Torsional Waves Research Articles

Modeling the Effects of a Light Bridge on Properties of Magnetohydrodynamic Waves in Solar Pores

Solar pores are ideal magnetic structures for wave propagation and transport of energy radially outwards across the upper layers of the solar atmosphere. We aim to model the excitation and propagation of magnetohydrodynamic waves in a pore with a light bridge modeled as two interacting magnetic flux tubes separated by a thin, weaker-field layer. We solve the three-dimensional magnetohydrodynamic equations numerically and calculate the circulation as a measure of net torsional motion. We find that the interaction between flux tubes results in the natural excitation of propagating torsional Alfvén waves but find no torsional waves in the model with a single flux tube. The torsional Alfvén waves propagate with wave speeds matching the local Alfvén speed where wave amplitude peaks.

Comparison of Torsional and SH Waves in Isotropic and Anisotropic Media Based on Laboratory Measurements

Abstract Utilization of the torsional wave signal has been reported in medical testing and engineering detection. A torsional wave is a shear-wave train whose vibrating direction (polarization) forms a torsional motion. However, there are a lack of understanding of its characteristics and potential for subsurface investigations. Here, compressional (P), shear (S) and torsional (T) transducers are constructed using different piezoelectric-transformer (PZT) chips in the laboratory and the characteristics of the torsional (T) wave propagating in isotropic and fracture-induced anisotropic media are analyzed in line with conventional P- and S-waves, covering waveform, amplitude, arrival time and velocity at different propagating angles. The results indicate that the velocity and anisotropy values measured using the T transducer are almost the same as the SH wave. For propagation in isotropic and anisotropic media, the wavefield generated by the T transducer is very simple with no mode conversions and source-generated interferences, which is similar to the SH wavefield, whilst the SV wavefield comprises of a series of complex events from mode conversions and interferences. For propagating in fluid- saturated fractured rocks, the torsional wavefield also comprises of a fast and slow wave train, which is referred to as torsional-wave splitting, and is similar to the shear wave splitting from S transducers. Furthermore, the anisotropy parameters measured using P, S and T transducer show a good correlation with the fracture density, and the P wave anisotropy is higher in air saturated rocks than water saturated rocks, while the shear wave anisotropy measured by S transducer and T transducer are sensitive to fracture density. Similar to the P transducer, the T transducer is polarization-independent, or directional invariant. Therefore, utilizing the T transducer may simplify the field logistics during 3D shear-wave surveys. However, field torsional wave generation is a major issue that needs further study.

Waveguide Acoustic Control of Pipes - Billets of Deep Rod Pumps

Deep rod pumps are expensive maintenance-free equipment for extracting oil from wells. The exclusion of defective billet pipes from the technological cycle of manufacturing elements of such pumps significantly affects both the cost of their production and the cost of production. A waveguide method is proposed for continuous input testing of tube billets of rod pump cylinders. It does not require scanning and is highly sensitive to both internal and surface defects. An experimental assessment of the sensitivity of the method to defects in the form of an influx located on the outer and inner surfaces of a thick-walled pipe with a diameter of 59.3 mm and a wall thickness of 14 mm was carried out. The echo signal from the artificial reflector decreased by 2 dB when the reflector was moved from the outside of the pipe to the inside. The criteria for rejection of the blank pipe are determined by the signal level at the first reflection R1, at the 8th reflection RN and by the attenuation coefficient b. As a result of flaw detection of billet pipes, a pipe with a significant defect was found. An experimental study of the acoustic properties of a batch of pipes with a diameter of 58 mm in the delivery state was carried out. For the billets of the cylinder of the deep rod pump in the delivery state, the lower acceptance limit for the torsional wave velocity of 3255 m/s has been determined. The influence of technological operations of high tempering and straightening on their acoustic properties is estimated. The possibility of quality control when performing the release operation by the guided wave method is shown. It was revealed that during the tempering procedure, the velocity of the torsional wave increases, on average, by 27 m/s per batch.

