On wave propagation in periodic structures with smoothly varying parameters

The wave propagations in the periodic structure composed of auxetic star-shaped honeycombs are investigated. The matrix of the periodic structure is filled with polymer. The effective material properties of the unit cell of the periodic structure such as the Poisson’s ratio, the Young’s modulus, and the shear modulus are varied with different filling materials. The finite element method is used to solve the wave propagation within the auxetic star-shaped honeycombs. The dispersion analysis of the band structures and iso-frequency contour are presented. The auxeticity is found to have a significant effect on the wave propagation in the honeycomb structure, and the collimation of the auxetic star-shaped honeycomb structure is also studied. Effects of different types of filling on the wave propagation are also investigated. Among three filling types, the outer-filled honeycomb has the best self-collimation effect. The self-collimation of the polymer-filled auxetic honeycomb structure presented in this study can be applied to various acoustic devices.

This review covers the propagation of acoustic surface waves (ASW) in periodic structures. The authors discuss the main types of ASW: Rayleigh waves, Gulyaev?Bleustein waves, Love waves. Shear surface waves which can propagate along a periodically uneven surface of an elastic solid are described in detail. The authors rigorously treat the Bragg reflection of ASW from periodic arrays of grooves on the substrate for the cases of normal, oblique, and side incidence. Reciprocal conversion effects between bulk and surface waves in an array whose period is close to the ASW wavelength are discussed, together with such related effects as the interaction between Rayleigh waves and Lamb modes, acoustic wave transmission through a gap in a piezoelectric material, etc. Laser excitation of ASW and magnetostatic wave propagation in periodic structures are also reviewed.

Metal bellows were found to produce a pure note when air was passed through them over a small range of velocity. An axial rod, restricting the stream to a narrow annular cross-section, was usually essential for speech, and sound was produced also by a narrow stream between the bellows and an external pipe. More powerful notes were obtained when the bellows inside the pipe were replaced by helically finned tubes. The pressure distribution in this arrangement was examined. The phase velocity of the waves inside the pipe was much less than the velocity of sound, and this effect is explained by applying the theory of wave propagation in periodic structures. The ratio of the average frequency, at which an air particle passed the protuberances, to the frequency of the sound emitted was usually about 1·6.

A generic numerical method for predicting the wave propagation in structures with two-dimensional periodicity is presented. The method is based on a combination of Finite Elements and periodic structure theory. A unit cell of the periodic structure is described with finite elements, and a Craig-Bampton reduction is applied to reduce the number of degrees of freedom. Periodic boundary conditions are then applied and the waves propagating in the structure are obtained by solving an algebraic eigenvalue problem. A number of analytical expressions are then used to derive the vibro-acoustic properties of the finite or infinite periodic structure. The method was recently extended to account for heavy fluid loading and material with frequency-dependent properties (typical of acoustic treatments). A number of examples are presented to validate the formulation and demonstrate the possible use of the method for design.

Vichnevetsky Robert. Wave propagation in periodic structures and quantum mechanics. In: Bulletin de la Classe des sciences, tome 75, 1989. pp. 135-163.

Recently significant advances have been made in the development of magnetostatic wave devices for microwave signal processing. This technology, based on slow dispersive magnetostatic wave propagation in magnetically biased films of Yttrium iron garnet, grown by liquid phase epitaq on substrates of gadolinium gallium garnet, has many similarities to SAW technology, and comparisons will be made as appropriate, will be briefly reviewed, together with methods for efficient microstrip transduction, weighting, controlled tapping, and terminations. Wave propagation in periodic structures and application of these structures to the development of tunable high Q two-port resonators will be discussed. The status oblique incidence reflective array devices will be discussed including possible reflecting structures, weighting, and dispersion modification. The paper concludes with a survey of possible magnetostatic devices for GHz signal processing. Wave characteristics

Rayleigh wave manipulation based on phase shift between two periodic surface corrugations

