer–Stavrinou, which consists in modeling the fractal material as a porous medium with a non-integer dimensional space. This paper is devoted to the time-domain analytical calculus of the reflection and transmission operators that are expressed in terms of Mittag-Leffler functions. A sensitivity numerical study using ultrasonic reflected and transmitted waves is performed, highlighting the effect of the material’s physical parameters (fractal dimension, tortuosity, viscous characteristic length and porosity) on the waveforms.

Transient wave propagations with the Noh-Bathe scheme and the spectral element method

The spectral elements of the Lobatto family provide desirable characteristics of convergence and accuracy using a diagonal mass matrix in dynamic analysis. These characteristics might be expected to render the spectral element method with the use of an explicit time integration scheme effective for the transient analysis of wave propagations. In this paper we study the use of the central difference method and the recently proposed Noh-Bathe method for explicit time integration in the use of the spectral finite element method. The Noh-Bathe scheme is a second-order accurate procedure with small solution errors in the required frequency range while suppressing spurious high frequencies. We calculate appropriate CFL numbers for the time integrations and give an analysis of the dispersion errors for different orders of spectral elements. Finally, we demonstrate the capabilities of the Noh-Bathe scheme compared to the central difference method through the solution of several numerical examples of wave propagations.

Transient wave propagation in a multi‐layered soil with a fluid surface layer: 1D analytical/semi‐analytical solutions

AbstractThis paper studies one‐dimensional transient wave propagation in a saturated multi‐layered soil with a fluid surface layer. Based on Biot theory, the eigenfunction expansion method, the transfer matrix method, the state‐space method, and the precise time step integration method are employed to develop analytical/semi‐analytical solutions. For a special case (large dynamic permeability coefficient), we obtain an analytical solution. For a general case (arbitrary dynamic permeability coefficient), due to the influence of the damping term, we develop a semi‐analytical solution that can be used to evaluate sediment with small dynamic permeability coefficients. The newly derived solutions are verified with solutions obtained by the Laplace transformation and numerical inverse Laplace transformation, which are also presented here. The newly derived solutions are presented in series form in the time domain and are straightforward and explicit so that the solutions are easy to implement. Through numerical examples, we analyse the influences of the dynamic fluid permeability coefficients on the transient response of the model, which is important in marine seismic and ocean acoustics applications.

AN ANALYTICAL SOLUTION OF THE SATURATED AND INCOMPRESSIBLE POROELASTIC MODEL FOR TRANSIENT WAVE PROPAGATION

A transient wave propagation model is provided as a consequence of a new theory of porous media and wave propagation in saturated poroelastic media. This theory, in the linear case, becomes to be equivalent to the theory proposed by de Boer, R., Ehlers, W. & Liu, Z. in 1993. It leads to a model for the 1-D porous saturated column problem, which after the appropriate establishment of boundary and initial conditions, can be solved analytically with the aid of the Laplace transform concerning time. Numerical experiments are performed to illustrate the behavior of constituents displacement fields. The theory results in having an inertial effect on the motion of solid constituents as commonly expected. However, in contrast to Biot’s theory, is not introduced by the present theory the relative acceleration as an interactive force between solid and fluid constituents to account for the apparent inertial effect.

Spectral variational multiscale enrichment method—A new computational approach to transient dynamics of phononic crystals and acoustic metamaterials

Phononic crystals and acoustic metamaterials hold tremendous potential in controlling mechanical and acoustic waves, thereby enabling remarkable and novel engineering applications such as seismic wave mitigation, impact wave mitigation, elastic cloaking, and acoustic superlens. Given the potential complexity associated with the microstructure of these materials, direct numerical simulation of irregularly shaped and/or large engineering components could be computationally very costly and in many cases prohibitive. Multiscale computational modeling, coupled with model order reduction methodologies present a feasible strategy to simulate the dynamic response of phononic crystals and acoustic metamaterials. In this study, we present the spectral variational multiscale enrichment approach that allows the analysis of a broad range of material microstructures for phononic crystals and acoustic metamaterials. The spectral coarse-scale representation is proposed to capture the salient transient wave phenomena, such as wave dispersion and band gaps that occur in the short wavelength regime. A material phase based model order reduction strategy is devised at the fine-scale. By using the reduced basis for the fine-scale problem, significant numerical efficiency is achieved. Transient elastic wave propagation in two-dimensional phononic crystals and acoustic metamaterials are investigated and the proposed multiscale approach is verified against direct numerical simulations.

