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应用数学和力学（英文版）
应用数学和力学（英文版）

周哲玮

月刊

0253-4827

amm@department.shu.edu.cn

021-66135601，66135219

200444

上海市上大路99号

应用数学和力学（英文版）/Journal Applied Mathematics and MechanicsCSCDEISCI
查看更多>>1980年5月由我国著名科学家、上海大学校长钱伟长院士创办。创刊至2002年底，钱伟长院士一直亲自担任主编。2003年改由我校副校长、博导周哲玮教授担任主编。钱伟长院士亲自制定办刊的宗旨是：发表力学、力学中的数学方法和近代力学密切相关的应用数学的创造性学术性论文。所谓创造性学术论文是指具有新思想、新观点、新方法的原创性学术论文。我刊对应的中文版由重庆交通大学主办并出版。英文版由上海大学主办，上海大学出版社出版。国外由德国Springer出版社发行。我刊的读者对象主要是从事与力学和应用数学有关的科研人员、工程技术人员和大专院校师生。被收录的数据库《科学引文索引（扩大版）》（SCIE）、《工程索引》（EI Compendex）、《世界译文索引》、美国《数学评论（MR）》、《应用力学评论（AMR）》、《力学》、《宇航文摘》、《当代数学》、俄罗斯《文摘杂志》力学、数学专辑，德国《数学文摘》及中国《中国力学文摘》、《中国数学文摘》、《中国物理文摘》、中国科技期刊光盘版《中国期刊网》、中国台湾《中文电子期刊服务数据库（CEPS）》、中国西南信息研究中心《中文科技期刊数据库》、中国信息研究所《万方数据库——数字化期刊群》等21种国内外权威文摘刊物及其数据库均收录我刊全文、题录和文摘。《应用数学和力学》被美国力学科学院评为17种国际力学刊物之一。
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    Mass-spring model for elastic wave propagation in multilayered van der Waals metamaterials

    Yabin JINGLifeng WANGYuqiang GAO
    1107-1118页
    查看更多>>摘要：Multilayered van der Waals(vdW)materials have attracted increasing in-terest because of the manipulability of their superior optical,electrical,thermal,and mechanical properties.A mass-spring model(MSM)for elastic wave propagation in multilayered vdW metamaterials is reported in this paper.Molecular dynamics(MD)simulations are adopted to simulate the propagation of elastic waves in multilayered vdW metamaterials.The results show that the graphene/MoS2 metamaterials have an elastic wave bandgap in the terahertz range.The MSM for the multilayered vdW metamate-rials is proposed,and the numerical simulation results show that this model can well describe the dispersion and transmission characteristics of the multilayered vdW meta-materials.The MSM can predict elastic wave transmission characteristics in multilayered vdW metamaterials stacked with different two-dimensional(2D)materials.The results presented in this paper offer theoretical help for the vibration reduction of multilayered vdW semiconductors.
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    Topology optimization of chiral metamaterials with application to underwater sound insulation

    Chao WANGHonggang ZHAOYang WANGJie ZHONG...
    1119-1138页
    查看更多>>摘要：Chiral metamaterials have been proven to possess many appealing me-chanical phenomena,such as negative Poisson's ratio,high-impact resistance,and energy absorption.This work extends the applications of chiral metamaterials to underwater sound insulation.Various chiral metamaterials with low acoustic impedance and proper stiffness are inversely designed using the topology optimization scheme.Low acoustic impedance enables the metamaterials to have a high and broadband sound transmission loss(STL),while proper stiffness guarantees its robust acoustic performance under a hy-drostatic pressure.As proof-of-concept demonstrations,two specimens are fabricated and tested in a water-filled impedance tube.Experimental results show that,on average,over 95％incident sound energy can be isolated by the specimens in a broad frequency range from 1 kHz to 5 kHz,while the sound insulation performance keeps stable under a certain hydrostatic pressure.This work may provide new insights for chiral metamaterials into the underwater applications with sound insulation.
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    On Klein tunneling of low-frequency elastic waves in hexagonal topological plates

