Blocking property of energy vortices in elastic waveguides

Abstract

Energy vortices in time-averaged energy flows of time-harmonic fields are considered. The purpose of the paper is to verify the supposition that the energy flux along an elastic waveguide with an obstacle is blocked completely at the stop frequencies by the vortices. It is hoped that this work will draw attention to the analogy between energy and fluid flows which is potentially fruitful for understanding various wave phenomena. The normal-mode diffraction by a surface punch on an elastic layer is taken as an example. For tracing energy streamlines in the near field up to the obstacle, a special efficient semianalytical approach has been developed. To illustrate the stated supposition, plots of transmission coefficients versus frequency and figures of the near-field streamline structures are given.

Elastic wave excitation in a layer by piezoceramic patch actuators

“…The following steps (derivation of the final form of the matrix elements of the system, substitutions for the elimination of exponentially growing components, and regularization by taking into account the asymptotics of the unknown t m, k at k ∞) are more cumbersome but basically similar to those described in [13,14]. A detailed description of the scheme is given in [15] together with the results of a numerical analysis of the wave and energy characteristics of the system under study.…”

“…Later, this method was generalized to the case of matrix integral equations (a contact with adhesion) and to plane-strain problems with an integral operator of type (2.10), but with a given right-hand side f(x) instead of the unknown v(x) and with a single segment Ω = [-a, a] instead of the set of strips under consideration, Ω = ∪Ω m [14]. These changes required some modification of the method, whose general scheme used for solving the equation q = f, |x| < a, is as follows.…”

“…The regularization of system (3.3) that provides for the stable numerical truncation is performed by replacing t k with their asymptotics for ∀k > N 1 > N. The behavior of t k with k ∞ is determined by the order of singularity of q(x) at x ±a (see [14]). …”

Wave refraction at an interface: Snell’s law versus Chapman’s law

“…3), the vector nature of acoustic intensity measurements, as opposed to measurements of scalar acoustic pressure, revolutionized the practice of noise control. Modern applications of wave energy streamlines include studies of wave front dislocations, 8,9 source localization, 7,10 energy vortices in compressible fluids 3,6 and elastic waveguides, 11,12 nanoscale thermal radiation, 13,14 photon tunneling, 13 and bounded beam diffraction, including the Goos-Hänchen shift. 13 Examples of energy streamlines for various wave fields can be found in Refs.…”

Wave Propogation and Crack Detection in Layered Structures

“…Therefore, the integral equation methods give the chance to discover and explore fine wave phenomena escaping usually with other approaches. It allowed us, in particular, to investigate the structure of averaged time-harmonic energy flows in layered and stepped waveguides with energy vortices and backward fluxes [5,6], as well as to clear up their role in resonance extinguishing of surface waves [7,8].…”