Propagation Of Torsional Waves Research Articles

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.

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.

Analysis of the interaction between torsion wave and phononic crystal in pipes

This article presents an analysis of torsional wave propagation in phononic crystal-based metamaterials. Such structures hold great promise as tools for wave manipulation. The unit cell of the presented structure was meticulously examined to obtain dispersion curves, revealing the presence of bandgaps and negative group velocities. The calculations of effective material parameters, based on eigenfrequencies, are presented to substantiate the existence of the bandgap and the negative value of group velocity. Time-domain simulations were conducted at various frequencies to analyze the wave behavior. In the case of negative group velocity, the wave inside the metamaterial propagates in the same direction as the incident wave. To verify the existence of negative velocity, a 2D Fast Fourier Transform (FFT) was performed, and the results from the 2D FFT data analysis align perfectly with the eigenfrequency analysis.

Deep learning algorithms for design of periodic structures and dispersion curves calculation

Periodic structure is useful and powerful tool for the wave manipulation. The development of design and analysis of periodic structures using traditional methods (analysis of eigenfrequencies by the finite element method) takes quite a lot of time. Machine learning and deep learning algorithms can speed up the development and subsequent analysis of periodic structures. In this work, we consider a particular case of the propagation of torsional waves in cylindrical objects, the calculation of their dispersion curves, and methods for generating the design of a unit cell of periodic structure by a given bandgap configuration. To achieve this goal, autoencoders and diffusion models were used. A dataset of unit cell shapes and their dispersion curves were used as training data. First, the dispersion curves were analysed to form a bandgap configuration, which was then fed to the input of the neural network. The neural network generates unit cell shape as the output data. Information about dispersion curves is also very important for the analysis of periodic structures. To calculate the dispersion curves, the possibility of using deep learning methods is considered - the problem is the opposite of the previous one. According to the given form, the neural network should calculate dispersion curves. The paper presents the results of applying this method for calculating dispersion curves.

Analysis of integrated effect of irregularity and corrugated interfaces of doubly layered half space on torsional surface wave propagation

Present geophysical model analyzes the propagation characteristics of torsional wave in an inhomogeneous viscoelastic fiber‐reinforced layer sandwiched between superior porous layer and transversely isotropic piezoelectric subspace with imperfect interfaces. Porous layer and intermediate reinforced layer are endowed with initial stress and corrugated interfaces, whereas the lower piezoelectric half space possesses rectangular cavity at the welded contact. Earth's adjacent layers near mountainous region often endowed with initial stresses resemble the present geological setup. The material properties of intermediate layer are considered to be varying exponentially. Particular cases have been deduced for electrically open and short condition for validation with the standard Love wave expressions. Effects of the relevant parameters on resultant torsional velocity have been explored through numerical simulation and depicted for electrically short and open conditions. Findings of present model may be utilized in the field of signal testing, sensors design, seismic acoustic wave (SAW) devices, and geophysical application concerned with torsional wave based on non‐destructive evaluation.

On torsional wave in void type porous layers between viscoelastic and piezoelectric media with parabolic irregularity

The viscoelastic earth model is increasingly utilized by seismologists for studying surface seismic wave propagation through Earth’s porous crustal regions such as granular materials, including rock, soils, and synthetic porous bodies. The present study characterizes torsional wave propagation in an irregular void-type porous layer sandwiched between an initially stressed inhomogeneous viscoelastic layer and a piezoelectric substratum. Displacement fields for the layer and half spaces are obtained separately using a variable separable technique, whereas volume fraction and electric potential field are derived for layer and substratum, respectively using the matrix calculus approach. Dispersion relations have been derived for both electrically open and short circuit conditions and agree with standard results. Particular cases have been deduced to validate the finding of the study with literature results. Effects of change in relevant parameters such as initial stress, heterogeneities, attenuation coefficient, void parameters, piezoelectricity and dissipation factor have been analyzed on the phase velocity of the torsional wave through various plots and summarized in a tabular form for ready reference to researchers. Analysis of the present geophysical problem may be useful in characterizing torsional velocity in porous silicate rocks which are abundantly found in the transition zone between oceanic and continental crust called Conrad discontinuity. Highlights Torsional propagation in a void-type porous layer crammed between an initially stressed inhomogeneous viscoelastic layer and piezoelectric half-space has been investigated. Variable separable technique, the matrix calculus approach is used for computing the displacement fields of respective media. A comparative study has been carried out for both electrically open and short conditions. The impact of pertinent parameters including initial stress, heterogeneities, attenuation coefficient, void parameters, piezoelectricity, and dissipation factor on the phase velocity of the torsional wave has been examined.