Semi-analytical formulation to predict the vibroacoustic response of a fluid-loaded plate with ABH stiffeners

Stiffened structures are widely used in aeronautics, marine and rail industries. When stiffeners are integrated into host structures, so-called Bloch-Floquet waves are generated due to interactions between the host’s flexural waves and the stiffeners’ flexural and torsional waves. It is reported in the literature that these waves are often the source of undesirable noise and vibrations when the stiffened structure is excited by a force. To mitigate unwanted noise and vibrations from the stiffened structures, this study proposes to replace common rectangular stiffeners with acoustic black hole (ABH) stiffeners. To do this, a semi-analytical model is initially developed in the wavenumber domain to predict the forced vibroacoustic response of a 2D fluid-loaded infinite plate with stiffeners on one side. In the proposed model, the stiffeners are characterised by their translational and rotational dynamic stiffnesses which can be estimated by a finite element method (FEM). These dynamic stiffnesses are then coupled with the analytical formulation of the fluid-loaded plate to obtain the expressions of the spectral displacement and radiated pressure. Comparisons of the results in terms of the plate’s mean quadratic velocity and radiated sound power for the rectangular and ABH stiffeners show that by using the ABH stiffeners instead of the conventional stiffeners, one can significantly reduce the vibroacoustic response of light/heavy fluid-loaded plates.

Joint action of phase mixing and nonlinear effects in MHD waves propagating in coronal loops

Context. The evolution of Alfvén waves in cylindrical magnetic flux tubes, which represent a basic model for loops observed in the solar corona, can be affected by phase mixing and turbulent cascade. Phase mixing results from transverse inhomogeneities in the Alfvén speed, causing different shells of the flux tube to oscillate at different frequencies, thus forming increasingly smaller spatial scales in the direction perpendicular to the guide field. Turbulent cascade also contributes to the dissipation of the bulk energy of the waves through the generation of smaller spatial scales. Both processes present characteristic timescales. Different regimes can be envisaged according to how those timescales are related and to the typical timescale at which dissipation is at work. Aims. We investigate the interplay of phase mixing and the nonlinear turbulent cascade in the evolution and dissipation of Alfvén waves using compressible magnetohydrodynamic numerical simulations. We consider perturbations in the form of torsional waves, both propagating and standing, or turbulent fluctuations, or a combination of the two. The main purpose is to study how phase mixing and nonlinear couplings jointly work to produce small scales in different regimes. Methods. We conducted a numerical campaign to explore the typical parameters, such as the loop length, the amplitude and spatial profile of the perturbations, and the dissipative coefficients. A pseudo-spectral code was employed to solve the three-dimensional compressible magnetohydrodynamic equations, modeling the evolution of perturbations propagating in a flux tube corresponding to an equilibrium configuration with cylindrical symmetry. Results. We find that phase mixing takes place for moderate amplitudes of the turbulent component even in a distorted, nonaxisymmetric configuration, building small scales that are locally transverse to the density gradient. The dissipative time decreases with increasing the percentage of the turbulent component. This behavior is verified both for propagating and standing waves. Even in the fully turbulent case, a mechanism qualitatively similar to phase mixing occurs: it actively generates small scales together with the nonlinear cascade, thus providing the shortest dissipative time. General considerations are given to identify this regime in the parameter space. The turbulent perturbation also distorts the background density, locally increasing the Alfvén velocity gradient and further contributing to accelerating the formation of small scales. Conclusions. Our campaign of simulations is relevant for the coronal plasma where Reynolds and Lundquist numbers are extremely high. For sufficiently low perturbation amplitudes, phase mixing and turbulence work synergically, speeding up the dissipation of the perturbation energy: phase mixing dominates at early times and nonlinear effects at later times. We find that the dissipative time is shorter than those of phase mixing and the nonlinear cascade when individually considered.

