Longitudinal Propagation Research Articles

Thermoelastic wave propagation in thin beams under thermal shock loading

An analytical solution is presented for the thermoelastic longitudinal and flexural wave propagation in transversely isotropic thin beams subjected to a thermal shock loading using the Lord–Shulman generalized thermoelasticity theory. The formulation considers a general through-thickness profile of the applied thermal loading, does not assume the across-thickness distribution of the temperature field and considers a general convective boundary condition at the beam surfaces. The thin beam is modeled using the Euler–Bernoulli beam theory. The governing equations of motion and the variationally consistent boundary conditions are derived from the extended Hamilton’s principle. The coupled thermoelastic equations are solved in the Laplace domain satisfying the thermal and mechanical boundary conditions using the homotopy perturbation method. The Laplace inversion to obtain the final solution in the time domain is performed numerically by using Durbin’s method. The formulation is validated by comparing the results for longitudinal wave propagation response under uniform thermal loading with those available in the literature. The developed solution is then employed to study the longitudinal and flexural wave propagation behaviour of a cantilever beam subject to uniform and non-uniform symmetric, and linear and non-linear anti-symmetric thermal shock loading applied at the free end. The effects of thermal boundary conditions at the beam surfaces and the relaxation time parameter on the response of the beam are illustrated.

Evaluation of [formula omitted]-curves and cohesive law in mode I of European beech

This work addresses the determination of the cohesive laws in Mode I and tangential–longitudinal (TL) crack propagation system of Fagus Sylvatica L. This species is one of the ever-growing and most widely used hardwood species in Europe for engineered timber products. Double Cantilever Beam (DCB) tests are performed. The strain energy release rate (GI) is derived from the R-curves by applying the Compliance-Based Beam Method (CBBM), which has the advantage of not requiring the measurement of the crack length during propagation, but only the global load–displacement curves. The cohesive law of the material is determined from the relationship between GI, and the crack tip opening displacement (CTOD) monitored for each specimen using Digital Image Correlation (DIC). Numerical finite element models are developed by implementing the average cohesive law through Cohesive Zone Models (CZM). An average GI value of 0.46 kJ/m2 is obtained for this species. The numerical load–displacement curves are consistent with the experimental results, which demonstrates the suitability of the method for the identification of the cohesive laws in beech. The fracture properties obtained are essential in the development of advanced and reliable numerical models in timber engineering design using this species.

Metamaterial Liner for MRI Excitation—Part 2: Design and Performance at 4.7T

The theoretical foundations of a metamaterial (MM) liner for the MRI bore that facilitates the propagation of reduced-cutoff cylindrical waveguide modes are presented in the Part 1 companion paper to this work. Here, in Part 2, the practical design and modelling of the novel MM liner is applied to a body MRI radio-frequency (RF) transmitter for 4.7T. An equivalent network mesh model is developed to reduce the distributed structure of the MM to one that uses lumped discrete tuning elements. The close match between full-wave simulation and the network model is demonstrated by comparison of the longitudinal propagation dispersion curves and input impedance. The application of the methods developed for analysis of the MM liner behavior are demonstrated in the design of a practical MM liner as an effective MRI RF transmitter. The liner’s simulated performance was evaluated using three key metrics of MR radio-frequency (RF) coil performance: transmit efficiency, the variation of the transmit field (a measure of homogeneity), and the 10g averaged local specific absorption rate (SAR). These metrics are compared to those of the commonly used birdcage (BC) coil. The main advantage of the MM liner is the 29.6% reduction in maximum SAR normalized to transmit field relative to the BC coil, with comparable transmit efficiency and homogeneity. Thus, the liner can potentially replace the BC coil as an RF transmitter and provide an enhanced safety margin, or allow the use of faster, more SAR-aggressive imaging sequences.

