Pub Date : 2025-11-01Epub Date: 2025-06-06DOI: 10.1016/j.wavemoti.2025.103582
W. Rodríguez-Cruz , D.M. Uriza-Prias , M. Roque-Vargas , A. Díaz-de-Anda
We develop a theory that significantly improves the correspondence between theoretical and experimental results in beams with structures excited with bending waves. We use beam theory and Timoshenko-Ehrenfest continuity conditions with the transfer matrix method to solve the fourth-order differential equation. First, we analyze the continuity conditions to understand the deformation in the cross-section between the notch-body interface. Then, using analytical and numerical methods, we determine an effective cross-section between the notch-body interface that, when included in the continuity conditions of the Timoshenko–Ehrenfest beam theory, brings the theoretical results into a high agreement with the experimental results with a relative error of less than 12%.
{"title":"Correction in the continuity conditions for beams with structure governed by the Timoshenko–Ehrenfest equation","authors":"W. Rodríguez-Cruz , D.M. Uriza-Prias , M. Roque-Vargas , A. Díaz-de-Anda","doi":"10.1016/j.wavemoti.2025.103582","DOIUrl":"10.1016/j.wavemoti.2025.103582","url":null,"abstract":"<div><div>We develop a theory that significantly improves the correspondence between theoretical and experimental results in beams with structures excited with bending waves. We use beam theory and Timoshenko-Ehrenfest continuity conditions with the transfer matrix method to solve the fourth-order differential equation. First, we analyze the continuity conditions to understand the deformation in the cross-section between the notch-body interface. Then, using analytical and numerical methods, we determine an effective cross-section between the notch-body interface that, when included in the continuity conditions of the Timoshenko–Ehrenfest beam theory, brings the theoretical results into a high agreement with the experimental results with a relative error of less than 12%.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103582"},"PeriodicalIF":2.1,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144229919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-06-24DOI: 10.1016/j.wavemoti.2025.103592
Xue-Hui Zhao , Guo-Hong Yang , Zhong-Zhou Lan
In this paper, We investigate the dynamics and interactions of bound-state solitons in a coupled Hirota system with negative coherent coupling. Using the th-order binary Darboux transformation, we derive -soliton solutions and analyze four distinct cases of bound-state soliton dynamics through spectral parameter constraints. Our results demonstrate how the higher-order perturbation parameter modulates nonlinear coupling, governing transitions between fusion, fission, and mixed interaction states. These findings provide new insights into soliton manipulation in nonlinear optical media and complex coupled systems, with potential applications in optical communications and signal processing.
{"title":"Dynamics and interactions of bound-state Solitons for a coupled Hirota system with negative coherent coupling","authors":"Xue-Hui Zhao , Guo-Hong Yang , Zhong-Zhou Lan","doi":"10.1016/j.wavemoti.2025.103592","DOIUrl":"10.1016/j.wavemoti.2025.103592","url":null,"abstract":"<div><div>In this paper, We investigate the dynamics and interactions of bound-state solitons in a coupled Hirota system with negative coherent coupling. Using the <span><math><mi>N</mi></math></span>th-order binary Darboux transformation, we derive <span><math><mi>N</mi></math></span>-soliton solutions and analyze four distinct cases of bound-state soliton dynamics through spectral parameter constraints. Our results demonstrate how the higher-order perturbation parameter <span><math><mi>ɛ</mi></math></span> modulates nonlinear coupling, governing transitions between fusion, fission, and mixed interaction states. These findings provide new insights into soliton manipulation in nonlinear optical media and complex coupled systems, with potential applications in optical communications and signal processing.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103592"},"PeriodicalIF":2.1,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144480101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-06-20DOI: 10.1016/j.wavemoti.2025.103599
Tianshu Liang, Ying Liu, Qingxiao Gu
Based on the light sensitivity of liquid crystal elastomers, a Grille-like phononic crystal plate is proposed in this paper with the aim to achieve multi-mode band opto-tuning. The indirect coupling strategy is used to determine the opto-band variation in phononic crystal plate. The spontaneous deformation of the phononic crystal plate is firstly investigated. Then the wave dispersion in the opto-deformed phononic crystal plate is explored. The band structure in undeformed phononic crystal plate is also given for comparison. The effects of geometrical sizes of unit cells and light intensity are clarified in detail. The result indicates that the band structures in phononic crystal plates can be tuned by adjusting the light intensity, which displays sensitive dependence on the unit cell geometrical sizes. The phononic crystal plate with opto-deformable slabs provides a choice in design of opto-controlling phononic crystal plate, and has prospective applications in optical controlling of devices and systems.