Reproducibility and usability assessment of the novel Fine Birth device for threatened preterm labor diagnosis

Preterm delivery is considered the leading cause of mortality worldwide in children under five. Forty-five million pregnant women are hospitalized yearly for Threatened Preterm Labor (TPTL). However, only 50% of TPTLs end in delivery before the estimated date, classifying the rest as false TPTL. The ability of current diagnostic methods to predict TPTL is low (low positive predictive value), ranging between 8-30%. This highlights the need for a solution that accurately detects and differentiates between false and real TPTLs in women who attend obstetric clinics and hospital emergency departments with delivery symptoms. This is a pilot study aiming at first, to assess the reproducibility and usability of a novel medical device, the Fine Birth, aimed at accurately diagnosing TPTL through the objective quantification of pregnant women's cervical consistency. Secondarily, we aimed to evaluate the impact of training and the incorporation of a lateral micro camera on the device's reliability and usability outcomes. 77 singleton pregnant women were recruited during their follow-up visit to the obstetric and gynecological departments at five Spanish hospitals. Eligibility criteria were: pregnant women ≥ 18 years old, with a normal fetus and uncomplicated pregnancy, without prolapse of membranes, uterine anomalies, previous cervical surgery or latex allergy, and signing the informed written consent. Cervical tissue stiffness was assessed using the Fine Birth device, whose technology is based on the propagation of torsional waves through the studied tissue. Cervical consistency measurements were taken for each woman until obtaining two valid measurements by two different operators. The intra-observer and inter-observer reproducibility of the Fine Birth measurements was assessed using the Intraclass Correlation Coefficients (ICC) with a 95% confidence interval (CI) and the F-test p-value. The usability was evaluated based on clinicians' and participants' feedback. There was a good intra-observer reproducibility (ICC=0.88, 95% CI 0.84 to 0.95; F-test p-value < 0.05). Since the results obtained for the inter-observer reproducibility did not reach the desired acceptable values (ICC<0.75), a lateral micro camera was added to the Fine Birth intravaginal probe, and the operators involved in the clinical investigation received the corresponding training with the modified device. Analysis of 16 additional subjects demonstrated an excellent inter-observer reproducibility (ICC=0.93, 95% CI 0.78 to 0.97) and a clear improvement after the intervention (p<0.0001). The robust reproducibility and usability results obtained after the insertion of a lateral micro camera and the corresponding training make the Fine Birth a promising novel device to objectively quantify the patient's cervical consistency, diagnose TPTL and thus, predict the risk of spontaneous preterm birth. Further research is needed to demonstrate the clinical utility of the device.

Крутильні пружні хвилі. Деякі аспекти нелінійного аналізу

The features of the use of boundary conditions in the nonlinear problem of torsional wave propagation for an elastically deformable medium with an external boundary are analyzed. The formulation and wave analysis in the linear (classical) approach are briefly described, since the linear solution is used in the work as a first approximation in the nonlinear approach. The first feature for a torsional wave is a significant complication in the nonlinear approach of the boundary conditions due to the difference between the shape of the boundary before and after the deformation (in the linear approach, the shape of the boundary does not change). The second feature is the significant complication of the mathematical representation of the boundary conditions due to the appearance of additional nonlinear terms. For a torsional wave, it was found that the use of the condition of absence of stresses on the boundary surface (assumption of a free boundary) may not be completely correct.

