Wave Beam Research Articles

Lagrangian Manifolds in the Theory of Wave Beams and Solutions of the Helmholtz Equation

Lagrangian Manifolds in the Theory of Wave Beams and Solutions of the Helmholtz Equation

Coherent propagation of high-power wave beams in hollow gas-filled daisy-shaped waveguides

Coherent propagation of high-power wave beams in hollow gas-filled daisy-shaped waveguides

Transient resonant triads: An examination of turbulent patches injected into finite-width internal wave fields

This article presents an experimental investigation into the interaction of a freely evolving turbulent structure with a steadily forced, finite-width internal gravity wave beam. Specifically, a vortex ring is used as the simplified prototype for a propagating turbulent structure and we present an exploration into how it's passage affects the linear stability of the imposed (or forced) wave field. We use the term "vortex ring" to describe an initially axisymmetric, toroidal fluid structure with azimuthal vorticity. We first examine both the vortex ring and the imposed internal gravity wave beam separately and present how they develop in a quiescent, stratified environment. In the absence of any vortex ring, we find—in agreement with many previous studies—there is an amplitude threshold that the wave beam must surpass before it becomes linearly unstable by a process known as triadic resonance instability (TRI). In the absence of an imposed wave field, we present the propagation and collapse of a coherent vortex ring into a turbulent patch, and measure the transient spectrum of internal waves produced. We then combine these two phenomena and investigate how each impacts the other. While we find that the preexisting internal wave beam has no significant influence on the evolution of the incident vortex ring, we do find that the propagation and subsequent collapse of the ring provokes a response from the internal wave beam. This response allows us to demonstrate two key findings relating to the internal wave beams pathway to triadic resonance. First, the passage of a vortex ring propagating through a forced wave field can provide a nonlinear trigger for the transition to a triadic state when the amplitude of the imposed wave field is itself too small for the spontaneous growth of such a triadic state through TRI. Second, we find that in some cases the triadic states induced by this interaction are not self-sustaining and eventually decay, prompting the terminology "transient triads." These surprising findings are further confirmed by the unintentional release of trapped air arising from under our "magic carpet" wavemaker. These air bubbles turbulently propagate vertically through the imposed beam and, in some cases, induce similar triadic state transitions to those of the vortex ring. Our analysis leads to a discussion on the beam's pathway to instability and to question the structure of the underlying dynamical system arising from the distribution of spectral power in a finite-width beam. Published by the American Physical Society 2024

Tuneable vibration control of beams using granular multilayer composite

We explore a passive control solution of bending waves in beams, which takes advantage of the dissipative properties of granular media. It consists in a layer of particles confined between two beams and interacting with each other through their contacts. The inter-particles contacts are intrinsically dissipative due to friction, which efficiently works under shear. In practice, the mechanical response of such a multilayer inherit Hertz contact mechanics, thus conferring confining pressure dependent elasticity and dissipation. Previous work have shown that the hysteretic shear behaviour of a granular medium confined in a box can be reasonably captured by a single DOF model using Dahl model fed by an effective medium theory of granular media. Using this reduced model together with finite element method, we simulate the dynamic response of a three-layer composite beam whose core is made of confined frictional particles. This model makes it possible to characterize its elastic and damping properties, revealing in particular a high and tuneable loss factor with respect to shear strain amplitude and confining pressure, suitable for vibro-acoustics applications.

Herschel-Quincke filters adapted to bending waves in beams and plates

A Herschel-Quincke (HQ) filter is a device for controlling the transmission of guided waves: by adding one or more auxiliary branches to a waveguide, it is possible to construct delay lines, which induce destructive interference effects and consequently zero-transmission phenomena at targeted frequencies. We explore the use of this principle in the context of elastic waves in beams.The dispersive nature of bending waves and their coupling with longitudinal waves introduces complexity into the tuning of the zero transmission frequencies. A model, developed within the framework of Timoshenko's beam theory, provides the scattering matrix of an HQ filter composed of several branches. The model is confirmed by FE and thus demonstrates the interest of the approach for the control of vibrations. The architecture of the HQ device and the modelling approach are extended to a 3 branches configuration. The properties of the filter are analysed, leading to a discussion of the advantages and disadvantages of the HQ strategy.