{"title":"Opto-band tuning in a liquid crystal elastomer phononic crystal plate","authors":"Tianshu Liang, Ying Liu, Qingxiao Gu","doi":"10.1016/j.wavemoti.2025.103599","DOIUrl":"10.1016/j.wavemoti.2025.103599","url":null,"abstract":"<div><div>Based on the light sensitivity of liquid crystal elastomers, a Grille-like phononic crystal plate is proposed in this paper with the aim to achieve multi-mode band opto-tuning. The indirect coupling strategy is used to determine the opto-band variation in phononic crystal plate. The spontaneous deformation of the phononic crystal plate is firstly investigated. Then the wave dispersion in the opto-deformed phononic crystal plate is explored. The band structure in undeformed phononic crystal plate is also given for comparison. The effects of geometrical sizes of unit cells and light intensity are clarified in detail. The result indicates that the band structures in phononic crystal plates can be tuned by adjusting the light intensity, which displays sensitive dependence on the unit cell geometrical sizes. The phononic crystal plate with opto-deformable slabs provides a choice in design of opto-controlling phononic crystal plate, and has prospective applications in optical controlling of devices and systems.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103599"},"PeriodicalIF":2.1,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144471574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-06-21DOI: 10.1016/j.wavemoti.2025.103598
Maoxun Sun , Miaohong Tan , Cheng Shan , Yue Zhang , Hongye Liu
Underground or underwater pipe-like structures are usually subjected to corrosion or plastic deformation, during which the micro-cracks probably appear and gradually evolve into macro-cracks, resulting in the leakage of pipes. Therefore, to avoid catastrophic accidents, it is necessary to locate micro-cracks accurately and repair or replace pipes in time. Wave mixing has the advantages of micro-crack localization compared with second harmonics, and it can avoid the interference of nonlinearities in measurement systems. However, few reports are available on nonlinear mixing of counter-propagating guided waves caused by contact acoustic nonlinearity (CAN) in pipes. In this paper, the interaction of the guided wave mixing and micro-cracks in pipe-like structures is theoretically and numerically investigated via CAN and vector analyses, as well as pulse-inversion techniques and two-dimensional fast Fourier transforms (2D-FFT), respectively. It is theoretically demonstrated that the amplitudes of second-order harmonics increase monotonically with ε0/ε0, while the amplitudes of third-order harmonics first increase and then drop with ε0/ε0. In simulations, nonlinear mixing of counter-propagating guided waves occurs in the regions that contain micro-cracks, and the generated difference-frequency components or sum-frequency components propagate to both ends of pipes at the same time. The difference-frequency components mainly contain F(m,1) modes, and the sum-frequency components mainly contain F(m,2) modes and F(m,3) modes, which are predicted in advance by theoretical investigations. In addition, the normalized amplitudes of difference-frequency components and sum-frequency components exhibit “mountain-shape” trends between 0° and 90° as well as during 90° and 180°, with the peaks corresponding to micro-crack angles of 45° and 135° Note that they reach the minimums when angles of micro-cracks equal to 0°, 90° or 180°, which is in a good agreement with the theoretical investigations. Finally, the z-coordinates of micro-cracks can be determined by the relationship between the normalized amplitudes of difference-frequency components or sum-frequency components and positions of mixing zones. The φ-coordinates of micro-cracks can be obtained based on normalized amplitudes of difference-frequency components in Uz with respect to φ-coordinates.