A 90-meter Split Hopkinson Tension–Torsion Bar: Design, Construction and First Tests

AbstractThis article describes the design, construction, and first experimental results of a 90 m-long Hopkinson bar which can perform high strain rate tests in a combined tension–torsion state. The system configuration is analogous to the classic Hopkinson bar technique, consisting of three bars: a pre-stressed bar, an input bar, and an output bar; the sample is placed between the input and output bar. The measurement is also based on the classical three-wave method, where the incident, transmitted and reflected waves are measured. Incident compression and torsional waves are simultaneously generated by the failure of a fragile element that connects the pre-stressed bar to electromechanical actuators; the indirect Hopkinson tension bar technique is exploited, where the compression wave reaches the end of the output bar without stressing the sample and is reflected as a tensile input wave. The length of the bars is designed so that the tensile wave reaches the sample from the output bar side at the same time as the torsion wave comes from the input bar. Void tests were carried out first, for preliminary analysis of the system behaviour. Then, successful tests have been conducted on samples made of AA7075 T6, both in combined and pure tension–torsion states; it has been possible to measure the tension–torsion stress–strain curves, from which the equivalent flow stress–strain curve has been evaluated and compared to the quasi-static ones.

Elastodynamic Response of Torsional Waves in Sinusoidal Conical Notch (SCN)

Elastodynamic Response of Torsional Waves in Sinusoidal Conical Notch (SCN)

Reliability and robustness of a novel preclinical torsional wave-based device for stiffness evaluation

In this work, we present a novel preclinical device utilizing Torsional Wave Elastography (TWE). It comprises a rotational actuator element and a piezoceramic receiver ring circumferentially aligned. Both allow the transmission of shear waves that interact with the tissue before being received. Our main objective is to demonstrate and characterize the reliability, robustness, and accuracy of the device for characterizing the stiffness of elastic materials and soft tissues. Experimental tests are performed using two sets of tissue mimicking phantoms. The first set consists of calibrated CIRS gels with known stiffness value, while the second test uses non-calibrated manufactured phantoms. Our experimental observations show that the proposed device consistently and repeatably quantifies the stiffness of elastic materials with high accuracy. Furthermore, comparison with established techniques demonstrates a very high correlation (> 95%), supporting the potential medical application of this technology. The results obtained pave the way for a cross-sectional study aiming to investigate the correlation between gestational age and cervical elastic properties during pregnancy.

Using torsional wave elastography to evaluate spring pot parameters in skin tumor mimicking phantoms

Estimating the tissue parameters of skin tumors is crucial for diagnosis and effective therapy in dermatology and related fields. However, identifying the most sensitive biomarkers require an optimal rheological model for simulating skin behavior this remains an ongoing research endeavor. Additionally, the multi-layered structure of the skin introduces further complexity to this task. In order to surmount these challenges, an inverse problem methodology, in conjunction with signal analysis techniques, is being employed. In this study, a fractional rheological model is presented to enhance the precision of skin tissue parameter estimation from the acquired signal from torsional wave elastography technique (TWE) on skin tumor-mimicking phantoms for lab validation and the estimation of the thickness of the cancerous layer. An exhaustive analysis of the spring-pot model (SP) solved by the finite difference time domain (FDTD) is conducted. The results of experiments performed using a TWE probe designed and prototyped in the laboratory were validated against ultrafast imaging carried out by the Verasonics Research System. Twelve tissue-mimicking phantoms, which precisely simulated the characteristics of skin tissue, were prepared for our experimental setting. The experimental data from these bi-layer phantoms were measured using a TWE probe, and the parameters of the skin tissue were estimated using inverse problem-solving. The agreement between the two datasets was evaluated by comparing the experimental data obtained from the TWE technique with simulated data from the SP- FDTD model using Pearson correlation, dynamic time warping (DTW), and time-frequency representation. Our findings show that the SP-FDTD model and TWE are capable of determining the mechanical properties of both layers in a bilayer phantom, using a single signal and an inverse problem approach. The ultrafast imaging and the validation of TWE results further demonstrate the robustness and reliability of our technology for a realistic range of phantoms. This fusion of the SP-FDTD model and TWE, as well as inverse problem-solving methods has the potential to have a considerable impact on diagnoses and treatments in dermatology and related fields.