Multi-objective model predictive control for ship roll motion with gyrostabilizers

Ships are prone to significant roll motion while sailing in adverse conditions, posing a serious threat to ship safety and maneuverability. Therefore, effective ship motion control is crucial. Integrating the MPC control algorithm with a gyrostabilizer can effectively achieve this goal. To evaluate and compare control strategies, a multi-objective model predictive control is proposed that integrates considerations of ship motion, safety, and energy consumption to conduct the operation concurrently. By assigning different weights to these factors, the study aims to discern the varying impacts on control effectiveness. The response of ship roll motion in beam waves is evaluated through roll hydrodynamic modelling, accounting for wave memory effects. A state-space model of ship and gyrostabilizers is proposed to represent their dynamic interaction and response to external moment. Subsequently, the influence of different weightings in the multi-objective model predictive control is compared, and the control performances of a frigate under different wave conditions are analyzed respectively. The multi-objective model predictive control, with varied weight assignments, leads to distinct reductions in roll motions. This investigation offers valuable insights into controlling roll motion in beam wave conditions, effectively reducing motion under varying sea conditions, and providing alternative guidance tailored to user preferences.

Lie symmetry analysis, traveling wave solutions and conservation laws of a Zabolotskaya-Khokholov dynamical model in plasma physics

This article analyzes the analytic and solitary wave solutions of the one-dimensional Zabolotskaya-Khokholov (ZK) dynamical model which provides information about the propagation of sound beam or confined wave beam in nonlinear media and studies of beam deformation. By the Lie symmetry analysis method, we acquire the vector fields, commutation relations, optimal system, reduction, and analytic solutions to the specified equation by exerting the Lie group method. Moreover, the solitary wave solutions of the ZK model are procured by exerting the new auxiliary equation method (NAEM). The behavior of the acquired outcomes for several cases is exhibited graphically through two and three-dimensional dynamical wave profiles. Furthermore, the conservation laws of the ZK model are acquired by Ibragimov’s new conservation theorem.

A frequency steerable electromagnetic acoustic transducer

Abstract Electromagnetic acoustic transducers (EMATs) are convenient for non-destructive evaluation of plate-like structures since they can generate, without the need for contact with the medium under test, different types of ultrasonic guided waves. Guided-wave EMATs usually generate waves omnidirectionally or in a principal propagation direction. Beam steering is desirable in several applications, such as in inspections of large-area structures. This is usually achieved with several independently controlled elements forming a phased array. Alternatively, mono-element transducers with directional-dependent spectral content can steer the generated wave beam by altering the frequency of the excitation signal. A piezoelectric transducer with this characteristic, namely a frequency steerable acoustic transducer, was previously proposed. Its design was addressed in the wavenumber domain, leading to unconventional transducer shapes, but still reproducible with a piezoelectric patch, albeit unfeasible to implement as an EMAT. Here, we propose a new kind of EMAT, namely, frequency steerable EMAT (FSEMAT), whose design is addressed in the spatial domain in order to ensure its physical realization with a coil-magnet arrangement whilst still effectively presenting steering capability. The novel EMAT was designed to generate the A 0 Lamb wave mode in a frequency range from approximately 100 to 600 kHz. The FSEMAT was fabricated and experimentally evaluated in an aluminium plate at different frequencies within the designed frequency range, where each frequency corresponded to a specific propagating direction with high directivity, assessed by half-power beam widths of approximately 10 degrees. Furthermore, its theoretical directivity was computed by means of a wavenumber spectrum-based model, and showed good agreement with experimental results. The new transducer allows great flexibility effectively providing beam steering with a single EMAT.

Phase and amplitude simultaneously coding metasurface with multi-frequency and multifunctional electromagnetic modulations

The integration of multiple functionalities into a single, planar, ultra-compact metasurface has presented significant opportunities for enhancing capacity and performance within compact 5G/6G communication systems. Recent advances in multifunctional metasurfaces have unveiled comprehensive wavefront manipulations utilizing phase, polarization transmission/reflection, and coding apertures. Despite these developments, there remains a critical need for multifunctional metasurfaces with expanded channel capabilities, including multiple operational frequencies, minimal crosstalk, and high-efficiency computable array factors. This study introduces a multifunctional metasurface that integrates phase- and amplitude simultaneous coding meta-atoms at dual frequencies. By altering the polarization of electromagnetic (EM) waves, it is possible to reshape the wave-fronts of reflected waves at these frequencies. The coding metasurface proficiently manipulates both x and y linearly polarized waves through phase and amplitude coding at dual frequencies, thereby enabling distinct functionalities such as anomalous reflection, reflection imaging, and vortex wave beam generation. Both theoretical analysis and full-wave simulation confirm the anticipated functionalities of the designed devices, paving the way for advancements in integrated communication systems with diverse functionalities.