{"title":"Analytical and numerical investigations of the interaction between nonlinear guided wave mixing and micro-cracks in pipe-like structures","authors":"Maoxun Sun , Miaohong Tan , Cheng Shan , Yue Zhang , Hongye Liu","doi":"10.1016/j.wavemoti.2025.103598","DOIUrl":"10.1016/j.wavemoti.2025.103598","url":null,"abstract":"<div><div>Underground or underwater pipe-like structures are usually subjected to corrosion or plastic deformation, during which the micro-cracks probably appear and gradually evolve into macro-cracks, resulting in the leakage of pipes. Therefore, to avoid catastrophic accidents, it is necessary to locate micro-cracks accurately and repair or replace pipes in time. Wave mixing has the advantages of micro-crack localization compared with second harmonics, and it can avoid the interference of nonlinearities in measurement systems. However, few reports are available on nonlinear mixing of counter-propagating guided waves caused by contact acoustic nonlinearity (CAN) in pipes. In this paper, the interaction of the guided wave mixing and micro-cracks in pipe-like structures is theoretically and numerically investigated via CAN and vector analyses, as well as pulse-inversion techniques and two-dimensional fast Fourier transforms (2D-FFT), respectively. It is theoretically demonstrated that the amplitudes of second-order harmonics increase monotonically with <em>ε</em><sub>0</sub>/<em>ε</em><sup>0</sup>, while the amplitudes of third-order harmonics first increase and then drop with <em>ε</em><sub>0</sub>/<em>ε</em><sup>0</sup>. In simulations, nonlinear mixing of counter-propagating guided waves occurs in the regions that contain micro-cracks, and the generated difference-frequency components or sum-frequency components propagate to both ends of pipes at the same time. The difference-frequency components mainly contain F(<em>m</em>,1) modes, and the sum-frequency components mainly contain F(<em>m</em>,2) modes and F(<em>m</em>,3) modes, which are predicted in advance by theoretical investigations. In addition, the normalized amplitudes of difference-frequency components and sum-frequency components exhibit “mountain-shape” trends between 0° and 90° as well as during 90° and 180°, with the peaks corresponding to micro-crack angles of 45° and 135° Note that they reach the minimums when angles of micro-cracks equal to 0°, 90° or 180°, which is in a good agreement with the theoretical investigations. Finally, the <em>z</em>-coordinates of micro-cracks can be determined by the relationship between the normalized amplitudes of difference-frequency components or sum-frequency components and positions of mixing zones. The <em>φ</em>-coordinates of micro-cracks can be obtained based on normalized amplitudes of difference-frequency components in U<em><sub>z</sub></em> with respect to <em>φ</em>-coordinates.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103598"},"PeriodicalIF":2.1,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144471576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-08-19DOI: 10.1016/j.wavemoti.2025.103623
Yanan Wang , Minghe Zhang
We construct novel non-autonomous positons, breather-positons, and breather molecules for the variable-coefficient Kundu-nonlinear Schrödinger equation —a key model for pulse propagation in optical fibers. Through degenerate Darboux transformation, we reveal intricate dynamics previously unattainable. For non-autonomous positon solution, generalized asymptotic analysis method yields exact expressions of asymptotic solitons with logarithmic trajectories. Arising from the different non-autonomous breather-positon, we give the non-autonomous rogue wave generation process and other results. For the non-autonomous breather molecule, the related dynamic behaviors under the periodic, exponential and hyperbolic function parameters are explored by the characteristic line analysis. This work provides a unified framework for investigating degenerate complex waves in inhomogeneous optical media.