Observations of fan-spine topology by Solar Orbiter/EUI: Rotational motions and indications of Alfvén waves

Context. Torsional Alfvén waves do not produce any intensity variation and are therefore challenging to observe with imaging instruments. Previously, Alfvén wave observations were reported throughout all the layers of the solar atmosphere using spectral imaging. Aims. We present a torsional Alfvén wave detected in an inverted Y-shaped structure observed with the HRIEUV telescope of the EUI instrument on board Solar Orbiter in its 174 Å channel. The feature consists of two footpoints connected through short loops and a spine with a length of 30 mm originating from one of the footpoints. Methods. We made use of the simultaneous observations from two other instruments on board Solar Orbiter. The first one is the Polarimetric and Helioseismic Imager, which is used to derive the magnetic configuration of the observed feature. The second is the Spectral Imaging of the Coronal Environment (SPICE) instrument, which provided observations of intensity maps in different lines, including Ne VIII and C III lines. We also address the issues of the SPICE point spread function and its influence on the Doppler maps via performed forward-modeling analysis. Results. The difference movie constructed from the HRIEUV images shows clear signatures of propagating rotational motions in the spine. We measured propagation speeds of 136 km s−1–160 km s−1, which are consistent with the expected Alfvén speeds. Evidence of rotational motions in the transverse direction with velocities of 26 km s−1–60 km s−1 serves as an additional indication of torsional waves being present. Doppler maps obtained with SPICE show a strong signal in the spine region. Under the assumption that the recovered point spread function is mostly correct, synthesized raster images confirm that this signal is predominantly physical. Conclusions. We conclude that the presented observations are compatible with an interpretation of either propagating torsional Alfvén waves in a low coronal structure or the untwisting of a flux rope. This is the first time we have seen signatures of propagating torsional motion in the corona as observed by the three instruments on board Solar Orbiter.

Massive propagating modes of torsion

The dynamics of the torsion field is analyzed in the framework of the Covariant Canonical Gauge Theory of Gravity (CCGG), a De Donder–Weyl Hamiltonian formulation of gauge gravity. The action is quadratic in both, the torsion and the Riemann–Cartan tensor. Since the latter adds the derivative of torsion to the equations of motion, torsion is no longer identical to spin density, as in the Einstein–Cartan theory, but an additional propagating degree of freedom. As torsion turns out to be totally anti-symmetric, it can be parametrised via a single axial vector. It is shown in this paper that, in the weak torsion limit, the axial vector obeys a wave equation with an effective mass term which is partially dependent on the scalar curvature. The source of torsion is thereby given by the fermion axial current which is the net fermionic spin density of the system. Possible measurable effects and approaches to experimental analysis are addressed. For example, neutron star mergers could act as a dipoles or quadrupoles for torsional radiation, and an analysis of radiation of pulsars could lead to a detection of torsion wave background radiation.

Riemann problem for longitudinal–torsional waves in nonlinear elastic rods

Riemann problem for longitudinal–torsional waves in nonlinear elastic rods

Effect of Non-Homogeneity and Initial Stress on Torsional Surface Wave Propagation in Initially Stressed Poroelastic Medium Bounded by a Heterogeneous Layer and Half-Space

Effect of Non-Homogeneity and Initial Stress on Torsional Surface Wave Propagation in Initially Stressed Poroelastic Medium Bounded by a Heterogeneous Layer and Half-Space

Damage Monitoring of Steel Bars Based on Torsional Guided Waves.

Ultrasonic guided waves represent a new development in the field of non-destructive testing. Longitudinal guided waves are mostly used to monitor the damage of steel bars, but the received signal is usually degraded and noisy owing to its dispersive propagation and multimodal behavior, making its implementation and location challenging. The torsional mode of T (0, 1) is not dispersive in the propagation of a steel bar and only produces circumferential displacement. It was chosen, in this study, to conduct guided wave-based damage monitoring on steel bars to reduce the signal processing complexity. The defects of steel bars, including circular surface defects, internal defects, and uniform damage defects, were thoroughly investigated, respectively, using numerical simulation. The waves were excited and received using the pitch-and-catch technique and the collected monitoring signals were processed using Hilbert transformation to highlight the amplitude and time-of-flight values of the wave signals, which were used for defect identification. In this paper, the reflectivity of guided waves is compared between torsional waves and longitudinal waves, in each case. The impact of defect size changes on damage monitoring is studied and the sensitivity of both the wave frequency and the wave mode (L and T) is also discussed. The results show that the monitoring method based on the torsional wave T (0, 1) is more sensitive to surface defects than the conventional method based on longitudinal waves. The reflectivity of the torsional wave T (0, 1) can be twice that of the longitudinal wave L (0, 1) when the depth of the defect in the circumferential grooves is less than 50% of the diameter of the steel bar. It is more sensitive to shallow surface defects within half of the bar's radius, and it can also effectively identify defects under the conditions of the uniform damage defects of steel bars, even when the measurements are heavily noise-polluted. This proves the superiority of the torsional guided wave T (0, 1) in defect monitoring and provides a theoretical basis for the application of the torsional guided wave T (0, 1) in actual monitoring.

