Waves In Cylinder Research Articles

The spectral methods for the propagation of thermoelastic waves in multilayer cylinders based on nonlocal strain gradient elasticity

The spectral methods for the propagation of thermoelastic waves in multilayer cylinders based on nonlocal strain gradient elasticity

Propagation phenomena for a nonlocal reaction-diffusion model with bounded phenotypic traits

In this paper we study the stability of cylinder front waves and the propagation of solutions of a nonlocal Fisher-type model describing the propagation of a population with nonlocal competition among bounded and continuous phenotypic traits. By applying spectral analysis and separation of variables we prove the spectral and local exponential stability of the cylinder waves with the noncritical speeds in some exponentially weighted spaces. By combining the detailed analysis with the spectral expansion and the special construction of sub-supersolutions, we further prove the uniform boundedness of the solutions and the global asymptotic stability of the cylinder waves for more general nonnegative bounded initial data, and prove that the spreading speeds and the asymptotic behavior of the solutions are determined by the decay rates of the initial data. Our results also extend some classical results on the stability of planar waves for Fisher-KPP equation to the nonlocal Fisher model in multi-dimensional cylinder case.

Effect of Electrical Boundary Conditions and Direction of Polarization of Piezoceramics on Spectral Characteristics of Axisymmetric Acoustoelectric Waves in Hollow Cylinder

Effect of Electrical Boundary Conditions and Direction of Polarization of Piezoceramics on Spectral Characteristics of Axisymmetric Acoustoelectric Waves in Hollow Cylinder

Circumferential Semianalytical Finite Element Method for the Analysis of Circumferential Guided Waves in an Anisotropic Hollow Cylinder

This paper presented a circumferential semianalytical finite element method (CSAFEM) to examine the distinctive wave characteristics of circumferential guided waves (CGWs) in anisotropic hollow cylinders. This methodology models the radial displacement using finite elements while expanding the circumferential displacements as harmonic exponentials. A weak‐form wave motion equation in an anisotropic hollow cylinder is formulated using Hamilton’s principle. Phase velocity curves are introduced to visualize the influence of anisotropy and the ratio of diameter to wall thickness (OD/WT) on wave propagation. The CSAFEM results are validated against analytical solutions for CGWs in isotropic hollow cylinders, achieving excellent agreement. This methodology extends to materials with complex symmetries, including triclinic and orthorhombic types. Numerical examples demonstrate that the OD/WT ratio significantly influences the phase velocity spectra of CGWs in the cylinders. In addition, the study explores the relationship between a planar structure and an annulus as the OD/WT ratio approaches infinity, highlighting unique wave phenomena specific to curved waveguides. This unique new mode appears at the initiation of the CA0 mode because the inner surface does not support the propagation of surface waves. This phenomenon is observed in isotropic, orthotropic, and triclinic materials.

FREE VIBRATION MODELING IN A FUNCTIONALLY GRADED HOLLOW CYLINDER USING THE LEGENDRE POLYNOMIAL APPROACH

Introduction: The building industry is under increasing pressure to maximize performance while reducing the costs and the environmental impact. To solve this problem, a new type of materials, i.e., functionally graded materials (FGMs), are proposed. These materials have the advantage of being able to withstand harsh environments without losing their properties. Purpose of the study: The paper aims to further extend the understanding of the propagation modes and characteristics of guided waves in FGM cylinders with infinite lengths. In the course of the study, we analyzed a cylindrical shell composed of three annular layers, each separated by a gradient layer across the wall thickness. A modeling tool based on the Legendre orthogonal polynomial method is proposed in the paper. Methods: The method applied results in an eigenvalue/eigenvector problem. The boundary conditions are integrated into the constitutive equations of guided wave propagation. The phase velocity and normalized frequency dispersion curves are calculated. Besides, the displacement distributions and stress field profiles for a functionally graded cylinder with various graded indices in both modes (axisymmetric and symmetric) are calculated and discussed. The results show a constant fluctuation of effective FGM material. Results: It was found that the phase velocity curves of the same mode decrease as the exponents of the power law increase. In addition, the boundary conditions have a greater impact on the normal stresses. The accuracy and effectiveness of the improved orthogonal polynomial method are demonstrated through a comparison of the exact solution obtained by an analytical-numerical method and our numerical results.