Uncertainty Quantification and Global Sensitivity Analysis for Transient Wave Propagation in Pressurized Pipes

AbstractAccurate simulation of pipe transient wave is crucial for the design, reliability assessment, and defect detection of water supply systems. However, this is a difficult task since the wave propagation media in pipeline systems are often highly complex and involve a range of uncertainties. Experimental data show that key parameters such as valve closure time, wave speed, and pipe material coefficients are strongly uncertain and stochastic that may vary in a wide range. To analyze the transient behavior in such complex environments, surrogate models are built to realize the fast computation of uncertainty propagation. Three surrogate modeling methods, i.e., the polynomial‐chaos‐expansion, ordinary‐Kriging, and polynomial‐chaos‐Kriging, are tested and compared in terms of transient wave forecast accuracy. The global sensitivity is then analyzed via the Sobol index method, by which the most influential uncertainty sources on various transient signal features are identified.

Model order reduction for efficient numerical room acoustic simulations with parametrized boundaries

This study presents a new model order reduction technique applied to room acoustic simulations using a high-order numerical scheme based on the spectral element method. The goal is to efficiently simulate iterative design processes in room acoustics, where the room acoustics with different boundary absorption properties are evaluated much quickly without solving the full wave equation. The wave-based methods are highly accurate but expensive when simulating high-frequencies and long simulation times in large and complex geometries, which are needed for industrial applications. Hence, it remains a key challenge to improve the computational performance of room acoustics simulations with different boundary material possibilities. With model order reduction, the boundary condition can be parametrized in the subsequent modelling. This allows to reduce the dimensionality of a wave-based simulator without compromising the transient wave propagation accuracy while enabling significant reductions of computational costs after initial training using proper orthogonal decomposition. We provide evidence that the combination of the high-order numerical scheme with model order reduction has significant potential value for building acoustics in terms of computational efficiency and accuracy.

Proper Generalized Decomposition with time adaptive space separation for transient wave propagation problems in separable domains

Transient wave propagation problems may involve rich discretizations, both in space and in time, leading to computationally expensive simulations, even for simple spatial domains. The Proper Generalized Decomposition (PGD) is an attractive model order reduction technique to address this issue, especially when the spatial domain is separable. In this work, we propose a space separation with a time adaptive number of modes to efficiently capture transient wave propagation in separable domains. We combine standard time integration schemes with this original space separated representation for empowering standard procedures. The numerical behavior of the proposed method is explored through several 2D wave propagation problems involving radial waves, propagation on long time analyses, and wave conversions. We show that the PGD solution approximates its standard finite element solution counterpart with acceptable accuracy, while reducing the storage needs and the computation time (CPU time). Numerical results show that the CPU time per time step linearly increases when refining the mesh, even with implicit time integration schemes, which is not the case with standard procedures.

Bayesian damage localization and identification based on a transient wave propagation model for composite beam structures

This paper proposes the use of a physics-based Bayesian framework for the localization and identification of damage in composite beam structures using ultrasonic guided-waves. The methodology relies on a transient wave propagation model based on wave and finite element scheme that efficiently provides time-domain signals that are compared with the ultrasonic measurements within a multilevel Bayesian framework. As a key contribution, the proposed methodology enables the localization and identification of damage using just the signals without any baseline comparison or further transformation, hence reducing additional sources of uncertainty. The proposed Bayesian approach allows (1) the localization of the defect, and (2) the identification of different candidate damage hypotheses and their ranking based on probabilities that measure their relative degree of belief. The methodology is illustrated in carbon fiber reinforced polymer beams with different layups. An investigation into how the measurement noise can impact the identified damage properties is also provided. The results show the effectiveness and efficiency of the proposed approach in reconstructing and identifying different types of damage in long and complex composite beams at a relatively low computational cost.

