Propagation Properties Of Elastic Waves Research Articles

Tunable wave coupling in periodically rotated Miura-ori tubes.

Origami folding structures are vital in shaping programmable mechanical material properties. Of particular note, tunable dynamical properties of elastic wave propagation in origami structures have been reported. Despite the promising features of origami metamaterials, the influence of the kinematics of tessellated origami structures on elastic wave propagation remain unexplored. This study proposes elastic metamaterials using connected Miura-ori tubes, the kinematics of which are coupled by folding and unfolding motions in a tubular axis; achieved by periodically connecting non-rotated and rotated Miura-ori tubes. The kinematics generate wave modes with localized deformations within the unit cell of the metamaterials, affecting the global elastic deformation of Miura-ori tubes via the coupling of wave modes. Dispersion analysis, using the generalized Bloch wave framework based on bar-and-hinge models, verifies the influence of kinematics in the connected tubes on elastic wave propagation. Furthermore, folding the connected tubes changes the coupling strength of wave modes between the kinematics and global elastic deformation of the tubes by breaking the ideal kinematics. The coupling of wave modescontributes to the formation of the band gaps and their tunability. These findings enable adaptive and in situ tunability of band structures to prohibit elastic waves in the desired frequency ranges.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Elastic waves in fluid-saturated porous materials with a couple-stress solid phase

Fluid-saturated porous materials have attracted extensive attention in micro/nanoscale applications owing to their excellent mechanical properties. Couple-stress theory can be used to depict the size effect of micro/nanoelastic materials, which cannot be ignored when the internal characteristic length of materials is comparable with the material size or wavelength. However, it has not been extended to porous materials. In this paper, we investigate the size effect of elastic-wave propagation in micro/nano fluid-saturated porous materials by combining couple-stress theory with Biot theory and introducing the higher order micro-inertia effect, establish the motion equations for elastic waves in fluid-saturated porous materials containing a couple-stress solid phase. The reflection and transmission properties of elastic waves at the interface between an elastic solid and a couple-stress fluid-saturated porous material are numerically analyzed. The results suggest that an increase in characteristic length can lead to an increase in the phase velocity of shear wave and further influence the reflection and transmission of elastic waves. A comparison among the proposed theory, Biot theory and experimental data indicates that the introduction of couple-stress and higher order micro-inertia effects allows for a more accurate calculation of the propagation properties of elastic waves in fluid-saturated porous materials, and it can provide a theoretical basis for applications of elastic waves in micro/nano porous materials, such as nondestructive testing.

Influence of boundary condition on the sound velocity in granular assembly: Spiral tube versus cylinder

The properties of elastic wave propagation in granular assemblies have become a subject of immense interest in recent years, however, the influence of different confinements on the sound velocity is seldom investigated. This study provides a method to determine the contact point between spherical, super-ellipsoidal particles and complex boundaries, in order to investigate how the anisotropy induced by particle shape or boundary affects velocity. Taking cylinder and spiral tube confinements as examples, the falling process of spherical and super-ellipsoidal assemblies are simulated to verify the validation by the discrete element method (DEM). The convergence of the kinetic energy during the falling process and the equilibrium state with zero residual kinetic energy guarantees the stability and correctness. On the basis, elastic wave propagation of spherical and super-ellipsoidal systems in spiral tube and cylindrical confinements under different pressures are modelled, and sound velocities are calculated. The effective medium theory (EMT), granular solid hydrodynamics (GSH), and elastic stiffness are used to interpret the relationship between velocity and stress in cylindrical confinement. However, the results in the spiral tube deviate from EMT and GSH, which means the boundary affects velocity significantly. The difference of velocity between spiral tube and cylinder is qualitatively explained from the perspective of anisotropy of contact force distribution in the system. The simulation results show that anisotropy introduced by the curved surface affects the acoustic properties greatly. The method used for spiral boundary is also suitable for other complicated confinements.