Excitation response analysis of hollow cylinders under helical surface tractions for dominant flexural guided wave generation

Dominant flexural mode excitation of helical waves in hollow cylinders by applying helical surface tractions, equivalent to exciting obliquely propagating plate waves in the unwrapped plate, is reported. However, this approach cannot be generalized with theoretical underpinnings. The response of hollow cylinders under helical surface tractions is investigated using normal mode expansion method. Purity of the target flexural mode depends on the mode wave structures at excitation frequencies and the helix angle of the helical excitation. With helical surface tractions, only flexural modes with large circumferential and longitudinal displacements, usually torsional flexural modes, can be effectively generated. The target flexural mode and excitation frequency should be selected carefully for better purity. The helix angle for the target mode should diverge considerably from other modes, especially those with large circumferential and longitudinal displacements. The apparently oblique propagation of the flexural mode can also be explained theoretically. The helically excited flexural mode comprises two orthogonal wave structures with identical flexural modes that are out of phase in the propagation direction, causing periodically changing circumferential orientation of the combined wave structure and oblique wave front. Finite element simulations and experiments agree well with theoretical predictions.

Propagation of electroelastic waves in a continuously inhomogeneous piezoceramic solid cylinder†

AbstractThe propagation of axisymmetric electroelastic waves in solid inhomogeneous piezoceramic cylinders based on 3D electroelasticity is considered. The surface of the cylinder is free of loads and covered with thin electrodes. A resolving system of differential equations in partial derivatives with variable coefficients is presented. An efficient numerical–analytical method to solve this problem is proposed. Components of the elasticity tensor, of the mechanical and electric displacement vector, the electrostatic potential and of the components of the stress tensor are presented by running waves in an axial direction. The three‐dimensional system of resolving equation is reduced to a boundary‐value problem described by a system of differential equations. The spectral characteristics of running waves in the solid cylinders for homogeneous and continuously heterogeneous piezoceramic materials are presented and comparative analysis is carried out.

Hydrodynamic performance of a horizontal cylinder wave energy converter in front of a partially reflecting vertical wall

Based on linear potential flow theory, this study investigates the hydrodynamic performance of a horizontal cylinder wave energy converter (WEC) in front of a wall. The wall is assumed to be a partially reflecting vertical one, and the circular cylinder is fully submerged and restricted to only heave motion. The structural hydrodynamic quantities, including wave excitation force, added mass coefficient and radiation damping coefficient, are estimated using the well-known wide-spacing approximation, and the wave energy capture performance of the device is investigated. The estimation only requires solving the problems of water wave diffraction and radiation by a submerged horizontal cylinder in an open fluid domain, which can be analytically solved using the multipole expansion method. The estimation is validated by comparison with numerical results based on the boundary element method (BEM), and analytical results for the limiting case of a fully reflecting wall. Case studies are presented to clarify the effects of wave frequency, spacing between cylinder and wall, wall reflection and cylinder size on the hydrodynamic quantities and energy capture performance of the WEC. The hydrodynamic problem for regular waves is also extended to irregular waves. The results indicate that the WEC's performance can be significantly improved owing to the presence of a wall, which provides several feasible approaches for capturing more wave energy, such as setting vertical plates behind WECs and installing WECs near caisson breakwaters. This study also provides a reliable method for evaluating the performance of other WECs.

Non-Linear Damping of Surface Alfvén Waves Due to Uniturbulence

This investigation is concerned with uniturbulence associated with surface Alfvén waves that exist in a Cartesian equilibrium model with a constant magnetic field and a piece-wise constant density. The surface where the equilibrium density changes in a discontinuous manner are the source of surface Alfvén waves. These surface Alfvén waves create uniturbulence because of the variation of the density across the background magnetic field. The damping of the surface Alfvén waves due to uniturbulence is determined using the Elsässer formulation. Analytical expressions for the wave energy density, the energy cascade, and the damping time are derived. The study of uniturbulence due to surface Alfvén waves is inspired by the observation that (the fundamental radial mode of) kink waves behave similarly to surface Alfvén waves. The results for this relatively simple case of surface Alfvén waves can help us understand the more complicated case of kink waves in cylinders. We perform a series of 3D ideal MHD simulations for a numerical demonstration of the non-linearly self-cascading model of unidirectional surface Alfvén waves using the code MPI-AMRVAC. We show that surface Alfvén waves damping time in the numerical simulations follows well our analytical prediction for that quantity. Analytical theory and the simulations show that the damping time is inversely proportional to the amplitude of the surface Alfvén waves and the density contrast. This unidirectional cascade may play a role in heating the coronal plasma.

Development of a mathematical model for propagation of ultrasonic waves in thick-walled cylinders in the presence of a thermal gradient – Case of axial scanning

Investigation of variations in ultrasonic wave velocity and travel path in the presence of thermal gradient is essential for accurate ultrasonic testing of engineering components which are subjected to high temperatures. In this paper, a mathematical model is developed for calculation of the wave velocity and travel path in thick-walled hollow cylinders that are subjected to thermal gradients during axial scanning. The cylinder is assumed to be homogeneous, isotropic, and made from Structural steel. The independent variables are incidence angle, cylinder outer radius, and temperature of the cylinder’s inner surface. The results obtained from the theoretical model indicate that the wave velocity and travel path are highly sensitive to inner-surface temperature of the cylinder. Moreover, at incidence angles much lower than critical angles (especially at low temperatures), the wave velocity is almost independent of the incidence angle and the travel path is very close to a straight line. However, as the incidence angle approaches one of the critical angles, the wave travel path considerably deviates from a straight line. An experimental setup was designed and built in-house for measuring the longitudinal wave velocity in a steel hollow cylinder in the presence of a thermal gradient. The preliminary experimental results were found to be in good agreement with theoretical results.

