Propagation Of Transverse Elastic Waves Research Articles

Tunable Wave-Propagation Band gap via Stretching Kirigami Sheets

This study examines Bragg's band gap and its mechanical tuning in a stretch-buckled kirigami sheet with ``zig-zag'' distributed parallel cuts. When stretched beyond a critical threshold, the kirigami buckles out of plane and generates a three-dimensional periodic architecture. Our theoretical calculation, numerical simulation, and experiments confirm the transverse elastic wave-propagation band gaps and their correlation to stretching. This result opens an avenue of using kirigami as a simple and effective approach for creating and adapting periodicity for wave-propagation control.

A Localized Collocation Solver Based on T-Complete Functions for Anti-Plane Transverse Elastic Wave Propagation Analysis in 2D Phononic Crystals

In this paper, we introduce a novel localized collocation solver for two-dimensional (2D) phononic crystal analysis. In the proposed collocation solver, the displacement at each node is expressed as a linear combination of T-complete functions in each stencil support and the sparse linear system is obtained by satisfying the considered governing equation at interior nodes and boundary conditions at boundary nodes. As compared with finite element method (FEM) results and the analytical solutions, the efficiency and accuracy of the proposed localized collocation solver are verified under a benchmark example. Then, the proposed method is applied to 2D phononic crystals with various lattice forms and scatterer shapes, where the related band structures, transmission spectra, and displacement amplitude distributions are calculated as compared with the FEM.

Valley anisotropy in elastic metamaterials

Valley, as a new degree of freedom, raises the valleytronics in fundamental and applied science. The elastic analogs of valley states have been proposed by mimicking the symmetrical structure of either two-dimensional materials or photonic valley crystals. However, the asymmetrical valley construction remains unfulfilled. Here, we present the valley anisotropy by introducing asymmetrical design into elastic metamaterials. The elastic valley metamaterials are composed of bio-inspired hard spirals and soft materials. The anisotropic topological nature of valley is verified by asymmetrical distribution of the Berry curvature. We show the high tunability of the Berry curvature both in magnitude and sign enabled by our anisotropic valley metamaterials. Finally, we demonstrate the creation of valley topological insulators and show topologically protected propagation of transverse elastic waves relying on operating frequency. The proposed topological properties of elastic valley metamaterials pave the way to better understanding the valley topology and to creating a new type of topological insulators enabled by an additional valley degree of freedom.

A meshfree local RBF collocation method for anti-plane transverse elastic wave propagation analysis in 2D phononic crystals

In this paper, a meshfree or meshless local radial basis function (RBF) collocation method is proposed to calculate the band structures of two-dimensional (2D) anti-plane transverse elastic waves in phononic crystals. Three new techniques are developed for calculating the normal derivative of the field quantity required by the treatment of the boundary conditions, which improve the stability of the local RBF collocation method significantly. The general form of the local RBF collocation method for a unit-cell with periodic boundary conditions is proposed, where the continuity conditions on the interface between the matrix and the scatterer are taken into account. The band structures or dispersion relations can be obtained by solving the eigenvalue problem and sweeping the boundary of the irreducible first Brillouin zone. The proposed local RBF collocation method is verified by using the corresponding results obtained with the finite element method. For different acoustic impedance ratios, various scatterer shapes, scatterer arrangements (lattice forms) and material properties, numerical examples are presented and discussed to show the performance and the efficiency of the developed local RBF collocation method compared to the FEM for computing the band structures of 2D phononic crystals.

Transient Response of a Multilayered Composite Rotating Airfoil Under Slicing-Impact Loading

In this paper, a semiclosed form of numerical solution is obtained for a slicing-impact edge loading on a multilayered composite airfoil. The analytical derivation of the governing partial differential equation simulates the transient event of the slicing process by considering the moving bird in the form of a soft-body impactor as it comes into contact with the rotating fan blades modeled as prestressed airfoil due to centrifugal force field. The oblique-impact formulation of a composite pretwisted fan blade includes the effect of both the contact-impact loads as well as the Coriolis forces. The consideration of coupled longitudinal–transverse elastic wave propagation in a rotating coordinate system is a key to correctly predict the impact response of a blade mounted on a rotor shaft. The dynamic loading on the airfoil and its transient response produced during the bird strike is determined by solving the coupled nonlinear dynamical equations governing the movement of the bird slice in the time domain using a sixth-order Runge–Kutta technique.

Mathematical modeling of elastic wave propagation in crystals: 3D-wave surfaces

A new method for pure modes of elastic waves search in crystals is presented. The method is based on the analysis of 3D-surfaces of phase velocities and differs from the known analogous methods by accounting for the piezoeffect. The piezoelectric corrections have an essential effect on the result of the search. The computer code is prepared to construct these surfaces and their sections by the base planes of a crystal. The code also permits to calculate the directions of pure longitudinal and pure transverse elastic wave propagation on these surfaces.

Modelling of wave propagation in composite plates using the time domain spectral element method

This paper presents results of numerical simulation of the propagation of transverse elastic waves corresponding to the A0 mode of Lamb waves in a composite plate. The problem is solved by the Spectral Element Method. Spectral plate finite elements with 36 nodes defined at Gauss–Lobatto–Legendre points are used. As a consequence of the selection of Lagrange polynomials for element shape functions discrete orthogonality is obtained leading to the diagonal form of the element mass matrix. This results in a crucial reduction of numerical operations required for the solution of the equation of motion by time integration. Numerical calculations have been carried out for various orientations and relative volume fractions of reinforcing fibres within the plate. The paper shows how the velocities of transverse elastic waves in composite materials depend on the orientation and the relative volume fraction of the reinforcement.