{"title":"Non-autonomous positon and breather molecule for the variable-coefficient Kundu-nonlinear Schrödinger equation","authors":"Yanan Wang , Minghe Zhang","doi":"10.1016/j.wavemoti.2025.103623","DOIUrl":"10.1016/j.wavemoti.2025.103623","url":null,"abstract":"<div><div>We construct novel non-autonomous positons, breather-positons, and breather molecules for the variable-coefficient Kundu-nonlinear Schrödinger equation —a key model for pulse propagation in optical fibers. Through degenerate Darboux transformation, we reveal intricate dynamics previously unattainable. For non-autonomous positon solution, generalized asymptotic analysis method yields exact expressions of asymptotic solitons with logarithmic trajectories. Arising from the different non-autonomous breather-positon, we give the non-autonomous rogue wave generation process and other results. For the non-autonomous breather molecule, the related dynamic behaviors under the periodic, exponential and hyperbolic function parameters are explored by the characteristic line analysis. This work provides a unified framework for investigating degenerate complex waves in inhomogeneous optical media.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103623"},"PeriodicalIF":2.5,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144890671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-08-21DOI: 10.1016/j.wavemoti.2025.103620
M.O. Sales , L.D. da Silva , M.S.S. Junior , F.A.B.F. de Moura
In this study, we investigate the propagation of shear vibrations in a rectangular system where disorder is introduced through the compressibility term, exhibiting Lorentzian spatial correlations. Our primary objective is to understand how these correlations influence the behavior and velocity of harmonic mode packets as they travel through the system. To achieve this, we employ a finite difference formalism to accurately capture the wave dynamics. Furthermore, we analyze how the spectral composition of the incident pulse affects wave propagation, shedding light on the interplay between disorder correlations and wave transport. By systematically exploring these factors, we aim to deepen our understanding of the fundamental mechanisms governing shear vibration propagation in disordered media.
{"title":"Investigation of shear wave propagation in two-dimensional systems with Lorentzian-correlated disorder","authors":"M.O. Sales , L.D. da Silva , M.S.S. Junior , F.A.B.F. de Moura","doi":"10.1016/j.wavemoti.2025.103620","DOIUrl":"10.1016/j.wavemoti.2025.103620","url":null,"abstract":"<div><div>In this study, we investigate the propagation of shear vibrations in a rectangular system where disorder is introduced through the compressibility term, exhibiting Lorentzian spatial correlations. Our primary objective is to understand how these correlations influence the behavior and velocity of harmonic mode packets as they travel through the system. To achieve this, we employ a finite difference formalism to accurately capture the wave dynamics. Furthermore, we analyze how the spectral composition of the incident pulse affects wave propagation, shedding light on the interplay between disorder correlations and wave transport. By systematically exploring these factors, we aim to deepen our understanding of the fundamental mechanisms governing shear vibration propagation in disordered media.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103620"},"PeriodicalIF":2.5,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-07-03DOI: 10.1016/j.wavemoti.2025.103600
Maria M. Vuin, Dmitri Kartofelev, Andrus Salupere, Päivo Simson
In this paper acoustic wave propagation through nonlinear porous felt-like material is studied numerically. A 1D model equation based on the experimentally obtained constitutive relation is used. A dispersion and dissipation analysis are performed. The possible effects of band gap (BG) and negative group velocity (NGV) on the wave propagation are investigated. For this reason, the propagation of pulses with characteristic widths corresponding to wavenumbers that are located in and near the BG and the region with NGV are studied. It is claimed that if the material loading and unloading timescale is much too great in comparison to the felt relaxation time, then any possible contribution of BG and NGV on the wave shape evolution is negligibly small. Paper concludes that felts are not metamaterials with noteworthy properties. Possible reasons for these conclusions are given. It is obvious that the proper understanding of NGV phenomenon will lead to significant breakthroughs in unwoven fibrous felt-type material engineering and applications. These applications may include vibration and noise control and even wave manipulation.