An X-band coaxial relativistic klystron oscillator with a novel diode structure packaged with permanent magnet

To achieve compactness and miniaturization for high-power microwave devices, this paper proposes an X-band permanent magnet-packaged coaxial relativistic klystron oscillator (RKO) with a novel diode structure featuring a stair-step cathode. First, by adopting a large-radius anode structure, the emission of beam currents from the side of the cathode surface is diminished, thereby reducing the proportion of the backward current in the beam current from 10% to 7%. Second, a stair-step cathode is used to inhibit the return flow of electron beams from striking the anode and generating plasma. Concurrently, a radially non-uniform coaxial resonant cavity structure is employed to enhance the fundamental wave modulation depth of the electron beam and improve the beam–wave interaction's efficiency. The experimental results show that the novel device outputs a microwave with a frequency of 9.46 GHz and a pulse width of 55 ns. It generates a power output of 1.5 GW with an efficiency of approximately 30.5%, in the case in which the diode voltage is 505 kV, the beam current is 9.7 kA, and the guiding magnetic flux density is 0.4 T. This novel structure surpasses traditional diode configurations by enhancing the beam-to-wave conversion efficiency by roughly 10%, thereby offering substantial support for the compactness and miniaturization of RKO.

Flexural wave propagation in canonical quasicrystalline-generated waveguides

We investigate the propagation of harmonic flexural waves in periodic two-phase phononic multi-supported continuous beams whose elementary cells are designed according to the quasicrystalline standard Fibonacci substitution rule. The resulting dynamic frequency spectra are studied with the aid of a trace-map formalism which provides a geometrical interpretation of the recursive rule governing traces of the relevant transmission matrices: the traces of three consecutive elementary cells can be represented as a point on the surface defined by an invariant function of the square root of the circular frequency, and the recursivity implies the description of a discrete orbit on the surface. In analogy with the companion axial problem, we show that, for specific layouts of the elementary cell (the canonical configurations), the orbits are almost periodic. Likewise, for the same layouts, the stop-/pass-band diagrams along the frequency domain are almost periodic. Several periodic orbits exist and each corresponds to a self-similar portion of the dynamic spectra whose scaling law can be investigated by linearising the trace map in the neighbourhood of the orbit. The obtained results provide a new piece of theory to better understand the dynamic behaviour of two-phase flexural periodic waveguides whose elementary cell is obtained from quasicrystalline generation rules.

Qualitative validation on a numerical model for the direct stability assessment of surf-riding and broaching

A previously developed numerical model for surf-riding and broaching is qualitatively validated based on the criteria of direct stability assessment (DSA) proposed in SDC 7. Roll decay tests are conducted to obtain roll backbone curves, which are compared with calculated GZ curve to demonstrate their consistency. Then, roll response curves under different wave frequencies in regular beam wave are obtained. It is verified that roll response curve “fold around” the newly defined “peak backbone curve”. Cases with fixed yaw under different Fn are chosen to demonstrate the numerical model's capability of reproducing surf-riding equilibrium. Turning circle test is conduced to demonstrate correct modelling of maneuvering forces and the capability to reproduce heel due to ship turning. Wave surging forces are calculated under different wave numbers and amplitudes. The correct tendency of phase difference between wave surging force and the incident wave is observed, which reveals the correct modelling of wave forces in the model. Moreover, a preliminary quantitative validation is conducted under various cases. Through comparison with experimental results, it is recommended that the wave diffraction correction of the wave surging forces should be included in the simulation model in order to avoid overestimation of surf-riding and broaching.

Tunable Photonic Hook Design Based on Anisotropic Cutting Liquid Crystal Microcylinder

The selective control and manipulation of nanoparticles require developing and researching new methods for designing optical tweeters, mainly based on a photonic hooks (PHs) effect. This paper first proposes a tunable PH in which a structured beam illuminates an anisotropic cutting liquid crystal microcylinder based on the Finite-DifferenceTime-Domain (FDTD) method. The PHs generated by plane wave, Gaussian, and Bessel beam are analyzed and compared. The impact of beams and LC particle parameters on the PHs are discussed. Where the influence of the extraordinary refractive index (ne) on PHs is emphasized. Our results reveal that introducing birefringence can change the bending direction of PH. Besides, the maximum intensity of the PHs increases as ne increases regardless of the beam type. The PH generated by a plane wave has a higher maximum intensity and smaller FWHM than that generated by the Gaussian and Bessel beams. The smallest FWHM and maximum intensity of the PHs generated by the Gaussian falls between that generated by the plane wave and the Bessel beam. The PH generated by a Bessel beam has the minor maximum intensity and the largest FWHM. Still, it exceeds the diffraction limit and exhibits bending twice due to its self-recovery property. This paper provides a new way to modulate PH. This work offers novel theoretical models and the degree of freedom for the design of PHs, which is beneficial for the selective manipulation of nanoparticles. It has promising applications in Mesotronics and biomedicine.

