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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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    Theoretical and experimental investigation of the resonance responses and chaotic dynamics of a bistable laminated composite shell in the dynamic snap-through mode

    Meiqi WUPengyu LVHongyuan LIJiale YAN...
    581-602页
    查看更多>>摘要：The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors.The existence of the 1∶1 resonance relationship between two order vibration modes of the system is verified.The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated,and the four-dimensional(4D)non-linear modulation equations are derived based on the 1∶1 internal resonance relationship by means of the multiple scales method.The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed.The discussion focuses on investigating the effects of key parameters,e.g.,excitation amplitude,damping coeffi-cient,and detuning parameters,on the resonance responses.The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system.Furthermore,the significant motions under particular excitation conditions are visualized by bifurcation diagrams,time histories,phase portraits,three-dimensional(3D)phase portraits,and Poincare maps.Finally,the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell,yielding results that are qualitatively consistent with the theoretical results.
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    Adaptive state-constrained/model-free iterative sliding mode control for aerial robot trajectory tracking

    Chen ANJiaxi ZHOUKai WANG
    603-618页
    查看更多>>摘要：This paper develops a novel hierarchical control strategy for improving the trajectory tracking capability of aerial robots under parameter uncertainties.The hierarchical control strategy is composed of an adaptive sliding mode controller and a model-free iterative sliding mode controller(MFISMC).A position controller is designed based on adaptive sliding mode control(SMC)to safely drive the aerial robot and ensure fast state convergence under external disturbances.Additionally,the MFISMC acts as an attitude controller to estimate the unmodeled dynamics without detailed knowledge of aerial robots.Then,the adaption laws are derived with the Lyapunov theory to guarantee the asymptotic tracking of the system state.Finally,to demonstrate the performance and robustness of the proposed control strategy,numerical simulations are carried out,which are also compared with other conventional strategies,such as proportional-integral-derivative(PID),backstepping(BS),and SMC.The simulation results indicate that the proposed hierarchical control strategy can fulfill zero steady-state error and achieve faster convergence compared with conventional strategies.
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    Love wave propagation in one-dimensional piezoelectric quasicrystal multilayered nanoplates with surface effects

    Xin FENGLiaoliang KEYang GAO
    619-632页
    查看更多>>摘要：The exact solutions for the propagation of Love waves in one-dimensional(1D)hexagonal piezoelectric quasicrystal(PQC)nanoplates with surface effects are de-rived.An electro-elastic model is developed to investigate the anti-plane strain problem of Love wave propagation.By introducing three shape functions,the wave equations and electric balance equations are decoupled into three uncorrelated problems.Satisfying the boundary conditions of the top surface on the covering layer,the interlayer interface,and the matrix,a dispersive equation with the influence of multi-physical field coupling is provided.A surface PQC model is developed to investigate the surface effects on the propagation behaviors of Love waves in quasicrystal(QC)multilayered structures with nanoscale thicknesses.A novel dispersion relation for the PQC structure is derived in an explicit closed form according to the non-classical mechanical and electric boundary conditions.Numerical examples are given to reveal the effects of the boundary condi-tions,stacking sequence,characteristic scale,and phason fluctuation characteristics on the dispersion curves of Love waves propagating in PQC nanoplates with surface effects.
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    Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses:discrete and continuum models