Engineering bandgaps in TPMS structures by breaking their underlying symmetries

Triply periodic minimal surface (TPMS) structures are an attractive choice for multifunctional applications—their surface curvature reduces stress concentration locations, they provide excellent stiffness- and strength-to-density scaling, and they are robust thermal and acoustic energy dissipators. Here, we study their elastic wave propagation properties and investigate the possibility of generating wave attenuation bandgaps by breaking their underlying symmetries. We limit our focus to the most used TPMS geometry: the gyroid lattice. We model three dimensional shell-based gyroid structures and calculate their dispersion properties using the finite element approach. Our analysis shows that a significant number of degeneracies exist within the gyroid lattice band structure. We then investigate the possibility of lifting these degeneracies by breaking the underlying symmetric architecture in two distinct ways. First, we disturb the symmetry by altering material properties across the line of symmetry; the effects of elastic and density perturbations are individually studied. Next, we break the symmetry by altering the lattice geometry by directionally stretching the lattice along the x, y, and z directions, individually. Our results show that while both material and geometrical perturbations help create additional directional and polarized bandgaps, both methods result in very different wave propagation and attenuation behaviors.

Thermoelastic wave characteristics in a hollow cylinder using the modified wave finite element method

This paper represents a modified formulation of the wave finite element (WFE) method for propagating analysis of thermoelastic waves in a hollow cylinder without energy dissipation. The 2D-high-order spectral element with the Gauss–Legendre–Lobatto integration is applied into the WFE method, which produces the diagonal mass matrix. Based on the assumption of harmonic displacement fields by Fourier series expansion, the general discretization wave equation is simplified from the 3D problem to 2D. Dispersion properties of elastic wave propagation in the hollow cylinder are computed considering the choice of the spectral element orders, and the results indicate the high efficiency and high accuracy of the modified formulation compared with that of the software Disperse. Then, using the modified formulation, the thermoelastic dynamic equation of the cylinder is derived from the generalized thermoelasticity theory. The propagation of the thermoelastic wave (including two kinds of wave modes) in the cylinder without energy dissipation is discussed in different cases. Finally, wave structures along the radial direction of thermoelastic wave modes are shown at the nondimensional frequency 1.25, which can be used for the recognition of different modes.

Analysis of a Phononic Crystal Constituted of Piezoelectric Layers Using Electrical Impedance Measurement

Active materials are investigated as a tuning possibility for phononic crystals. Electromechanical properties of piezoelectric materials electrical and mechanical variables are coupled. Thus, the propagation properties of elastic waves can be tuned using electrical impedance load connected to the piezoelectric layer. In this study, a theoretical one-dimensional model is proposed to calculate the electrical impedance of an active layer located inside a finite periodic structure including both piezoelectric and passive layers. Depending on the electrical impedance load, various effects on the position and the amplitude of the electrical resonance are observed in very good agreement, between experimental and theoretical results.

Dispersion Analysis of Triangle‐Based Finite Element Method for Acoustic and Elastic Wave Simulations

AbstractAcoustic and elastic wave equations are discretized by finite element method with triangles and central difference scheme in space and time, respectively. The generalized eigenvalue problems are constructed to analyze the numerical dispersion of the finite element method. Three types of mass finite element method, which are consistent finite element method (CFEM), lumped finite element method (LFEM) and mixed finite element method (MFEM), are implemented to the numerical scheme, and the numerical dispersion is under a comprehensive study. Then, the MFEM is adopted to investigate the behavior of numerical anisotropy in terms of four typical triangle meshes. Comparing the numerical dispersion and anisotropy behavior when MFEM uses different interpolation orders, one can easily find that numerical error decreases as the interpolation order increases. Specifically, the numerical dispersion and anisotropy are negligible when third‐order interpolation is used. Finally, controlling the other impact factors, the dispersive properties of elastic wave propagation in elastic medium with various velocity ratios are analyzed, and the results of numerical dissipation are presented at the end of this paper.