For applications in high-frequency medical ultrasonics, periodic composite materials made by combining a piezoelectric ceramic and an epoxy have aroused interest because of their high electromechanical coupl ing and low acoustic impedance. Composite transducers therefore have high sensitivity and broad band width. These significant advantages have led to considerable theoretical and experimental work on these kinds of new artificial materials. The general Bloch theory for solving acoustic wave propagation in periodic structures in two- and three-dimensions has already been presented in previous papers. Here, numerical calculations for one-dimensional Bloch coupled equation set will be described. This numerical result calculated using truncated Bloch matrix will be compared with the exact solution using the m atrix transmission line method. The purpose of this comparison is to test the accuracy of the truncated Bloch solution, which can not be done for the n ultidimension case, because no exact solution exists. Of special interest is the wide stopband splitting and material loss, characteristic of ceramic-epoxy compos i t es .

Dark matter-wave gap solitons of Bose-Einstein condensates trapped in optical lattices with competing cubic-quintic nonlinearities

We demonstrate existence of waves localized at the interface of two nonlinear periodic media with different coefficients of the cubic nonlinearity via the one-dimensional Gross–Pitaevsky equation. We call these waves the surface gap solitons (SGSs). In the case of smooth symmetric periodic potentials, we study analytically bifurcations of SGSs from standard gap solitons and determine numerically the maximal jump of the nonlinearity coefficient allowing for SGS existence. We show that the maximal jump vanishes near the thresholds of bifurcations of gap solitons. In the case of continuous potentials with a jump in the first derivative at the interface, we develop a homotopy method of continuation of SGS families from the solution obtained via gluing of parts of the standard gap solitons and study existence of SGSs in the photonic band gaps. We explain the termination of the SGS families in the interior points of the band gaps from the bifurcation of linear bound states in continuous nonsmooth potentials.

Scope of this chapter is to review the theory of surface wave propagation in linear, one-constituent, vertically inhomogeneous, dissipative continua. Subjects of discussion will include both forward and inverse modelling. Although the basic theory will be applicable to both Love and Rayleigh waves, most of the attention will be dedicated to Rayleigh waves due to their major relevance in the applications. After reviewing standard results of the theory of surface wave propagation in elastic and weakly dissipative media (including solution of the Lamb’s problem) using the formalism of variational calculus, the full theory of Rayleigh wave propagation is developed for arbitrarily dissipative linear viscoelastic materials. Emphasis is placed on illustrating a technique for the solution of the Rayleigh eigenproblem based on the application of Cauchy’s theorem of complex variable theory. The last section of the chapter is dedicated to illustrate the inverse problem associated with surface wave motion and its properties. The previous results obtained for the solution of the coupled forward problem are used to develop an algorithm for the joint inversion of Rayleigh dispersion and attenuation curves to determine the transversal phase velocity and quality factor of viscoelastic, layered systems. Application of the inversion algorithm is shown through examples using synthetic and real surface wave data.

The method of the parabolic equation and its application in the theory of wave propagation is discussed. Examples of solutions of various physical problems are presented, and the role played by the proposed method in the description of the wave beams and the wave packets in nonlinear and inhomogeneous media is shown. Different ways of moving from the initial equations to the approximate equations of parabolic type are shown, and methods for generalization and improvement are discussed.

On wave propagation in inhomogeneous systems

ABSTRACTThis paper proposes a systematic framework for the development and classification of higher‐order theories for modeling wave propagation in one‐dimensional structural elements. Building upon and organizing the existing higher‐order models, a generalized approach is introduced to construct an entire family of such theories with controllable complexity and accuracy. The methodology enables the inclusion of higher‐order terms in a physically meaningful and mathematically consistent manner, going beyond the classical polynomial extension of displacement fields. The proposed theories leverage traction‐free boundary conditions, leading to accurate wave representation. Preliminary considerations on their implementation in the finite element method are also discussed, laying the foundation for future work focused on advanced finite element formulations.

Interactions beyond nearest neighbors in a periodic structure: Force analysis