Waveguide Characteristics Near the Second Bragg Condition

We show that in an optical waveguide with no material losses at wavelengths near the second-order Bragg condition, there exists two pairs of modes. One pair has identical propagation constants but have different attenuation coefficients, while a second pair with identical propagation constants (different from the first pair) and have different attenuation coefficients. The four attenuation coefficients may have either a positive value, representing power leaking out of a waveguide mode or a negative value, representing power from an external source leaking into a mode. Moreover, a mode with a positive (negative) attenuation before the second Bragg condition, has a negative (positive) attenuation after the second Bragg condition. Radiation near the second-order Bragg condition of a periodic waveguide typically occurs at an angle perpendicular or nearly perpendicular to the propagation direction of the waveguide because the scattering centers have a period equal to or close to the period of the longitudinal propagation constant of the mode. In this paper, stable numerical solutions for the modes of periodic dielectric structures are developed using Floquet-Bloch theory. One primary focus in this paper illustrates a unique method of analyzing such modes using eigenvectors forming a Hilbert space, allowing for expansion of arbitrary vectors and their derivatives used for calculations such as that involving group velocities. The dimension of the vector space is determined by the number of space harmonics used in the solution of the Floquet-Bloch equations. The accuracy of the numerical solutions is affected by the number of space harmonics; as that number is increased, the number of waveguide partitions must be increased to maintain a given accuracy.

Mechanical property and failure mechanisms of hot rolling and aging treatment with different layer thickness on (CoCrNi)94Al3Ti3/ Maraging -C350 multilayer composite steel

The (CoCrNi)94Al3Ti3/Maraging-C350 multilayer composite steel with average thickness of 120 μm, 40 μm and 35 μm were prepared by vacuum hot rolling technique, which realized the combination of toughness and high strength. Meanwhile, the composite interface with good combination was obtained. Compared with 25 layers-120 μm (CoCrNi)94Al3Ti3/Maraging-C350 multilayer and 60 layers-40 μm (CoCrNi)94Al3Ti3/Maraging-C350, the tensile strength and interface shear strength of 100 layers-35 μm (CoCrNi)94Al3Ti3/Maraging-C350 sample increased to 1110 MPa and 382 MPa, the tensile specimen with a highest elongation of 44.2%. After 515 °C-5 h aging treatment, the tensile strength increased from 1100 MPa to 1710 MPa, and the shear strength increased to 461 MPa. Simultaneously, 100L-HR-A specimen had the highest uniform elongation of 20%. The decrease of elongation after aging treatment was due to the hardening and the transformation of the fracture mode of Maraging-C350 layers, and the deterioration of deformation coordination of (CoCrNi)94Al3Ti3/Maraging-C350 multilayer composite steel. Microcracks and plastic deformation occurred at the interface of the transition layer, delamination was formed because of their transverse propagation, the tunnel cracks were formed owing to its longitudinal propagation. The samples with small thickness scale showed higher fracture toughness. More interlaminar structures could enhance the passivation effect of the toughened layer on cracks, and delay the early necking and collapse of the samples.

Multi-layer longitudinally specular optics for distributing diffuse light.

Multi-layer optical thin films can reflect light to guide it along a hollow tube that they internally line. However, reflecting broadband white light for a range of angles requires many precise thin optical layers, which can be too expensive for large-scale applications such as architectural illumination. Here, we present an alternative configuration that requires only one readily achievable aspect of precision-having a substantially constant cross section, perpendicular to the planned longitudinal propagation direction. This aspect conserves a light ray's longitudinal directional component, while the ray's path in the perpendicular direction can be macroscopically chaotic, much like the diffuse reflection characteristic arising from many non-absorbing pigment particles. This macroscopic characteristic is described here as "longitudinally specular" and "transversely diffuse." This new design overcomes two problems that are found with current prism light guides (PLGs), which are a class of hollow light guides that also have a constant cross section. The PLG has two problems: (1) it requires structured surfaces having near-perfect linear prisms that are much larger than the wavelength of light, wasting optical material and increasing absorption; (2) it only works well with light that has been partially collimated, which limits étendue and requires expensive, inefficient input optics. In this paper, a new, to the best of our knowledge, approach, labeled a "multi-layer prism light guide," simultaneously addresses both problems. Although the new structure is more complex than a conventional PLG, it may be simpler to manufacture. One potential application is for guiding sunlight into buildings for illumination purposes, without requiring complex sun-tracking solar collection optics.