Bending-bending-torsion coupled wave propagation in thin-walled asymmetric metabeam: An analytical and experimental analysis

The primary focus of this paper is to analyze the impact of the periodic resonators on the wave dispersion phenomenon of a thin-walled asymmetric beam. An analytical framework has been developed to study the triply coupled flexural and torsional wave propagation in an asymmetric metabeam. The resonators are modeled as a beam with a lumped mass at the center and placed eccentrically from the shear center. Their periodicity allows them to generate a subwavelength attenuation band in the beam. The governing equations for the coupled bending-bending-torsion vibration of a metabeam having an asymmetric cross-section are considered for generating the dispersion phenomenon, including the warping effect. Applying the Bloch-Floquet principle, the dispersive characteristics of the asymmetric metabeam are obtained by using the transfer matrix method. The modal characteristics of an asymmetric beam without a resonator are computed using the spectral element method and are validated with previously published results. Subsequently, the attenuation band is investigated due to the presence of a resonator and followed by the transmittance spectrum to verify the suppression of the elastic waves in the attenuation band. The experimental analysis is carried out to validate the analytical framework by obtaining the modal frequencies from the frequency response function. The detailed parametric investigation reveals that the resonator’s position and characteristics significantly impact the occurrence of the band gap. A substantially wide attenuation band gap is attained by considering a continuous beam-mass resonator instead of a discrete spring-mass type resonator. This type of novel structure has the potential for the application of vibration control and acoustics.

Impact of surface/interface elasticity on the propagation of torsional vibration in piezoelectric fiber-reinforced composite and anisotropic medium

This work has explored surface/interface theory-based torsional wave propagation in a piezoelectric fiber-reinforced composite (PFRC) layer on top of a functionally graded elastic substrate. PFRC is assumed to be composed of piezoelectric fiber and epoxy matrix. Micro-mechanical investigations have been performed to determine the coefficients of PFRC using strength of materials (SM) and rule of mixtures (RM) techniques. The dispersion relation for the torsional wave under nonclassical boundary conditions is determined using surface/interface theory. The effects of surface/interface, fiber volume fractions, and heterogeneities on the phase velocity and the mode shapes of the wave have been demonstrated graphically.

Analysis of Torsional Vibration in a Fractured Poroelastic Half-Space Coated with Metal Foam and Sliding Interfaces

Metal foams are highly useful in industries because of their lightweight, energy and vibration absorption properties. This study investigated the propagation of torsional waves in an elastic layer over a fluid-saturated fractured poroelastic half-space with a metal foam coated layer. It is assumed that the interfaces are in sliding contact with two different sliding parameters. The coated layer is closed-cell aluminium foam. We use the separation variable technique and the Bessel function to solve the equation of motion in different layers. The displacement components are written in terms of the second kind Whittaker functions. Using an asymptotic formulation of the Whittaker function and appropriate boundary conditions, the dispersion equation is derived in terms of the determinant. The control of the vibration due to the metal foam-coated layer is one of the important goals of this study. Also, numerical and graphical analyses have been done with the help of Mathematica software to see the effect of different parameters on torsional wave propagation. It is found that the presence of coated metal foam layer decreases the phase velocity of the torsional wave propagation. The work may be helpful in the seismology, automobile, and aerospace industries.