Travelling waves in beam-like structures submerged in water

There are many examples in nature of travelling waves used for propulsion purposes, e.g., micro-organisms and sea creatures. Structural travelling waves can be used to induce momentum in a surrounding media creating a net propelling force. Recent research has tried to capture this interaction in engineering devices. Nonetheless, some challenges remain to fully exploit this phenomenon so that travelling-waves propelled devices can be optimally designed. One such challenge is that the interaction between the structure and the surrounding fluid heavily influences the amplitude of the waves and how they travel through the structure. This paper proposes a systematic qualitative and quantitative analysis of travelling waves in a slender cantilever beam submerged in water. The novelty of this work is demonstrated through two key aspects: The application of the Euler-Bernoulli beam equation combined with the Galerkin approximation, enabling a deeper understanding of how travelling waves form at resonant frequencies rather than non-resonant ones; and An analytical approach using a Galerkin approximation to characterise the nonlinear fluid-structure interaction, followed by linearisation for a comprehensive parametric study of the problem. In this investigation, the contributions of the first five vibration modes are considered in relation to the travelling waves observed near the resonant peaks. Experimental tests validate the analytical results and assess the accuracy of the proposed models. The results demonstrate that the model presented effectively characterises the travelling waves, making a suitable tool for the design of travelling-wave propelled devices.

Broadband controllable defect state of longitudinal waves in one-dimensional pillared phononic crystal beams

Broadband controllable defect state of longitudinal waves in one-dimensional pillared phononic crystal beams

A radar transducer for unidirectionally emitting and steering SH guided wave

It is of practical importance to emit a pure wave mode, focus its energy along a given direction, and then steer the wave beam in guide-wave-based structural health monitoring (SHM) because it can quickly scan the overall structure. Such a goal is usually realized using a two-dimensional (2D) phased array, which requires many transducer elements and expensive electronics. This work proposed a radar transducer (RD-T) for unidirectionally emitting and steering the fundamental shear horizontal wave (SH0 wave). The proposed RD-T consists of an annular metasubstrate and several rectangular thickness-shear (d15) piezoelectric wafers. The metasubstrate is designed to provide the required phase gradient for unidirectionally emitting and sensing a pure SH0 wave, so no extra time delay is required for driving the RD-T. The beam steering is obtained by activating the subunits one by one. The SH0 wavefields generated by the subunit are described by a theoretical model and the effects of dimension parameters are analyzed. Finite element simulations and experiments are conducted to examine the performances of the RD-T. Both simulated and experimental results indicate that from 200 kHz to 270 kHz, the RD-T can unidirectionally emit an SH0 wave with a high SNR (signal-to-noise ratio) and steer the wave beam along different directions. The performance of the RD-T on damage detection is then investigated by pulse-echo experiments. It can be found that the RD-T can successfully distinguish symmetric defects and locate defects with an acceptable error. Compared with the traditional 2D phased array, the RD-T can realize 360° scanning of the overall structure more efficiently, exhibiting great potential in the field of SHM.

A0 mode Lamb wave propagation in a nonlinear medium and enhancement by topologically designed metasurfaces for material degradation monitoring

This paper intends to provide an application example of using metamaterials for elastic wave manipulation inside a nonlinear waveguide. The concept of phase-gradient metasurfaces, in the form of artificially architectured structures/materials, is adopted in nonlinear-guided-wave-based structural health monitoring (SHM) systems. Specifically, the second harmonic lowest-order antisymmetric Lamb waves (2nd A0 waves), generated by the mutual interaction between primary symmetric (S) mode and antisymmetric (A) mode waves, show great promise for local incipient damage monitoring. However, the mixing strength is adversely affected by the wave beam divergence, which compromises the 2nd A0 wave generation, especially in the far field. To tackle this problem, a metasurface is designed to tactically enhance the 2nd A0 waves through manipulating the phases and amplitudes of both primary waves simultaneously. After theoretically revealing the features of the 2nd A0 wave generation in a weakly nonlinear plate, an inverse-design strategy based on topology optimization is employed to tailor-make the phase gradient while ensuring the high transmission of the primary waves, thus converting the diverging cylindrical waves into quasi-plane waves. The efficacy of the design is tested in a 2nd-A0-wave-based SHM system for material degradation monitoring. Results confirm that the manipulated S and A mode waves can propagate in a quasi-planar waveform after passing the surface-mounted metasurface. Changes in material properties inside a local region of the host plate can be sensitively captured through examining the variation of the 2nd A0 wave amplitude. The concept presented here not only showcases the potential of metamaterial-enhanced 2nd A0 waves for material degradation monitoring, but also illuminates the promising direction of metamaterial-aided SHM applications in nonlinear waveguides.