    E.GHAVANLOOS.EL-BORGI
    633-648页
    查看更多>>摘要：The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed masses.The developed model can represent the wave propagation prob-lem in a non-homogeneous material consisting of heavy inclusions embedded in a matrix.The inclusions are idealized by lumped masses,and the matrix between adjacent inclu-sions is modeled by a nonlinear spring with distributed masses.Additionally,the model is capable of depicting the wave propagation in bi-material bars,wherein the first material is represented by a rigid particle and the second one is represented by a nonlinear spring with distributed masses.The discrete model of the nonlinear monoatomic chain with lumped and distributed masses is first considered,and a closed-form expression of the dispersion relation is obtained by the second-order Lindstedt-Poincare method(LPM).Next,a continuum model for the nonlinear monoatomic chain is derived directly from its discrete lattice model by a suitable continualization technique.The subsequent use of the second-order method of multiple scales(MMS)facilitates the derivation of the cor-responding nonlinear dispersion relation in a closed form.The novelties of the present study consist of(ⅰ)considering the inertia of nonlinear springs on the dispersion behavior of the discrete mass-spring chains;(ⅱ)developing the second-order LPM for the wave propagation in the discrete chains;and(ⅲ)deriving a continuum model for the nonlinear monoatomic chains with lumped and distributed masses.Finally,a parametric study is conducted to examine the effects of the design parameters and the distributed spring mass on the nonlinear dispersion relations and phase velocities obtained from both the discrete and continuum models.These parameters include the ratio of the spring mass to the lumped mass,the nonlinear stiffness coefficient of the spring,and the wave amplitude.
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    Indentation behavior of a semi-infinite piezoelectric semiconductor under a rigid flat-ended cylindrical indenter

    Shijing GAOLele ZHANGJinxi LIUGuoquan NIE...
    649-662页
    查看更多>>摘要：This paper theoretically studies the axisymmetric frictionless indentation of a transversely isotropic piezoelectric semiconductor(PSC)half-space subject to a rigid flat-ended cylindrical indenter.The contact area and other surface of the PSC half-space are assumed to be electrically insulating.By the Hankel integral transformation,the problem is reduced to the Fredholm integral equation of the second kind.This equation is solved numerically to obtain the indentation behaviors of the PSC half-space,mainly including the indentation force-depth relation and the electric potential-depth relation.The results show that the effect of the semiconductor property on the indentation responses is limited within a certain range of variation of the steady carrier concentration.The dependence of indentation behavior on material properties is also analyzed by two different kinds of PSCs.Finite element simulations are conducted to verify the results calculated by the integral equation technique,and good agreement is demonstrated.
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    Supposition of graphene stacks to estimate the contact resistance and conductivity of nanocomposites

    Y.ZAREM.T.MUNIRG.J.WENGK.Y.RHEE...
    663-676页
    查看更多>>摘要：In this study,the effects of stacked nanosheets and the surrounding inter-phase zone on the resistance of the contact region between nanosheets and the tunneling conductivity of samples are evaluated with developed equations superior to those previ-ously reported.The contact resistance and nanocomposite conductivity are modeled by several influencing factors,including stack properties,interphase depth,tunneling size,and contact diameter.The developed model's accuracy is verified through numerous experimental measurements.To further validate the models and establish correlations between parameters,the effects of all the variables on contact resistance and nanocom-posite conductivity are analyzed.Notably,the contact resistance is primarily dependent on the polymer tunnel resistivity,contact area,and tunneling size.The dimensions of the graphene nanosheets significantly influence the conductivity,which ranges from 0 S/m to 90 S/m.An increased number of nanosheets in stacks and a larger gap between them en-hance the nanocomposite's conductivity.Furthermore,the thicker interphase and smaller tunneling size can lead to higher sample conductivity due to their optimistic effects on the percolation threshold and network efficacy.
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    Study of hybrid nanofluid flow in a stationary cone-disk system with temperature-dependent fluid properties

    A.S.JOHNB.MAHANTHESHG.LORENZINI
    677-694页
    查看更多>>摘要：Cone-disk systems find frequent use such as conical diffusers,medical de-vices,various rheometric,and viscosimetry applications.In this study,we investigate the three-dimensional flow of a water-based Ag-MgO hybrid nanofluid in a static cone-disk system while considering temperature-dependent fluid properties.How the variable fluid properties affect the dynamics and heat transfer features is studied by Reynolds's lin-earized model for variable viscosity and Chiam's model for variable thermal conductivity.The single-phase nanofluid model is utilized to describe convective heat transfer in hybrid nanofluids,incorporating the experimental data.This model is developed as a coupled system of convective-diffusion equations,encompassing the conservation of momentum and the conservation of thermal energy,in conjunction with an incompressibility condi-tion.A self-similar model is developed by the Lie-group scaling transformations,and the subsequent self-similar equations are then solved numerically.The influence of variable fluid parameters on both swirling and non-swirling flow cases is analyzed.Additionally,the Nusselt number for the disk surface is calculated.It is found that an increase in the temperature-dependent viscosity parameter enhances heat transfer characteristics in the static cone-disk system,while the thermal conductivity parameter has the opposite effect.
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    Analytical solutions of turbulent boundary layer beneath forward-leaning waves