Microglial activation and tau propagate jointly across Braak stages

AbstractBackgroundCompelling experimental evidence suggests that microglial activation is involved in the spread of tau neurofibrillary tangles over the neocortex in Alzheimer’s disease (AD). Here, we tested the hypothesis that the spatial propagation of microglial activation and tau accumulation colocalize in a Braak‐like pattern in the human brain.MethodWe studied 130 subjects (86 cognitively unimpaired and 44 cognitively impairment elderly) with microglia activation [11C]PBR28 PET, Amyloid [18F]NAV4694 PET, cognitive tests, magnetic resonance imaging, and cerebrospinal fluid (CSF) biomarkers. Participants also had baseline and follow‐up tau [18F]MK6240 PET scans. We used linear regressions and partial correlations to estimate the association between topographical distributions of microglial activation and tau accumulation.Result(A)Microglial activation (MA) connectivity analysis between regions comprising Braak histopathological stages (Braak I‐VI) across our population demonstrated that MA regions correlated hierarchically with each other, where a Braak‐like stage region only correlates with the previous and subsequent stage. (B)Tau tangles connectivity analysis between regions that comprise Braak stages (Braak I‐VI) across our population demonstrated that tau regions correlated hierarchically with each other, where a Braak stage only correlates with the previous/subsequent stage (C)The scatterplot shows that the elements of the MA‐MA matrix and tau‐tau matrix were highly positively correlated with each other, reinforcing the notion of a joint topographic propagation of MA and tau tangles through Braak stages. (D) Rates of tau propagation over 1‐year hierarchically correlated in Braak stages. (E)Significant Pearson correlation between longitudinal tau propagation and baseline tau network. (F)Significant Pearson correlation between longitudinal tau propagation and baseline microglia network. (G)Partial residuals plots show the results of regression between network of tau propagation over 1‐year and both baseline topographic circuits, MA‐MA and tau‐tau networks. The model suggests that the pathways of longitudinal tau propagation depended on underlying microglia, rather than tau circuits. (H)The figure shows thatmicroglial activation levels in the transentorhinal cortex predicted longitudinal tau spread over the neocortex.ConclusionOur results support a model in which an interaction between amyloid load and activated microglia set the pace for tau spread across Braak stages, while the simultaneous cerebral presence of these pathologies potentiates the development of dementia.

Ultrasonic Evaluation of Porosity in Out-of-Autoclave Carbon Fiber–Reinforced Polymer Composite Material

Ultrasonic longitudinal wave propagation is studied in out-of-autoclave (OoA) carbon fiber–reinforced polymer composite material with varying levels of porosity contents. A combination of cure pressures and a solvent is used to produce specimens with void contents in the range of 0% to 22%. Ultrasonic measurements are made in through-transmission mode, and the data is processed to study various aspects of wave interaction with porosity in OoA specimens. The specimens with a wide range of void contents have enabled the study of broader trends of ultrasonic center frequency, wave velocity, and attenuation with respect to porosity. Results show ultrasonic center frequency and wave velocity are decreased linearly as the void content increases. The relationship of ultrasonic wave attenuation can be approximated by a logarithmic relationship when considering the full range of void content studied. Strength measurements of specimens with varying void contents are made using the flatwise tensile (FWT) test. It is observed that the strength rapidly decreases with increasing porosity. Correlations made between FWT strength, ultrasonic wave velocity, and attenuation are best described by logarithmic relationships. The data shows a potential for inferring strength knockdowns due to the presence of porosity based on ultrasonic measurements.

Elastic three-dimensional metaframe for selective wave filtering and polarization control

We experimentally achieve selective wave filtering and polarization control in a three-dimensional elastic frame embedding local resonators. By connecting multi-resonating elements to a frame structure, a complete low-frequency, subwavelength bandgap with strong selective filtering properties is obtained. Theory and experiments demonstrate the metaframe capability to selectively stop transverse waves while allowing longitudinal wave propagation as in “fluid-like” elasticity. This peculiar behavior, together with the complete bandgap structure, may open opportunities in the context of wave control, envisaging concurrent applications for three-dimensional filters and elastic wave polarizers.