Field Measurements and Numerical Modeling of Hydraulic Transients in HDPE Pipeline with PRV Interaction

Pressure reducing valves (PRVs) and high-density polyethylene (HDPE) pipes are commonly used in urban water supply systems (UWSS). To study the joint effect of PRV and viscoelasticity on transient wave propagation, extensive experiments have been conducted in a field-scale reservoir-PRV-viscoelastic pipeline system covering a wide range of internal pressure heads (∼10 to 60 m) and air temperatures (12°C–33°C). In addition, a one-dimensional method of characteristics (MOC) based model that incorporates a PRV model and the generalized Kelvin-Voigt (K-V) model for pipe viscoelasticity is developed and validated against field data for the first time. The simulated transient pressures are in good agreement with field measurements. The K-V parameters exhibit a clustered distribution and the mean value for each element can provide a satisfactory simulation. The PRV in hydraulic transients can be interpreted as a quasi-dead-end with a self-adjusting opening, and causes additional positive pressure wave reflections that are gradually damped due to viscoelasticity. The dynamic changes in PRV opening, head loss, pressure wave reflection, and transmission induced by an incident pressure surge are predicted. Due to the joint action of PRV and pipeline viscoelasticity, the pressure oscillations in an intact pipe settle to a value that is considerably higher than the initial PRV set pressure. In a leaking pipe, the downstream pressure reverts to the original set pressure within a few wave cycles. Leaks can be detected by wave reflections in the time domain signals. The existence of leaks is also found to be associated with the the amplification and damping of the frequency response function (FRF) of the system at certain resonance peaks. This study provides new insights into wave propagation in HDPE pipeline with PRV interaction and an original data set for validation of leakage detection methods.

Non-convolutional second-order complex-frequency-shifted perfectly matched layers for transient elastic wave propagation

The numerical simulation of wave propagation in heterogeneous unbounded media using domain discretization techniques requires truncation of the physical domain: at the truncation boundary, Perfectly Matched Layers (PMLs) – buffers wherein wave attenuation is imposed – are often used to mimic outgoing wave motion and prevent waves from re-entering the interior computational domain. The PML’s wave-dissipative properties derive from a coordinate mapping concept, where the physical coordinate is mapped onto a frequency-dependent complex coordinate in the PML via a complex stretching function. The choice of the stretching function controls not only the spectral character and the absorptive properties of the PML, but also, more critically, the long-time stability when the computational domain-PML ensemble is used for transient wave simulations.The standard PML stretching function can lead to error growth, particularly when propagating waves impinge at grazing incidence on the truncation boundary. By contrast, a modification to the standard stretching function that has led to the Complex-Frequency-Shifted CFS-PML has been shown to alleviate the temporal instability. However, whereas PML formulations using the standard stretching function can lead to second-order in time semi-discrete forms, affording multifaceted benefits, all CFS-PML formulations to date require the evaluation of convolutions. In this paper, we discuss a new CFS-PML formulation that avoids the evaluation of convolutions, while preserving the second-order temporal character of elastic waves. It is shown that, upon spatial discretization, the CFS-PML can be completely described by a triad of stiffness, damping, and mass matrices, which can be readily incorporated into existing finite element codes originally designed for interior problems, to endow them with wave simulation capabilities on unbounded domains. Numerical experiments in the time-domain demonstrate the efficacy of the proposed approach; we also report long-time stability for problems involving waveguides and grazing wave incidence.

Application of Chebyshev collocation method to unified generalized thermoelasticity of a finite domain

In this article, the Chebyshev collocation numerical method is developed for solving generalized thermoelasticity problems of the isotropic layer. The coupled thermoelastic equations are derived based on Lord-Shulman (LS), Green-Lindsay (GL) and Green-Naghdi (GN) theories. Two kinds of shock loading are considered. In the first model, a temperature shock is applied at the left side of the layer, and in the second model a heat flux shock is applied at the mentioned side. The displacement and temperature fields are approximated in the layer by Chebyshev polynomials and then the collocation is imposed on some collocation points to derive the system of ordinary differential equations from the coupled partial differential equations. The derived system of differential equations is then solved by the Wilson method to achieve the displacement and temperature and also stress at any location and time. The obtained results from the present article are compared with the same results in the open literature and a very close agreement is observed. Finally, it is concluded that the Chebyshev collocation numerical method can be utilized as a very strong method for solving the transient wave propagation problems.