Reflective anomalous beam splitter (RABS) metasurface for millimeter-wave (mm-Wave) frequency

Metasurfaces have gained a considerable amount of interest in the past decade for their capabilities to manipulate electromagnetic (EM) waves in different manners. They have offered multiple functionalities in terms of wave control depending on the given application. In terms of wave control, particularly EM beam splitting, it can be challenging compared to the given literature review, to achieve a wide number of beam-splitting reflections and coverage for multiple incident angles simultaneously. In this paper, we focus on the design of a metasurface based on the methodology of high periodicity supercell design (5.76λ) and impedance modulation to achieve a various number of beam-splitting angles, while maintaining the same coverage at multiple incident angles for millimeter-wave (mm-Wave) frequencies. Following the generalized phase law of reflection alongside proper optimization of the surface impedance, the proposed reflective anomalous beam splitter (RABS) metasurface is designed to be polarization independent, and high reflection efficiency is achieved with a wave beam split into 11 different directions while operating for multiple incident angles simultaneously, making it a promising candidate to overcome challenges for various mm-Wave communication applications, especially in expanding 5G coverage in non-line of sight regions at a 28 GHz frequency band. The performance of the RABS metasurface is evaluated using both full-wave simulations and experimental measurements, which demonstrate its effectiveness in achieving 11 efficient reflective anomalous beams with a reflection efficiency of up to 96.65% and 97.36% in TE and TM modes at 28 GHz.

SN-FSAT system for single sensor ultrasonic guided wave beam steering and damage detection

In wireless communications as well as in structural health monitoring (SHM) beam steering presents interesting advantages. In the former it plays an important role for data directivity, which is also a perk for energy efficiency and data security; for the latter, directional inspection through guided waves leads also to energy efficiency, arbitrary dedicated space scanning, multi-function operation through multiple beams and even to application of a base-line free inspection concept. Normally, to enable this simultaneous beam control and data communication in arbitrary spatial directions (2D) over a structure, a large array of transducers is required, arranged to a similarly complex hardware and software support system. In this work, we present a system based on a dedicated sensor node (SN) and frequency steerable acoustic transducer (FSAT) combination. The SN-FSAT system is charged of the adequate power and signal management for acquisition, transmission, processing and data evaluation, required to perform spatial scanning and damage detection, as well as direction focused wireless communication tasks. These were tested over an isotropic aluminum plate-like structure by means of a double symmetric beam, via differential actuation signals, or in a high directive beam in a single direction by means of a quadrature driving signals. The complete guided wave-based setup consists of three SN-FSAT pairs. As damage a pseudo fault of a small added mass with damping tacky tape was used. The results show that damage located in different positions around the FSATs can be detected without a baseline reference and multiple directional communication paths between the SN-FSAT network can be established.

Effect of off-axis electron beam on the performance of a gyroklystron amplifier

A crucial part of a gyroklystron is an electron beam. For the efficient operation of the gyroklystron, effective interaction between the radio frequency wave and the electron beam is necessary. Although the manufacturing and assembly of the gyroklystron are complicated, during the assembly process of various components of the gyroklystron, there is some possibility that the components may be misaligned from their actual positions. The operation of a gyroklystron is very sensitive if its components are misaligned. Electron beam misalignment is one type of such misalignment. This paper studies the effect of an off-axis electron beam on gyroklystron performance. Due to misalignment, the electron beam radius will vary in its position as the electron beam gyrates. First, the nonlinear single-mode analysis describing the beam–wave interaction process within the gyroklystron amplifier is discussed. As reported in the literature, an experimental, two-cavity 35 GHz fundamental harmonic gyroklystron amplifier has been used to conduct the present study. The results obtained from the analytically developed approach are benchmarked by the results of the experimental device. Subsequently, the analysis developed has been extended to investigate the impact of the misaligned electron beam on the gyroklystron performance characteristics. The study shows that efficiency, output power and gain decrease with misalignment, whereas bandwidth does not change due to such misalignments. These findings demonstrate the critical role that the misaligned electron beam plays in the operation of a gyroklystron amplifier.