Auxetic meta-disk for independent control of flexural and torsional waves

Locally resonant elastic metamaterials have a unique characteristic of forming a low-frequency bandgap where wave propagation is inhibited. In this study, we present an auxetic meta-disk, a novel design of a local resonator capable of independent control of the flexural and torsional wave propagation in a pipe. The auxetic meta-disks are perforated with rationally designed auxetic patterns, whose mode-dependent deformation is the key mechanism enabling to manipulate the flexural and torsional natural frequencies of the meta-disks simultaneously. The capabilities of auxetic meta-disks in controlling wave propagation are thoroughly investigated using finite element analysis, and its applicability to elastic wave mode filtering is presented. Because of the simplicity in design and installation, the proposed concept is expected to be practical and applicable to various fields of vibration isolation or non-destructive inspection that require considering more than one vibration mode.

Effect of Periodic Structure on Torsional Wave Propagation

본 논문은 돌출 링 형태의 반복 형상을 갖는 구조물이 유도초음파 비틀림파에 미치는 영향에 대한 연구이다. Bloch-Floquet 경계 조건과 유한 요소 방법에 의한 고유 주파수 분석이 돌출 링의 높이, 간격 등 다양한 기하학적 치수에 대한 분산 곡선 계산을 위해 적용되었다. 계산된 분산선도와 전파 모델 해석은 모드 간의 밴드 갭과 음(negative)의 유도초음파 군속도 존재 가능성을 나타낸다. 시간 영역에서의 시뮬레이션 결과를 활용하여 고유 주파수 분석을 하였으며, 해석 결과는 음의 군속도를 검증하였다. 계산을 통해 획득된 시간 영역 결과는 고유 진동수 분석 결과와 상당히 일치하는 것을 확인하였다.

Torsional wave propagation on a penny-shaped crack in an orthotopic layer sandwiched between two rigid discs bonded by an orthotropic elastic half-space

The mechanical stability of the interface of two materials determines the stress behavior of the interface. So, observation of failure analysis in orthotropic composites with penny-shaped crack and circular disc in orthotropic materials due to the presence of torsional waves play a major role in structural design. The present article concerns the study of the torsional wave propagation of a penny-shaped crack in an orthotropic layer and two circular discs bonded between the layer and half-spaces. A general solution for the system is presented as a set of dual integral equations using the Hankel transform technique. Using Abel's transform method, the equations have been transformed into Fredholm integral equations of the second kind, which have been solved numerically to compute the stress intensity factors (SIFs) near the rims of crack and discs. Numerical results are obtained using material constants of two orthotropic mediums to demonstrate the impact of material non-homogeneity, normalized disc radius, and layer depth on SIFs and portrayed by virtue of graphs. The analysis of the physical quantity SIF in the present model leads to speculation about the stability of composites against the propagation of cracks in layered engineering solids by surveilling geometric parameters of orthotropic materials and layer depth.

Negative refraction and mode trapping of flexural-torsional waves in elastic lattices.

We consider the propagation of flexural and torsional waves in a square lattice of Euler–Bernoulli beams. The refraction and reflection of waves across interfaces between two dissimilar lattices is investigated. By carefully controlling the inertial and elastic properties of the lattice elements, we demonstrate that it is possible to induce negative refraction and other associated phenomena. These effects are shown to be broadband and are facilitated by the unprecedented control over wave propagation afforded by the interaction between torsional and flexural waves and the additional freedom associated with the applied forcing. Closed-form analytical findings are accompanied by numerical simulations, which demonstrate negative refraction, unidirectional reflection and mode trapping.This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)’.

Dispersion of torsional surface waves in a threefold concentric compounded cylinder with imperfect interface

The present paper investigates the torsional wave propagation in a threefold concentric pre-stressed compounded cylinder with imperfect contact conditions. The three-dimensional linearized theory of elastic waves and the piecewise homogeneous body model has been employed to formulate the problem. The mathematical modeling has been carried out in two independent cases. In the first case, a solid cylinder encased in a hollow cylinder embedded in an infinite elastic medium has been considered. Whereas the second case comprises a hollow cylinder of finite thickness in place of a solid cylinder. By means of Murnaghan potential, the mechanical characteristics of the three materials have been used. Further, the dispersion relations for both the cases have been obtained in terms of the Bessel and modified Bessel functions. In order to validate the present findings, two particular cases have been derived that matches with the previous works. The first case is obtained by removing the outermost cylinder, while the second case has been derived by removing the imperfection in addition to that. To summarize the computations, a complete numerical simulation has been carried out, and graphical illustrations have been shown to aid the mathematical analyses.