    Yiqin XIEJifu ZHOUXu WANGJinlong DUAN...
    695-710页
    查看更多>>摘要：As a typical nonlinear wave,forward-leaning waves can be frequently encoun-tered in the near-shore areas,which can impact coastal sediment transport significantly.Hence,it is of significance to describe the characteristics of the boundary layer beneath forward-leaning waves accurately,especially for the turbulent boundary layer.In this work,the linearized turbulent boundary layer model with a linear turbulent viscosity co-efficient is applied,and the novel expression of the near-bed orbital velocity that has been worked out by the authors for forward-leaning waves of arbitrary forward-leaning degrees is further used to specify the free stream boundary condition of the bottom boundary layer.Then,a variable transformation is found so as to make the equation of the tur-bulent boundary layer model be solved analytically through a modified Bessel function.Consequently,an explicit analytical solution of the turbulent boundary layer beneath forward-leaning waves is derived by means of variable separation and variable transfor-mation.The analytical solutions of the velocity profile and bottom shear stress of the turbulent boundary layer beneath forward-leaning waves are verified by comparing the present analytical results with typical experimental data available in the previous litera-ture.
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    The viscous strip approach to simplify the calculation of the surface acoustic wave generated streaming

    F.JAZINI DORCHEHM.GHASSEMI
    711-724页
    查看更多>>摘要：In recent decades,the importance of surface acoustic waves,as a biocompati-ble tool to integrate with microfluidics,has been proven in various medical and biological applications.The numerical modeling of acoustic streaming caused by surface acoustic waves in microchannels requires the effect of viscosity to be considered in the equations which complicates the solution.In this paper,it is shown that the major contribution of viscosity and the horizontal component of actuation is concentrated in a narrow region alongside the actuation boundary.Since the inviscid equations are considerably easier to solve,a division into the viscous and inviscid domains would alleviate the computational load significantly.The particles'traces calculated by this approximation are excellently alongside their counterparts from the completely viscous model.It is also shown that the optimum thickness for the viscous strip is about 9-fold the acoustic boundary layer thickness for various flow patterns and amplitudes of actuation.
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    Aerodynamic/stealth design of S-duct inlet based on discrete adjoint method

    Jun DENGKe ZHAOLin ZHOUWei ZHANG...
    725-746页
    查看更多>>摘要：It is a major challenge for the airframe-inlet design of modern combat aircrafts,as the flow and electromagnetic wave propagation in the inlet of stealth aircraft are very complex.In this study,an aerodynamic/stealth optimization design method for an S-duct inlet is proposed.The upwind scheme is introduced to the aerodynamic adjoint equation to resolve the shock wave and flow separation.The multilevel fast multipole algorithm(MLFMA)is utilized for the stealth adjoint equation.A dorsal S-duct inlet of flying wing layout is optimized to improve the aerodynamic and stealth characteristics.Both the aerodynamic and stealth characteristics of the inlet are effectively improved.Finally,the optimization results are analyzed,and it shows that the main contradiction between aerodynamic characteristics and stealth characteristics is the centerline and cross-sectional area.The S-duct is smoothed,and the cross-sectional area is increased to improve the aerodynamic characteristics,while it is completely opposite for the stealth design.The radar cross section(RCS)is reduced by phase cancelation for low frequency conditions.The method is suitable for the aerodynamic/stealth design of the aircraft airframe-inlet system.
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