Longitudinal craze line propagation in human root dentin after instrumentation with NiTi rotary files of different instrument tapers after long-term chewing simulation

ObjectivesThe aim of this study was to investigate whether file design and taper significantly influence microcrack initiation during machine preparation.Materials and methodsSixty extracted teeth with straight single canals were selected. The teeth were randomly assigned to four groups based on their root canal anatomy and the corresponding NiTi rotary file system (I, Mtwo; II, ProTaper Universal; III, F6 SkyTaper; control, no preparation and filling). The root canals of the experimental groups were filled using the single-cone technique. The tested teeth were all subjected to a mechanical chewing simulation with flat lead loading over a period of 3 years (corresponding to 150,000 cycles). The teeth were checked for dentinal defects (accumulative crack growth in length) under the digital microscope (Keyence VHX-5000) at time 0 (baseline prior to chewing simulation) and after 3, 6, 12, 24, and 36 months of loading. The cumulative crack increase was statistically analyzed using the Kruskal–Wallis test, Jonckheere–Terpstra test, and the Wilcoxon rank-sum test. The significance was set at p < 0.05.ResultsIn contrast to preparation with greater-tapered instruments, ProTaper Universal (group II) and F6 SkyTaper (group III) instrumentation with the smaller tapered Mtwo files (group I) showed less accumulative propagation of craze lines (p < 0.05) at all time points.ConclusionInstruments with greater taper for root canal instrumentation should be used with care to avoid negative long-term effects in the form of propagation of dentinal defects over time. A positive cutting-edge angle and a smaller taper have a positive effect on a lower craze line development.Clinical relevanceInstruments with a positive cutting-edge angle and a smaller taper are beneficial for the long-term preservation of dentinal tooth structure.

Effects of the magnetic field on the viscoelastic wave propagation and dynamic material properties

In this paper, the longitudinal wave propagation of a thin ferromagnetic (Fe-Cr-Al alloy) rod under the transverse magnetic field is investigated analytically without ignoring the viscoelastic characteristics of this alloy. The analysis is based on the Bernoulli-Euler rod theory and a 4-element viscoelastic model based on the experimental observation. The viscoelastic wave characteristics and the behaviours of dynamic material properties under the magnetic field are investigated. The analytically results show that the longitudinal wave propagation and the dynamic material properties of the rod are affected by the magnetic field existence (for magnetic field magnitude values greater than about 107A/m), except the imaginary part of the complex elasticity modulus. Furthermore, in a large frequency range, depending on the ratio of the group velocity to the phase velocity an abnormal dispersion characteristic is observed.

Bright-dark wave envelopes of nonlinear regularized-long-wave and Riemann wave models in plasma physics

The nonlinear regularized-long-wave (RLW) and the Riemann wave (RW) models are physically significant in plasma physics and in further study of nonlinear dispersive waves, namely shallow water, ion-acoustic and magneto-sound waves in plasmas, anharmonic lattice and pressure waves in liquid-gas bubble mixtures, tidal and tsunami waves in rivers and oceans, longitudinal electromagnetic wave propagation in plasma, etc. The advanced generalized (G'/G)-expansion scheme is facilitated in this article for retrieving the bright-dark exact solitary wave solutions generated in the form of hyperbolic, trigonometric, and rational structures to the above-stated models. To figure out the internal contrivance of the solutions, 3D and contour plots concerning bright parabolic wave shape, compacton wave shape, bell-shaped soliton, kink wave type soliton, dark anti-parabolic wave shape, anti-compacton wave shape, bright propagation of solitary wave shape solutions are depicted for definite free parametric values. The characteristic feature of the wave envelops fluctuates taking into consideration the changes of free parameters and they are essentially dominated by the linear and nonlinear impact.

Microglial activation and tau propagate jointly across Braak stages.