    Yuxin YAOYuansheng MAFang HONGKai ZHANG...
    1139-1154页
    查看更多>>摘要：Incident particles in the Klein tunnel phenomenon in quantum mechanics can pass a very high potential barrier.Introducing the concept of tunneling into the analysis of phononic crystals can broaden the application prospects.In this study,the structure of the unit cell is designed,and the low frequency(＜1kHz)valley locked waveguide is realized through the creation of a phononic crystal plate with a topological phase transition interface.The defect immunity of the topological waveguide is verified,that is,the wave can propagate along the original path in the cases of impurities and disorder.Then,the tunneling phenomenon is introduced into the topological valley-locked waveguide to analyze the wave propagation,and its potential applications(such as signal separators and logic gates)are further explored by designing phononic crystal plates.This research has broad application prospects in information processing and vibration control,and potential applications in other directions are also worth exploring.
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    Modeling and analysis of gradient metamaterials for broad fusion bandgaps

    Changqi CAIChenjie ZHUFengyi ZHANGJiaojiao SUN...
    1155-1170页
    查看更多>>摘要：A gradient metamaterial with varying-stiffness local resonators is proposed to open the multiple bandgaps and further form a broad fusion bandgap.First,three local resonators with linearly increasing stiffness are periodically attached to the spring-mass chain to construct the gradient metamaterial.The dispersion relation is then derived based on Bloch's theorem to reveal the fusion bandgap theoretically.The dynamic char-acteristic of the finite spring-mass chain is investigated to validate the fusion of multiple bandgaps.Finally,the effects of the design parameters on multiple bandgaps are dis-cussed.The results show that the metamaterial with a non-uniform stiffness gradient pattern is capable of opening a broad fusion bandgap and effectively attenuating the lon-gitudinal waves within a broad frequency region.
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    A low-frequency and broadband wave-insulating vibration isolator based on plate-shaped metastructures

    Wei WEIFeng GUANXin FANG
    1171-1188页
    查看更多>>摘要：A metamaterial vibration isolator,termed as wave-insulating isolator,is proposed,which preserves enough load-bearing capability and offers ultra-low and broad bandgaps for greatly enhanced wave insulation.It consists of plate-shaped metacells,whose symmetric and antisymmetric local resonant modes offer several low and broad mode bandgaps although the complete bandgap remains high and narrow.The bandgap mechanisms,vibration isolation properties,effects of key parameters,and robustness to complex conditions are clarified.As experimentally demonstrated,the wave-insulating isolator can improve the vibration insulation in the ranges of[50 Hz,180 Hz]and[260 Hz,400 Hz]by 15 dB and 25 dB,respectively,in contrast to the conventional isolator with the same first resonant frequency.
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    Multi-layer quasi-zero-stiffness meta-structure for high-efficiency vibration isolation at low frequency

    Jiahao ZHOUJiaxi ZHOUHongbin PANKai WANG...
    1189-1208页
    查看更多>>摘要：An easily stackable multi-layer quasi-zero-stiffness(ML-QZS)meta-structure is proposed to achieve highly efficient vibration isolation performance at low frequency.First,the distributed shape optimization method is used to design the unit cel,i.e.,the single-layer QZS(SL-QZS)meta-structure.Second,the stiffness feature of the unit cell is investigated and verified through static experiments.Third,the unit cells are stacked one by one along the direction of vibration isolation,and thus the ML-QZS meta-structure is constructed.Fourth,the dynamic modeling of the ML-QZS vibration isolation meta-structure is conducted,and the dynamic responses are obtained from the equations of motion,and verified by finite element(FE)simulations.Finally,a prototype of the ML-QZS vibration isolation meta-structure is fabricated by additive manufacturing,and the vibration isolation performance is evaluated experimentally.The results show that the vibration isolation performance substantially enhances when the number of unit cells increases.More importantly,the ML-QZS meta-structure can be easily extended in the direction of vibration isolation when the unit cells are properly stacked.Hence,the ML-FQZS vibration isolation meta-structure should be a fascinating solution for highly efficient vibration isolation performance at low frequency.
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    A low-frequency pure metal metamaterial absorber with continuously tunable stiffness

    Xingzhong WANGShiteng RUIShaokun YANGWeiquan ZHANG...
    1209-1224页
    查看更多>>摘要：To address the incompatibility between high environmental adaptability and deep subwavelength characteristics in conventional local resonance metamaterials,and overcome the deficiencies in the stability of existing active control techniques for band gaps,this paper proposes a design method of pure metal vibration damping meta-material with continuously tunable stiffness for wideband elastic wave absorption.We design a dual-helix narrow-slit pure metal metamaterial unit,which possesses the triple advantage of high spatial compactness,low stiffness characteristics,and high structural stability,enabling the opening of elastic flexural band gaps in the low-frequency range.Similar to the principle of a sliding rheostat,the introduction of continuously sliding plug-ins into the helical slits enables the continuous variation of the stiffness of the meta-material unit,achieving a continuously tunable band gap effect.This successfully extends the effective band gap by more than ten times.The experimental results indicate that this metamaterial unit can be used as an additional vibration absorber to absorb the low-frequency vibration energy effectively.Furthermore,it advances the metamaterial absorbers from a purely passive narrowband design to a wideband tunable one.The pure metal double-helix metamaterials retain the subwavelength properties of metamaterials and are suitable for deployment in harsh environments.Simultaneously,by adjusting its stiffness,it substantially broadens the effective band gap range,presenting promising po-tential applications in various mechanical equipment operating under adverse conditions.
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    Reconfigurable mechanism-based metamaterials for ternary-coded elastic wave polarizers and programmable refraction control

