Active exterior cloaking of an inclusion with evanescent multipole devices for flexural waves in thin plates.

We present an active exterior cloak for flexural waves propagating in a Kirchhoff plate of infinite extent. The evanescent multipole devices are characterized by Macdonald functions [Formula: see text] of the required order, which, assuming time-harmonic vibrations, are solutions of the fourth-order biharmonic equation. It is shown that in the region of interfering waves, which emanate from the devices, a field is recreated which cancels the incident wave to yield a region of 'stillness'. An inclusion is then positioned in this region for further investigation, with additional attention given to the boundary condition. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

Modeling Full-Field Transient Flexural Waves on Damaged Plates with Arbitrary Excitations Using Temporal Vibration Characteristics.

We propose an efficient semi-analytical method capable of modeling the propagation of flexural waves on cracked plate structures with any forms of excitations, based on the same group of vibration characteristics and validated by a non-contact scanning Laser Doppler Vibrometer (LDV) system. The proposed modeling method is based on the superposition of the vibrational normal modes of the detected structure, which can be applied to analyze long-time and full-field transient wave propagations. By connecting the vibration-based transient model to a power flow analysis technique, we further analyze the transient waves on a cracked plate subjected to different excitation sources and show the influence of the damage event on the path of the propagating waves. The experimental results indicate that the proposed semi-analytical method can model the flexural waves, and through that, the crack information can be revealed.

One-way interfacial waves in a flexural plate with chiral double resonators.

In this paper, we demonstrate a new approach to control flexural elastic waves in a structured chiral plate. The main focus is on creating one-way interfacial wave propagation at a given frequency by employing double resonators in a doubly periodic flexural system. The resonators consist of two beams attached to gyroscopic spinners, which act to couple flexural and rotational deformations, hence inducing chirality in the system. We show that this elastic structure supports one-way flexural waves, localized at an interface separating two sub-domains with gyroscopes spinning in opposite directions, but with otherwise identical properties. We demonstrate that a special feature of double resonators is in the directional control of wave propagation by varying the value of the gyricity, while keeping the frequency of the external time-harmonic excitation fixed. Conversely, for the same value of gyricity, the direction of wave propagation can be reversed by tuning the frequency of the external excitation. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 2)'.

Flexural vibration systems with gyroscopic spinners.

In this paper, we study the spectral properties of a finite system of flexural elements connected by gyroscopic spinners. We determine how the eigenfrequencies and eigenmodes of the system depend on the gyricity of the spinners. In addition, we present a transient numerical simulation that shows how a gyroscopic spinner attached to the end of a hinged beam can be used as a 'stabilizer', reducing the displacements of the beam. We also discuss the dispersive properties of an infinite periodic system of beams with gyroscopic spinners at the junctions. In particular, we investigate how the band-gaps of the structure can be tuned by varying the gyricity of the spinners. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 1)'.

Dynamic characterization of a periodic microstructured flexural system with rotational inertia.

We consider the propagation of waves in a flexural medium composed of massless beams joining a periodic array of elements, elastically supported and possessing mass and rotational inertia. The dispersion properties of the system are determined and the influence and interplay between the dynamic parameters on the structure of the pass and stop bands are analysed in detail. We highlight the existence of three special dynamic regimes corresponding to a low stiffness in the supports and/or low rotational inertia of the masses; to a high stiffness and/or high rotational inertia regime; and to a transition one where dispersion degeneracies are encountered. In the low-frequency regime, a rigorous asymptotic analysis shows that the structure approximates a continuous Rayleigh beam on an elastic foundation. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 1)'.

Ultrasonic Sensing and Actuation in Laminate Structures Using Bondline-Embedded d35 Piezoelectric Sensors.

Ultrasonic systems employing embedded piezoelectric transducers have seen increased interest in recent years. The ability to sense, actuate, and analyze the wave propagation modes in engineering structures has been fundamental to the advancement of ultrasonic structural health monitoring (SHM). This paper presents a study into the sensing and actuation properties of shear-mode (d35) piezoelectric transducers made of lead zirconate titanate (PZT) that are internally embedded in the bondline of laminate structures. The manuscript presents analytical analysis, finite element simulation, and experimental validation building from an individual piezoelectric element to a full laminate structure. The validated model was then used to perform a parametric study into the effects of d35 PZT transducer size on the strength of actuation and sensing output signal. The selectivity of d35 PZT sensors was also investigated by generating multiple wave modes in the laminate structure and inspecting the output signals. The d35 PZT sensors were found to selectively detect only certain modes of the wave propagation providing a fundamental hardware filter that could be employed to simplify signal analysis and processing. The results of this study indicate that d35 PZTs embedded in the bondline have multiple properties that can potentially be employed for ultrasonic SHM.