Compelling experimental evidence suggests that microglial activation is involved in the spread of tau tangles over the neocortex in Alzheimer's disease (AD). We tested the hypothesis that the spatial propagation of microglial activation and tau accumulation colocalize in a Braak-like pattern in the living human brain. We studied 130 individuals across the aging and AD clinical spectrum with positron emission tomography brain imaging for microglial activation ([11C]PBR28), amyloid-β (Aβ) ([18F]AZD4694) and tau ([18F]MK-6240) pathologies. We further assessed microglial triggering receptor expressed on myeloid cells 2 (TREM2) cerebrospinal fluid (CSF) concentrations and brain gene expression patterns. We found that [11C]PBR28 correlated with CSF soluble TREM2 and showed regional distribution resembling TREM2 gene expression. Network analysis revealed that microglial activation and tau correlated hierarchically with each other following Braak-like stages. Regression analysis revealed that the longitudinal tau propagation pathways depended on the baseline microglia network rather than the tau network circuits. The co-occurrence of Aβ, tau and microglia abnormalities was the strongest predictor of cognitive impairment in our study population. Our findings support a model where an interaction between Aβ and activated microglia sets the pace for tau spread across Braak stages.

A Study of Longitudinal Waveguide with Band Gap Using Cylindrical and Conical Shape Periodic Structure

This research presents the theoretical and experimental studies for cylindrical and conical periodic structures to control longitudinal wave motion. Many relevant researches exist to stop and pass a certain frequency wave without active devices with periodic structures called metamaterials. To modify or control longitudinal wave propagation, i.e., passing or blocking mechanical wave within specific frequency ranges, repeated mass-spring systems or metamaterials can be applied. By integrating a few identical structural components to form a whole structure, it is possible to make a mechanical filter for wave propagation. Most studies rely on straight bar with cylindrical structure. Thus, with a unit cell that have a cylindrical and conical structure, this research presents the extensions toward the studies of the wave motions for straight and curved bars with finite element simulations and experiment studies. The results show that the hybrid cylindrical and conical periodic structures can be effective in terms of wave motion control and stiffness.

On propagation of harmonic plane waves under the Moore–Gibson–Thompson thermoelasticity theory

ABSTRACT The present work is aimed at a detailed investigation of harmonic plane wave propagation through an isotropic, unbounded and homogeneous thermoelastic medium under the recently proposed Moore–Gibson–Thompson (MGT) thermoelasticity theory. The dispersion relation is derived and its solution for the longitudinal plane wave propagation is obtained analytically. Two different modes of longitudinal wave are identified as elastic and thermal mode waves. The asymptotic expressions of various important characteristics of the wave fields such as phase velocity, specific loss and penetration depth for both the waves are obtained for limiting cases of very high and low frequency values. The Whitham stability of harmonic plane waves is established. Further, the computational tool is used to achieve numerical results for these wave characteristics and to illustrate the analytical findings graphically. Some important observations about the prediction of the MGT model in comparison to the other existing models, i.e. classical coupled thermoelastic model, LS model and GN-III model, are highlighted. Effects of material parameters on the propagation of waves are analyzed in a detailed manner. From the theoretical as well as numerical results, it is investigated that the MGT model accounts for finite speed of elastic wave as well as thermal wave.

Longitudinal and shear waves propagation in a periodic foundation with negative Poisson's ratio

The introduction of negative Poisson's ratio materials in engineering has opened new possibilities in materials science, acoustics, and civil engineering. Isotropic elastic foam with a negative Poisson's ratio of -0.7 has been produced which expands laterally when stretched, in contrast to ordinary materials. In this work, a new arrangement of seismic isolation foundation containing a unit cell of concrete - anti rubber and concrete/steel layers is proposed. The novelty lies in application of anti-rubber material as one of the three different layers periodically placed to form a periodic foundation. The auxetic material inclusion in this new arrangement broaden the no pass band of the periodic foundation compared to the earlier investigations. To demonstrate the effectiveness of this metamaterial foundation, an axially loaded column placed under three different foundations are numerically investigated. It is observed that the response of the metamaterial foundation with auxetic inclusion attenuated the elastics waves greatly compared to the foundations with rubber and traditional foundations. The results of the study could be used in developing new foundation materials for vibration attenuation for seismic waves which may cause destruction to engineering structures.