Size-dependent dispersion characteristics in piezoelectric nanoplates with surface effects

In this paper, surface effects on the dispersion characteristics of elastic waves propagating in an infinite piezoelectric nanoplate are investigated by using the surface piezoelectricity model. Based on the surface piezoelectric constitutive theory, the presence of surface stresses and surface electric displacements exerting on the boundary conditions of the piezoelectric nanoplate is taken into account in the modified mechanical and electric equilibrium relations. The partial wave technique is employed to obtain the general solutions of governing equations, and the dispersion relations with surface effects are expressed in an explicit closed form. The impacts of surface piezoelectricity, residual surface stress and plate thickness on the propagation properties of elastic waves are analyzed in detail. Numerical results show that the dispersion behaviors in piezoelectric nanoplates are size-dependent, and there exists a critical plate thickness above which the surface effects may vanish.

A new type of multilayered resonant structure

We propose a new type of multilayered resonant structure that is named as tail-resonant structure. It is composed of two components, i.e., a tail component and a resonance component. Compared with traditional monolayered resonant structures, tail-resonant structures have a unique advantage, i.e., it can realize the effective coupling of waves from one medium with large impedance to the other medium with extremely small impedance. By using analytical and numerical methods, we discuss propagation properties of elastic waves in two kinds of tail-resonant structures. In these resonant structures, the tail component can amplify the amplitude of waves; the resonant component can choose proper frequencies of waves for realizing the effective coupling of waves between two media with large impedance mismatching.

Elements of study on dynamic materials

As a preliminary study to more complex situations of interest in small-scale technology, this paper envisages the elementary propagation properties of elastic waves in one-spatial dimension when some of the properties (mass density, elasticity) may vary suddenly in space or in time, the second case being of course more original. Combination of the two may be of even greater interest. Toward this goal, a critical examination of what happens to solutions at the crossing of pure space-like and time-like material discontinuities is given together with simple solutions for smooth transitions and numerical simulations in the discontinuous case. The effects on amplitude, speed of propagation, frequency changes and the appearance of a Doppler-like effect are demonstrated although the whole physical system remains linear.

Steady state and time-dependent energy equilibration in two-dimensional random elastic slabs

The static and dynamic transport properties of elastic wave propagation through two-dimensional random slabs without internal reflection were studied at two different scattering parameters: one for Rayleigh scattering and the other for Rayleigh-Gans scattering. The spatial distribution and temporal evolution of shear (s-) and compressional (p-) wave energy densities inside the slabs were calculated by solving the radiative transfer equation and the generalized diffusion equation (GDE). The comparison of their results can determine the region of validity of the GDE. The process of energy equilibration between the two wave modes was demonstrated explicitly as well as the process of diffusion. The depth inside a slab that is needed to reach energy equilibration or diffusive behavior is found to be dependent on source polarization. The results also show that the bulk equilibration ratio can be found inside a sample only when the sample is sufficiently thick. Deviations of the equilibration ratio from its bulk value are found near the output surface due to the absence of in-flow energy flux. The behavior of the deviations is sensitive to the scattering parameter but independent of source polarization.

Propagation properties of elastic waves in semi-infinite phononic crystals and related waveguides

The transmission and reflection coefficients of two-dimensional semi-infinite solid-solid phononic crystal systems and fluid-fluid phononic waveguide structures have been investigated. The numerical results show that the transmission spectra for longitudinally and transversally polarized incident waves are different, and the spectra of the transmission and reflection coefficients of the semi-infinite system agree well with the band structure. The numerical results show that when a guided wave incident, localized modes are excited, and different polarities have different coupling efficiencies with the incident guided wave. At the same time, far from the cutoff frequency, the guided wave couples out of semi-infinite waveguide highly efficiently.

Finite element equations and numerical simulation of elastic wave propagation in two-phase anisotropic media

Based on Biot theory of two-phase anisotropic media and Hamilton theory about dynamic problem, finite element equations of elastic wave propagation in two-phase anisotropic media are derived in this paper. Numerical solution of finite element equations is given. Finally, properties of elastic wave propagation are observed and analyzed through FEM modeling.