    Zhou HUZhibo WEIYan CHENRui ZHU...
    1225-1242页
    查看更多>>摘要：Elastic metamaterials with unusual elastic properties offer unprecedented ways to modulate the polarization and propagation of elastic waves.However,most of them rely on the resonant structural components,and thus are frequency-dependent and unchangeable.Here,we present a reconfigurable 2D mechanism-based metamaterial which possesses transformable and frequency-independent elastic properties.Based on the proposed mechanism-based metamaterial,interesting functionalities,such as ternary-coded elastic wave polarizer and programmable refraction,are demonstrated.Particu-larly,unique ternary-coded polarizers,with 1-trit polarization filtering and 2-trit polar-ization separating of longitudinal and transverse waves,are first achieved.Then,the strong anisotropy of the proposed metamaterial is harnessed to realize positive-negative bi-refraction,only-positive refraction,and only-negative refraction.Finally,the wave functions with detailed microstructures are numerically verified.
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    A viscoelastic metamaterial beam for integrated vibration isolation and energy harvesting

    Long ZHAOZeqi LUHu DINGLiqun CHEN...
    1243-1260页
    查看更多>>摘要：Locally resonant metamaterials have low-frequency band gaps and the ca-pability of converging vibratory energy in the band gaps at resonant cells.It has been demonstrated by several researchers that the dissipatioin of vibratory energy within the band gap can be improved by using viscoelastic materials.This paper designs an in-tegrated viscoelastic metamaterial for energy harvesting and vibration isolation.The viscoelastic metamaterial is achieved by a viscoelastic beam periodically arrayed with spatial ball-pendulum nonlinear energy harvesters.The nonlinear resonator with an en-ergy harvesting function is achieved by placing a free-rolling magnetic ball in a spherical cavity with an additional induction coil.The dynamic equations of viscoelastic metamate-rials under transverse excitation are established,and the energy harvesting and vibration isolation characteristics within the dispersion relation of viscoelastic metamaterials are analyzed.The results show that the vibrations of the main body of the viscoelastic meta-material beam are significantly suppressed in the frequency range of the local resonance band gap.At the same time,the elastic waves are limited in the nonlinear resonator with an energy harvesting function,which improves the energy output.Finally,an experimen-tal platform of viscoelastic metamaterial vibration is established for validation purposes.
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    Ultra-wide band gap and wave attenuation mechanism of a novel star-shaped chiral metamaterial

    Shuo WANGAnshuai WANGYansen WUXiaofeng LI...
    1261-1278页
    查看更多>>摘要：A novel hollow star-shaped chiral metamaterial(SCM)is proposed by incorporating chiral structural properties into the standard hollow star-shaped metamaterial,exhibiting a wide band gap over 1500 Hz.To broaden the band gap,solid single-phase and two-phase SCMs are designed and simulated,which produce two ultra-wide band gaps(approximately 5116 Hz and 6027Hz,respectively).The main reason for the formation of the ultra-wide band gap is that the rotational vibration of the concave star of two novel SCMs drains the energy of an elastic wave.The impacts of the concave angle of a single-phase SCM and the resonator radius of a two-phase SCM on the band gaps are studied.Decreasing the concave angle leads to an increase in the width of the widest band gap,and the width of the widest band gap increases as the resonator radius of the two-phase SCM increases.Additionally,the study on elastic wave propagation characteristics involves analyzing frequency dispersion surfaces,wave propagation directions,group velocities,and phase veloci-ties.Ultimately,the analysis focuses on the transmission properties of finite periodic structures.The solid single-phase SCM achieves a maximum vibration attenuation over 800,while the width of the band gap is smaller than that of the two-phase SCM.Both metamaterials exhibit high vibration attenuation capabilities,which can be used in wideband vibration reduction to satisfy the requirement of ultra-wide frequencies.
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