Highly efficient gas sensor based on quasi-periodic phononic crystals

Highly sensitive gas sensors have been introduced for the sensing of air, NH3, O2, CO2, or CH4 gases. The quasi-periodic structures of simple and generalized Fibonacci, simple and generalized Thue-Morse, Rudin-Shapiro, and symmetry structures have been regarded composed of diverse materials of PDMS, Epoxy, Al, and Steel and the detection gas. The proposed quasi-periodic structures have been investigated for maximum 10 alternating layers of solid-fluid arrangement with thickness ratio of (dsoild:dfluid)=(9:1). The study has been carried out by the transfer matrix method for the longitudinal wave propagation and the FC(5,1) and RS(4) structures composed of Al and Steel as solid material presented single peak shift for different gas infiltration. The sensitivities of 0.5988 MHz.m3. kg−1, 0.7777 MHz.m3. kg−1, 0.8738 MHz.m3. kg−1, and 0.9346 MHz.m3. kg-1 have been obtained in the frequency range of MHz for pure CO2, O2, NH3, and CH4 gases, respectively. Also, the best layer sequence for highly efficient gas sensor in 1D phononic quasi-crystals has been obtained, discussed, and optimized to get high quality factor.

Effect and identification of parametric distributed uncertainties in longitudinal wave propagation

Uncertainties play an important role in dynamic systems regarding their vibration and wave propagation behaviour. Stochastic methods have been used to address the randomness incorporated in numerical models. The spectral element method (SEM) is suitable to perform vibration and wave propagation analysis based on large frequency ranges with accuracy and low computational cost. This paper explores the longitudinal wave propagation considering uncertainties in the media aside from demonstrating and quantifying the effect of randomness inherent in the material. The stochastic Love rod spectral elements are proposed, and the parameters were assumed to be spatially distributed alongside the structure expressed as a random field. It is expanded using the Karhunen-Loève spectral decomposition and memoryless transformation. The Wentzel-Kramers-Brillouin (WKB) approximation is a powerful tool to evaluate local impedance changes slowly. It is used to indicate and quantify a changing rate related to material properties varying along the rod. Numerical examples analyse wave propagation in a longitudinal waveguide with distributed parameters.

Wildfires increasingly impact western US fluvial networks

Wildfires are increasing globally in frequency, severity, and extent, but their impact on fluvial networks, and the resources they provide, remains unclear. We combine remote sensing of burn perimeter and severity, in-situ water quality monitoring, and longitudinal modeling to create the first large-scale, long-term estimates of stream+river length impacted by wildfire for the western US. We find that wildfires directly impact ~6% of the total stream+river length between 1984 and 2014, increasing at a rate of 342 km/year. When longitudinal propagation of water quality impacts is included, we estimate that wildfires affect ~11% of the total stream+river length. Our results indicate that wildfire activity is one of the largest drivers of aquatic impairment, though it is not routinely reported by regulatory agencies, as wildfire impacts on fluvial networks remain unconstrained. We identify key actions to address this knowledge gap and better understand the growing threat to fluvial networks, water security, and public health risks.

Investigation on the Fracturing Permeability Characteristics of Cracked Specimens and the Formation Mechanism of Inrush Channel from Floor

To study the fracture characteristics and the permeability change law of the cracked specimens during the complete stress-strain process, a mechanical model was constructed, from which different types of crack initiation angles were obtained. The crack inclination angles under uniaxial compression, confining compression, and confining tension, and the influence of confining pressure and pore water pressure on the crack propagation and permeability of rock mass were investigated and simulated with RFPA-Flow software using prefabricated crack models with crack initiation angles of 30°, 45°, and 60°. Furthermore, the formation mechanism of inrush channel from floor was qualitatively analyzed. The results indicated that the theoretical initiation angles of wing cracks, secondary coplanar cracks, and secondary inclined antiwing cracks were found to be 70.53°, 0°, and 123.8°, which were consistent with the simulation results. The crack propagation was mainly concentrated at the postpeak stage of the complete stress-strain curve, causing the peak of seepage velocity to lag behind the stress peak. For the case with a constant confining pressure, the rate of crack initiation and propagation to final failure was positively correlated with the internal pore pressure. For the case with a constant water pressure, the speed of crack initiation and propagation to final failure decreased first and then increased as the confining pressure increased. In addition, the longitudinal propagation of wing cracks and the increase in permeability were prone to occur in the low confining pressure zone, which induced the formation of water inrush channels. The research result provides an improved understanding for predicting and preventing water inrush disasters.