Torsional Wave Propagation and Vibration Reducing of Phononic Crystal Pipe With Periodic Torsional Support

Abstract In this paper, torsional vibration band gap properties of a fluid filled pipe were studied by using the transfer matrix method (TMM). By comparing the results obtained from the fem software, the established torsional dynamic model and the proposed method were verified. The effects of pipe wall's material and parameters of support on the torsional vibration band gap properties were analyzed. Furthermore, the relationship between torsional displacement and vibration band gaps was investigated. These attenuation regions of responses show good agreement with the frequency of Bragg band gaps. Explained the locally resonant (LR) phononic crystals (PCs) band gaps form mechanism from the point of mechanical impedance mismatch theory, the results show that the peak frequency of impedance mismatch defines the beginning of both LRs and Bragg band gaps. In essence, the locally resonant is the same as periodic support from the impedance theory. The results of this paper could give some valuable suggestions on the vibration control of the pipeline system.

Size-dependent torsional wave propagation in FG flexoelectric micro/nanotubes

Size-dependent torsional wave propagation in FG flexoelectric micro/nanotubes

Dynamic behavior of material strength due to the effect of prestress, aeolotropy, non-homogeneity, irregularity, and porosity on the propagation of torsional waves

Dynamic behavior of material strength due to the effect of prestress, aeolotropy, non-homogeneity, irregularity, and porosity on the propagation of torsional waves

Two different temporal domain integration schemes combined with compact finite difference method to solve modified Burgers’ equation

The modified Burgers’ equation has application in various fields such as explosions and sonic boom theory, propagation of torsional waves in thin circular viscoelastic rod, acoustic waves produced by laser radiations, etc. A sixth-order compact finite difference scheme has been used for the space integration. Two different approaches have been followed for time integration. One is the Crank-Nicolson scheme in which the nonlinear term is handled with a quasilinearization process. Another is the strong stability preserving Runge-Kutta method of four stage, third-order convergence (SSP-RK43), in which no linearization is required. The stability analysis for both the schemes has been presented and is shown to be stable. Few test problems have been solved, demonstrating the performance of the proposed techniques. The L2 and L∞ error norms are calculated and are compared with the previous work. The aim of the paper is to solve such an important equation with better accuracy and less computational efforts.

Torsional Wave in a Dissipative Cylindrical Shell Under Initial Stresses

The dispersion relation of torsional wave in a dissipative, incompressible cylindrical shell of infinite length incorporating initial stresses effects is investigated. The governing equation and closed form solutions are derived with the aid of Biot's principle. Phase velocity and damping of torsional wave are obtained analytically and the influences of dissipation and initial stresses are studied in details. We proposed a new method for obtaining the phase and damping velocities of torsional wave in a complex form. Numerical results analyzing the torsional wave propagation incorporating initial stress effects are analyzed and presented in graphs. The analytical and numerical solutions reveal that, the dissipation as well as the initial stresses have notable impacts on the phase velocity of torsional wave in a pre-stressed dissipative cylindrical shell. The numerical results reveal that, the initial stresses and dissipation, considerably, effect the phase velocity of the torsional wave. It has been observed that, any change in dissipation parameter (δ) produces a substantial change in damping velocity of torsional wave. In addition, it can be seen that, the phase velocity increases as the initial stress parameter increases. Finally, the result of numerical simulation illustrated the influence of dissipation and initial stresses on damping and phase velocities of torsional wave propagation. The conclusion made shown the consistency with the Biot's incremental deformation theory, and the effective on model such as engineering mechanics and displacement of particles.