Healthy human skin Kelvin-Voigt fractional and spring-pot biomarkers reconstruction using torsional wave elastography

This paper presents a novel method for reconstructing skin parameters using Probabilistic Inverse Problem (PIP) techniques and Torsional Wave Elastography (TWE) rheological modeling. A comprehensive examination was conducted to compare and analyze the theoretical, time-of-flight (TOF), and full-signal waveform (FSW) approaches. The objective was the identification of the most effective method for the estimation of mechanical parameters. Initially, the most appropriate rheological model for the simulation of skin tissue behavior was determined through the application and comparison of two models, spring pot (SP) and Kevin Voigt fractional derivative (KVFD). A numerical model was developed using the chosen rheological models. The collection of experimental data from 15 volunteers utilizing a TWE sensor was crucial for obtaining significant information for the reconstruction process. The study sample consisted of five male and ten female subjects ranging in age from 25 to 60 years. The procedure was performed on the ventral forearm region of the participants. The process of reconstructing skin tissue parameters was carried out using PIP techniques. The experimental findings were compared with the numerical results. The three methods considered (theoretical, TOF, FSW) have been used. The efficacy of TOF and FSW was then compared with theoretical method. The findings of the study demonstrate that the FSW and TOF techniques successfully reconstructed the parameters of the skin tissue in all of the models. The SP model’s the skin tissue η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta $$\\end{document} values ranged from 8 to 12 Pa·s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Pa \\cdot s$$\\end{document}, as indicated by the TOF reconstruction parameters. η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta $$\\end{document} values found by the KVFD model ranged from 4.1 to 9.3 Pa·s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Pa \\cdot s$$\\end{document}. The μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu $$\\end{document} values generated by the KVFD model range between 0.61 and 96.86 kPa. However, FSW parameters reveal that skin tissue η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta $$\\end{document} values for the SP model ranged from 7.8 to 12 Pa·s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Pa \\cdot s$$\\end{document}. The KVFD model determined η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta $$\\end{document} values between 6.3 and 9.5 Pa·s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Pa \\cdot s$$\\end{document}. The KVFD model presents μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu $$\\end{document} values ranging between 26.02 and 122.19 kPa. It is shown that the rheological model that best describes the nature of the skin is the SP model and its simplicity as it requires only two parameters, in contrast to the three parameters required by the KVFD model. Therefore, this work provides a valuable addition to the area of dermatology, with possible implications for clinical practice.

An investigation of torsional surface wave in a piezoelectric fiber-reinforced composite layer imperfectly bonded to a functionally graded half-space

This article presents a comprehensive study of torsional surface wave propagation in a piezoelectric fiber-reinforced composite (PFRC) layer bonded to functionally graded (FG) half-space considering electrically short and open boundary conditions. The Strength of Materials (SM) and Rule of Mixtures (ROM) approaches have been adopted to determine the effective properties of the PFRC. The non-ideal mechanical and electrical interfacial boundary has been considered for the problem which appears in various realistic scenarios. For the torsional surface wave propagation through PFRC bonded to FG half-space, the dispersion equation has been derived analytically using Whittaker function. The obtained results are validated and matched with existing results by considering special cases. The variation of phase velocity due to the influence of fiber volume fraction, interfacial imperfection parameters and functionally grading parameters have been analyzed and illustrated by means of graphs. Furthermore, the distribution of the field variables, stress and electric displacements across the composite are presented through surface plots. The model holds potential applications in designing and manufacturing transducers, actuators and sensors. The use of PFRC can be found in a wide range of cutting-edge technology, including vibration-canceling gadgets, energy harvesters, and pressure sensors.

Torsional waves in hyperelastic shells: Appearing shock waves and energy dissipation

Nonlinear torsional waves propagating in cylindrical shells made of hyperelastic material obeying Ogden model, are studied by a combined approach comprising theoretical and finite element analysis. It was found, apparently for the first time, that delta-like pulses of torsional waves attenuate with distance due to the appearance of shock wave fronts. Moreover, both strain and kinetic mechanical energy dissipate due to the release of thermal energy.