{"title":"Numerical investigation into acoustic wave propagation in felt-type material with band gap and negative group velocity","authors":"Maria M. Vuin, Dmitri Kartofelev, Andrus Salupere, Päivo Simson","doi":"10.1016/j.wavemoti.2025.103600","DOIUrl":"10.1016/j.wavemoti.2025.103600","url":null,"abstract":"<div><div>In this paper acoustic wave propagation through nonlinear porous felt-like material is studied numerically. A 1D model equation based on the experimentally obtained constitutive relation is used. A dispersion and dissipation analysis are performed. The possible effects of band gap (BG) and negative group velocity (NGV) on the wave propagation are investigated. For this reason, the propagation of pulses with characteristic widths corresponding to wavenumbers that are located in and near the BG and the region with NGV are studied. It is claimed that if the material loading and unloading timescale is much too great in comparison to the felt relaxation time, then any possible contribution of BG and NGV on the wave shape evolution is negligibly small. Paper concludes that felts are not metamaterials with noteworthy properties. Possible reasons for these conclusions are given. It is obvious that the proper understanding of NGV phenomenon will lead to significant breakthroughs in unwoven fibrous felt-type material engineering and applications. These applications may include vibration and noise control and even wave manipulation.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103600"},"PeriodicalIF":2.1,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144597539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-08-10DOI: 10.1016/j.wavemoti.2025.103622
Andi Lai, Yuhang Li, Kai Wu, Guo Fu
Nonreciprocal linear elastic responses in active systems are described by the non-Hermitian elasticity tensor, referred to as odd elasticity. Existing studies have focused on the propagation characteristics of waves in infinite domains and the skin effects at the boundary, while the dynamics of odd elasticity in geometries with rotational symmetry remain unclear. In this work, we develop a dynamic model for odd elastic circular domain in polar coordinates and derive the wave solutions. We report a novel type of nonreciprocal rotating wave in rotationally symmetric geometries. This phenomenon is characterized by invariant modes, with amplitude either increasing or decaying depending on the direction of propagation. Furthermore, we demonstrate that when the gain and loss induced by two independent odd elastic effects are balanced, the system generates rotating waves with constant amplitude and chiral modes. These findings provide a foundation for the study of nonreciprocal angular momentum transfer and chiral mechanical resonators.
{"title":"Nonreciprocal rotating waves and energy-balanced modes in odd elastic circular domain","authors":"Andi Lai, Yuhang Li, Kai Wu, Guo Fu","doi":"10.1016/j.wavemoti.2025.103622","DOIUrl":"10.1016/j.wavemoti.2025.103622","url":null,"abstract":"<div><div>Nonreciprocal linear elastic responses in active systems are described by the non-Hermitian elasticity tensor, referred to as odd elasticity. Existing studies have focused on the propagation characteristics of waves in infinite domains and the skin effects at the boundary, while the dynamics of odd elasticity in geometries with rotational symmetry remain unclear. In this work, we develop a dynamic model for odd elastic circular domain in polar coordinates and derive the wave solutions. We report a novel type of nonreciprocal rotating wave in rotationally symmetric geometries. This phenomenon is characterized by invariant modes, with amplitude either increasing or decaying depending on the direction of propagation. Furthermore, we demonstrate that when the gain and loss induced by two independent odd elastic effects are balanced, the system generates rotating waves with constant amplitude and chiral modes. These findings provide a foundation for the study of nonreciprocal angular momentum transfer and chiral mechanical resonators.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103622"},"PeriodicalIF":2.5,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144831307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-09-04DOI: 10.1016/j.wavemoti.2025.103632
Biao Li , Yongyan Zhang , Xiangjie Miao , Zebo Zhao , Liming Chen , Hui Liu
In this paper, we propose a lightweight helical plate elastic metamaterial with gradient springs for low-frequency vibration suppression, leveraging the local resonance effect of helical gradient springs to achieve both an ultra-wide complete bandgap and a bending wave bandgap in the low-frequency range. Theoretical analysis and finite element simulations reveal the critical role of helical gradient springs in stiffness tuning and the local resonance mechanism. By integrating multiple pitches and radii, the design offers greater flexibility in stiffness adjustment compared with conventional single-pitch and single-radius springs. This enables the realization of negative stiffness characteristics and allows more flexible optimization of the bandgap range and performance. Moreover, adjusting the number of helical gradient spring arrays further enhances the bandgap width, system stability, and lightweight properties. After determining suitable geometric parameters through parametric analysis, the proposed structure achieves bending wave bandgaps from 29 Hz to 454 Hz and a complete bandgap from 72 Hz to 436 Hz, both representing ultra-wide low-frequency ranges. Additionally, intrinsic modal analysis and transmission spectrum characterization elucidate the physical mechanisms of bandgap formation and validate the design. This helical gradient spring-based local resonance structure addresses the challenges posed by the high mass and volume of traditional phononic crystals, offering a promising approach for engineering applications in low-frequency acoustic isolation metamaterials.