Finite Element Simulation of Axisymmetric Elastic and Electroelastic Wave Propagation Using Local-Domain Wave Packet Enrichment

Abstract A local-domain wave packet enriched multiphysics finite element (FE) formulation is employed for accurately solving axisymmetric wave propagation problems in elastic and piezoelastic media, involving complex wave modes and sharp jumps at the wavefronts, which pose challenges to the conventional FE solutions. The conventional Lagrangian interpolations for the displacement and electric potential fields are enriched with the element-domain sinusoidal functions that satisfy the partition of unity condition. The extended Hamilton’s principle is employed to derive the coupled system of equations of motion which is solved using the simple Newmark-β direct time integration scheme without resorting to any remeshing near the wavefronts or post-processing. The performance of the enrichment is assessed for the axisymmetric problems of impact waves in elastic and piezoelectric cylinders and elastic half-space, bulk and Rayleigh waves in the semi-infinite elastic domain and ultrasonic Lamb wave actuation and propagation in plate-piezoelectric transducer system. The element shows significant improvement in the computational efficiency and accuracy over the conventional FE for all problems, including those involving multiple complex wave modes and sharp discontinuities in the fields at the wavefronts.

Efficient semi-analytical simulation of elastic guided waves in cylinders subject to arbitrary non-symmetric loads

In this paper, we present an approach to model the propagation of high-frequency elastic guided waves in solid or hollow cylinders. This formulation requires only discretization of the radial direction, whereas the circumferential direction is approximated via a truncated Fourier series, and the axial direction is described analytically. The model is extended to allow applying arbitrary non-symmetric loads f(r,θ) on the flat cylinder surface. Efficiency is increased by a proposed methodology to limit the number of Fourier coefficients and by the implementation of hierarchical shape functions to dynamically adjust discretization with respect to frequency. Results are validated against conventional finite element applications, demonstrating the accuracy of the model and a reduction of the computing time by three orders of magnitude. Additionally, we apply a matrix function solution for the scaled boundary finite element method leading to a linear solution in the static case.

Stress waves in thick porous graphene-reinforced cylinders under thermal gradient environments

In this paper, the propagation of stress waves in thick porous graphene-reinforced cylinders (TPGRCs) is investigated using a meshless solution based on an axisymmetric model and moving least squares (MLSs) interpolation functions. The cylinders are assumed under a steady state thermal gradient effect along with an initial deflection response obtained from the static solution of the same cylinder subjected to a static internal pressure. To improve the design of such TPGRCs, functionally graded (FG) profiles are considered for the distribution of graphene nanofillers along their radial direction. Moreover, pores are non-uniformly embedded inside the cylinders to decrease the weight of TPGRCs. The material properties of porous and nanocomposite materials are calculated as functions of temperature using a closed cell model and a modified Halpin-Tsai (HS) technique, respectively. Considering structural damping for the system, the influences of embedding porosity, the temperature of each surface, reinforcing with graphene and the thickness of cylinder on the stress wave responses of TPGRCs have been investigated. The results reveal that the increase of porosity volume inside TPGRCs significantly increases the amplitudes and stationary time of deflections; however, it reduces the values of stationary deflections and stresses, along with the reduction of propagation speeds.

A numerical solution of the wave–body interactions for a freely floating vertical cylinder in different water depths using OpenFOAM

In the present study, a finite volume method based on Reynolds-averaged Navier–Stokes equations is developed numerically in OpenFOAM to simulate two-phase flows around a freely floating cylinder in a numerical wave tank (NWT). All numerical computations are carried out using interDyMFoam solver, manipulating dynamic mesh. The left wall of NWT oscillates as a paddle wave-maker to produce desired waves. The accuracy of the current numerical method is confirmed by evaluating the results of some published experimental benchmarks, including the generation of regular waves in NWT and also the response of two fixed and floating objects in waves. Based on the current study findings, OpenFOAM is capable of predicting these cases of wave–structure interaction with good delicacy. Additionally, the moving wall of NWT as a flap-type wave-maker can produce waves with different attributes sufficiently. In the following, the influence of regular waves on a circular cylinder, operating freely in deep water, as well as the effect of the water depth on the cylinder’s movement and forces acting on it are assessed. The results indicated that the change in the water depth has a significant effect on the response of the freely floating cylinder in waves.