Research on propagation properties of elastic waves in two-phase anisotropic media

With the development of seismic engineering and seismic exploration of energy, the underground media that we study are more and more complicated. Conventional anisotropy theory or two-phase isotropy theory is difficult to describe anisotropic media containing fluid, such as fractures containing gas, shales containing water. Based on Biot theory about two-phase anisotropy, with the use of elastic plane wave equations, we get Christoffel equations. We calculate and analyze the effects of frequency on phase velocity, attenuation, amplitude ratio and polarization direction of elastic waves of two-phase, transversely isotropic media. Results show that frequency affects slow P wave the greatest among the four kinds of waves, i.e., fast P wave, slow P wave, fast S wave and slow S wave. Fluid phase amplitude to solid phase amplitude ratio of fast P wave, fast S wave and slow S wave approaches unit for large dissipation coefficients. Polarization analysis shows that polarization direction of fluid phase displacement is different from, not parallel to or reverse to, that of solid phase displacement in two-phase anisotropic media.

Effects of tensile loading on the properties of elastic-wave propagation in a strand

Effects of tensile loading on the properties of longitudinal-mode elastic-wave propagation in a 1.52-cm-diam, seven-wire strand used for prestressed concrete structures were investigated experimentally. In an unloaded state, the wave propagation properties in strand matched those seen in individual wires comprising the strand, namely, straight center wire and helical outer wires. In the strand, however, extraneous signals were found to be produced from the propagating wave due to physical interactions between the adjacent wires. Under tensile loading, it was observed that a certain portion of the frequency components of the wave became highly attenuative and, thus, absent in the frequency spectrum of the wave. The center frequency of this missing portion, called notch frequency, was found to increase linearly with log N, where N is the applied tensile load. In addition, on both sides of the notch frequency, the wave exhibited a large dispersion in a manner similar to the behavior near a cutoff frequency. Possible causes of the observed behavior under tensile loading are discussed.

Radiation and propagation properties of elastic waves on conical shells

This talk discusses the radiation and propagation properties of elastic waves on conical shells by making use of a previously developed theory [Y. P. Guo, J. Acoust. Soc. Am. 92, 2388 (A) (1992)]. The three types of dominant waves in the mid-frequency domain, namely, the compressional, shear, and flexural waves are examined. It is shown that when propagating toward the apex of the cone, shear waves are turned back at caustics but compressional waves are cut off only where they have become subsonic. The radiation losses of these waves are also discussed. It is found that compressional waves radiate much more efficiently than shear waves on a cone, indicating that much less compressional wave energy would be reflected by a cone-shaped endcap. This is indeed what was observed in these scattering experiments.

Signal Generated Seismic Noise

Summary A typical seismic pulse generates a certain amount of incoherent wavemotion due to the scattering effect of small variations in the elastic properties of the Earth. This is recorded as ‘noise’ along with the main signal. When the problem is treated statistically, mean square amplitudes of the scattered waves, and fluctuations in amplitude and phase of the incident signal, can be calculated for wave-motion which is simpleharmonic in time. The results at low frequencies for an incident plane wave in an unbounded medium have already been reported. Extension to higher frequencies shows that the Rayleigh fourth-power law holds only for wavelengths greater than the linear extent of the scattering centres. If the inhomogeneities lie near a plane free surface, Rayleigh waves are generated. Amplitudes have been calculated for incident plane P and S waves. 1. Theory Even if the detailed structure of a heterogeneous Earth were known, the calculation of the precise properties of an elastic wave passing through such a region would be difficult if not impossible, depending upon the degree of heterogeneity. If we consider a completely heterogeneous region, one whose properties are only describable statistically, then the calculation of the properties of elastic wave propagation again becomes feasible. But now the properties of the scattered waves are themselves only describable statistically. If the scattering region is large compared with the size of individual scattering centres and the fluctuations in the elastic parameters are generally small, then the variation of the elastic parameters can be considered to be random and the properties of the scattered waves can be calculated in terms of the correlation functions. These functions are defined in the following manner :