Trapping of vibrational energy in crumpled sheets.

We investigate the propagation of transverse elastic waves in crumpled media. We set up the wave equation for transverse waves on a generic curved, strained surface via a Langrangian formalism and use this to study the scaling behavior of the dispersion curves near the ridges and on the flat facets. This analysis suggests that ridges act as barriers to wave propagation and that modes in a certain frequency regime could be trapped in the facets. A simulation study of the wave propagation qualitatively supported our analysis and showed interesting effects of the ridges on wave propagation.

Acoustic properties of a layered medium with randomly distributed layer thicknesses

We study here the acoustic properties of a layered medium with randomly distributed layer thicknesses. The propagation of transverse elastic waves with polarization in the direction parallel to the laminations is investigated. The bulk modes and the transmission coefficients in a finite sample are calculated by the use of the transfer-matrix method. It is found that the density of states of these modes is drastically affected by the extent of disorder of such a system. Owing to the randomness, most of the waves are localized in the direction perpendicular to the laminations, but there still exist some waves with special frequencies which are completely extended. In some special cases we can analytically determine the frequencies of these extended waves. On the basis of this calculation a possible application of such structures is suggested.

Thermoelasticity at cryogenic temperatures

A theory of thermoelasticity is developed which is suitable for application at cryogenic temperatures. The thermodynamic functions are so chosen as to give correct predictions with experimental findings of second-sound wave speeds in NaF, in the temperature range 8–20 K and in Bi, in the temperature range 1–4 K. After the non-linear theory is presented, a linearized theory is developed. A uniqueness theorem is provided for the linearized theory on an unbounded domain. The question of a half-space heated on its boundary is addressed and, in particular, the question of transverse elastic wave propagation is studied. Finally, a simplified theory in which only unidirectional solutions are allowed is examined.

Transverse elastic waves in periodically layered infinite and semi-infinite media

The propagation of transverse elastic waves both perpendicular and parallel to the laminations of infinite and semi-infinite periodically layered media is studied. The displacement fields and the dispersion relations for such waves are obtained analytically, and the latter are solved numerically to yield the corresponding dispersion curves. It is shown that a semi-infinite medium layered periodically parallel to its stress-free surface can support shear horizontal surface acoustic waves that have no counterpart in a homogeneous medium. Finally, the dynamical elastic Green's function for a semi-infinite medium layered periodically parallel to its stress-free surface is obtained, and its possible application to Brillouin scattering studies of the surface acoustic waves on such a medium is discussed.

Transverse elastic waves in periodically layered infinite, semi-infinite, and slab media

The propagation of transverse elastic waves both perpendicular and parallel to the laminations of infinite and semi-infinite periodically layered media is studied. The displacement fields and the dispersion relations for such waves are obtained analytically, and the latter are solved numerically to yield the corresponding dispersion curves. It is shown that a semi-infinite medium layered periodically parallel to its stress-free surface can support shear horizontal surface acoustic waves that have no counterpart in a homogeneous medium. Finally, the dynamical elastic Green’s function for a semi-infinite medium layered periodically parallel to its stress-free surface is obtained, and its possible application to Brillouin scattering studies of the surface acoustic waves on such a medium is discussed.

A comparative study on transverse elastic wave propagation in laminates: Subsonic case

Many approximate theories have been advanced for the analysis of elastic wave propagation in layered composites. Most comparisons between these theories and the linear theory of elasticity have been restricted to cases of harmonic wave propagation. In this paper, such comparisons are made in a somewhat more demanding context: namely, the steady-state response of an unbounded periodically layered medium to a moving subsonic load, simulated by a self-equilibrating body force. Both the load speed and load thickness are adjustable, lending a valuable flexibility to the study. The approximate models treated are as follows: the effective stiffness theory, the effective modulus theory, a Nayfeh and Gurtman-type mixture theory, and a Hegemier-type theory of interacting continua. All responses are assumed to have achieved a steady state, and a Fourier transform is used with the linear theory of elasticity. Inversion is achieved numerically, through use of the Fast Fourier Transform. It is found that the effective stiffness theory is the most accurate overall of the approximate theories considered though not entirely satisfactory, and that, for this theory, load thickness, rather than load speed, is the decisive parameter.

Propagation of Transverse Elastic Waves in Polyisobutylene under Various Pressures

The velocity and the absorption coefficient of 2-Mc transverse elastic waves in polyisobutylene (molecular weight, 1.35 × 106) have been measured at pressures up to 1400 atm for temperatures of 10°C and 20°C. Pulsed signals are conducted into and out of a thin sample via Y-cut cylinders of crystalline quartz to which the sample is bonded. The object of the measurements is to determine δT/δP for constant behavior—in this case, for constant dynamic mechanical properties in shear. Closely similar derivatives are already known on the basis of (1) the behavior of the absorption maximum for bulk waves; (2) dynamic mechanical properties in compression; (3) hydrogen nuclear magnetic resonance absorption line width; (4) calculations based on a theory due to F. Bueche. All of these results, as well as the present measurement, yield values in the neighborhood of 0.02 C°/atm for δT/δP. (Assisted by the Office of Naval Research.)

A New Method for Continuous Viscosity Measurement. General Theory of the Ultra-Viscoson

A new continuous ultrasonic viscometer employing a pulsed resonant exponentially damped magnetostrictive strip is described and treated theoretically. Properties of viscoelastic materials affecting the propagation of transverse elastic waves are derived and are related to the response of the viscometer. Typical applications of the use of the ultrasonic viscometer are presented.