{"title":"A lightweight helical plate elastic metamaterial for low-frequency vibration suppression","authors":"Biao Li , Yongyan Zhang , Xiangjie Miao , Zebo Zhao , Liming Chen , Hui Liu","doi":"10.1016/j.wavemoti.2025.103632","DOIUrl":"10.1016/j.wavemoti.2025.103632","url":null,"abstract":"<div><div>In this paper, we propose a lightweight helical plate elastic metamaterial with gradient springs for low-frequency vibration suppression, leveraging the local resonance effect of helical gradient springs to achieve both an ultra-wide complete bandgap and a bending wave bandgap in the low-frequency range. Theoretical analysis and finite element simulations reveal the critical role of helical gradient springs in stiffness tuning and the local resonance mechanism. By integrating multiple pitches and radii, the design offers greater flexibility in stiffness adjustment compared with conventional single-pitch and single-radius springs. This enables the realization of negative stiffness characteristics and allows more flexible optimization of the bandgap range and performance. Moreover, adjusting the number of helical gradient spring arrays further enhances the bandgap width, system stability, and lightweight properties. After determining suitable geometric parameters through parametric analysis, the proposed structure achieves bending wave bandgaps from 29 Hz to 454 Hz and a complete bandgap from 72 Hz to 436 Hz, both representing ultra-wide low-frequency ranges. Additionally, intrinsic modal analysis and transmission spectrum characterization elucidate the physical mechanisms of bandgap formation and validate the design. This helical gradient spring-based local resonance structure addresses the challenges posed by the high mass and volume of traditional phononic crystals, offering a promising approach for engineering applications in low-frequency acoustic isolation metamaterials.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103632"},"PeriodicalIF":2.5,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The numerical approximation of wave propagation problems in nearly or pure incompressible solids faces several challenges such as locking and stability constraints. In this work we propose a stabilized Leapfrog scheme based on the use of Chebyshev polynomials to relax the stability condition, which is strongly limited by the enforcement of incompressibility. The scheme is fully explicit, second order accurate and energy-preserving. For the space discretization we use a mixed formulation with high-order spectral elements and mass-lumping. A strategy is proposed for an efficient and accurate computation of the pressure contribution with a new definition of the discrete Grad-div operator. Finally, we consider linear wave propagation problems in nearly-incompressible hyperelastic solids subject to static preload.
{"title":"Fully explicit numerical scheme for linearized wave propagation in nearly-incompressible soft hyperelastic solids","authors":"Giulia Merlini, Jean-Marc Allain, Sébastien Imperiale","doi":"10.1016/j.wavemoti.2025.103594","DOIUrl":"10.1016/j.wavemoti.2025.103594","url":null,"abstract":"<div><div>The numerical approximation of wave propagation problems in nearly or pure incompressible solids faces several challenges such as locking and stability constraints. In this work we propose a stabilized Leapfrog scheme based on the use of Chebyshev polynomials to relax the stability condition, which is strongly limited by the enforcement of incompressibility. The scheme is fully explicit, second order accurate and energy-preserving. For the space discretization we use a mixed formulation with high-order spectral elements and mass-lumping. A strategy is proposed for an efficient and accurate computation of the pressure contribution with a new definition of the discrete Grad-div operator. Finally, we consider linear wave propagation problems in nearly-incompressible hyperelastic solids subject to static preload.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103594"},"PeriodicalIF":2.1,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144557373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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