Development of a Mathematical Model for Propagation of Ultrasonic Waves in Thick-Walled Cylinders in the Presence of a Thermal Gradient – Case of Circumferential Scanning

Development of a Mathematical Model for Propagation of Ultrasonic Waves in Thick-Walled Cylinders in the Presence of a Thermal Gradient – Case of Circumferential Scanning

Real-time nonlinear cylinder wave force reconstruction in stochastic wave field considering second-order wave effects

This study provides a novel method for reconstructing real-time nonlinear wave forces on a large-scale circular cylinder by considering second-order wave effects. Potential theory is utilized for deriving the expression of wave forces with the measured data of wave elevation. Approximate expressions of quadratic transfer functions are built with undetermined coefficients, which are resolved by using the historical data of measured wave elevation. Two different algorithms, including fast Fourier transform (FFT) and recursive least squares (RLS), are adopted for real-time reconstruction. Hydrodynamic tests are conducted in the wave flume on a circular cylinder to examine the effectiveness of the nonlinear reconstruction method. Comparative results demonstrate that the accuracy of real-time reconstructed wave forces is significantly enhanced by the present method. The over-prediction errors at force crests and the under-prediction errors at force troughs have been reduced. Furthermore, comparative results show that the nonlinear method implemented by the FFT algorithm provides more accurate results, whereas the RLS algorithm is more time cost efficient.

The fractional Kelvin-Voigt model for circumferential guided waves in a viscoelastic FGM hollow cylinder

Compared to the traditional integer order viscoelastic model, a fractional order derivative viscoelastic model is shown to be more accurate. A thorough knowledge of the dispersive characteristics of such model is very essential to the application of guided wave testing technique. In this paper, the guided waves in a fractional Kelvin-Voigt viscoelastic FGM hollow cylinder with material changing in the thickness direction are investigated. The Weyl definition of fractional order derivatives and the extended Legendre polynomial approach are employed for the derivations of the governing equations. The presented approach has the advantage that the solution of the complex partial differential wave equations with variable coefficients is reduced to an eigenvalue problem, which overcomes the shortcomings of the existing iterative methods such as the Newton downhill method and improves computation efficiency. The previous methods for dealing with viscoelastic guided wave transform the wave equations into a matrix determinant problem solved by the iterative methods, which has a very slow calculation speed. Comparisons with the related studies are conducted to validate the correctness of the presented approach, and the convergence of the approach is discussed. The full three dimensional spectrum, phase dispersion curves and attenuation curves are illustrated for various fractional order viscoelastic FGM hollow cylinders. The influences of fractional order, grade field and radius-thickness ratio on dispersion and attenuation curves are illustrated. The difference of the dispersion characteristics between the viscoelastic model and the elastic one is discussed. The influences of fractional order on displacement distributions are also studied.

Viscous Mean Drift Forces on a Floating Vertical Cylinder in Waves and Currents

Viscous Mean Drift Forces on a Floating Vertical Cylinder in Waves and Currents

Detecting lateral inhomogeneity using a 3D Rayleigh wave survey based on numerical simulation and on-site experiment

To deal with the narrow field limitation for the 3D lateral inhomogeneity investigation in the geotechnical engineering, or in urban areas, the paper proposes a radial line survey grid in a cylindrical coordinate system for the Rayleigh wave method. Based upon the cylinder wave features of the wave and the Huygens' principle, the wavefield of the Rayleigh wave recorded by the survey grid can be regarded as a complete 3D wavefield record excited only by one virtual source at the origin, if the energy attenuation is discarded, and the effects of the multiple sources with the conventional 3D survey grid in a rectangular coordinate system are removed. The numerical method simulates the 3D wavefield for homogeneous half-space model and lateral inhomogeneity half-space model (represented by a cavity). The wavefronts of the 3D seismic records with the grid for the numerical models are imaged and the 3D dispersion features of the velocity and ellipticity of the Rayleigh wave are analyzed. Following these, an on-site experiment is carried out using the grid for a 3D detection of a sewage well. The results showed that the 3D seismic records in the far-source region acquired by the survey grid, can directly image the wavefront features of the Rayleigh wave and its distortion by the lateral inhomogeneity in a 3D domain. They also show that the anomalies of the 3D velocity and ellipticity dispersion of the local inhomogeneity are similar to that of water waves are scattered by a solid obstacle, which makes it much easier to recognize a cavity compared to that using the complex dispersion anomalies in a 2D profile or the conventional 3D survey grid in a rectangular system. Moreover, the grid can greatly reduce the work-cost of a 3D survey and be adapted well to narrow areas if the excited source is set at the origin of the radial lines.

Mean viscous drift forces on a fixed vertical cylinder in waves and currents

Mean viscous drift forces on a fixed vertical cylinder in waves and currents