Diffraction by a rigid strip in a plate modelled by Mindlin theory.

We consider a plane flexural wave incident on a semi-infinite rigid strip in a Mindlin plate. The boundary conditions on the strip lead to three Wiener-Hopf equations, one of which decouples, leaving a scalar problem and a 2 × 2 matrix problem. The latter is solved using a simple method based on quadrature. The far-field diffraction coefficient is calculated and some numerical results are presented. We also show how the results reduce to the simpler Kirchhoff model in the low-frequency limit.

On the Wiener-Hopf solution of water-wave interaction with a submerged elastic or poroelastic plate.

A solution to the problem of water-wave scattering by a semi-infinite submerged thin elastic plate, which is either porous or non-porous, is presented using the Wiener-Hopf technique. The derivation of the Wiener-Hopf equation is rather different from that which is used traditionally in water-waves problems, and it leads to the required equations directly. It is also shown how the solution can be computed straightforwardly using Cauchy-type integrals, which avoids the need to find the roots of the highly non-trivial dispersion equations. We illustrate the method with some numerical computations, focusing on the evolution of an incident wave pulse which illustrates the existence of two transmitted waves in the submerged plate system. The effect of the porosity is studied, and it is shown to influence the shorter-wavelength pulse much more strongly than the longer-wavelength pulse.

Localization in semi-infinite herringbone waveguides.

The paper includes novel results for the scattering and localization of a time-harmonic flexural wave by a semi-infinite herringbone waveguide of rigid pins embedded within an elastic Kirchhoff plate. The analytical model takes into account the orientation and spacing of the constituent parts of the herringbone system, and incorporates dipole approximations for the case of closely spaced pins. Illustrative examples are provided, together with the predictive theoretical analysis of the localized waveforms.

Helical comb magnetostrictive patch transducers for inspecting spiral welded pipes using flexural guided waves.

A wavefront analysis indicates that a flexural wave propagates at a helix angle with respect to the pipe axis. The expression for calculation of the helix angle for each flexural mode is given, and the helix angle dispersion curves for flexural modes are calculated. According to the new understanding of flexural guided waves, a helical comb magnetostrictive patch transducer (HCMPT) is proposed for selectively exciting a single predominant flexural torsional guided wave in a pipe and inspecting spiral welded pipes using flexural waves. A HCMPT contains a pre-magnetized magnetostrictive patch that is helically coupled with the outer surface of a pipe, and a novel compound comb coil that is wrapped around the helical magnetostrictive patch. The proposed wideband HCMPT possesses the direction control ability. A verification experiment indicates that flexural torsional mode T(3,1) at center frequency f=64kHz is effectively actuated by a HCMPT with 13-degree helix angle. Flexural torsional modes T(N,1) with circumferential order N equals 1-5 are selected to inspect a seamless steel pipe, artificial defects are effectively detected by the proposed HCMPT. A 20-degree HCMPT is adopted to inspect a spiral welded pipe, an artificial notch with cross section loss CSL=2.7% is effectively detected by using flexural waves.

Dynamic interfacial trapping of flexural waves in structured plates.

The paper presents new results on the localization and transmission of flexural waves in a structured plate containing a semi-infinite two-dimensional array of rigid pins. In particular, localized waves are identified and studied at the interface boundary between the homogeneous part of the flexural plate and the part occupied by rigid pins. A formal connection has been made with the dispersion properties of flexural Bloch waves in an infinite doubly periodic array of rigid pins. Special attention is given to regimes corresponding to standing waves of different types as well as Dirac-like points that may occur on the dispersion surfaces. A single half-grating problem, hitherto unreported in the literature, is also shown to bring interesting solutions.

Propagation of flexural waves in inhomogeneous plates exhibiting hysteretic nonlinearity: Nonlinear acoustic black holes.

Theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous material on flexural wave in the plates of continuously varying thickness is developed. For the wedges with thickness increasing as a power law of distance from its edge strong modifications of the wave dynamics with propagation distance are predicted. It is found that nonlinear absorption progressively disappearing with diminishing wave amplitude leads to complete attenuation of acoustic waves in most of the wedges exhibiting black hole phenomenon. It is also demonstrated that black holes exist beyond the geometrical acoustic approximation. Applications include nondestructive evaluation of micro-inhomogeneous materials and vibrations damping.