Femtosecond laser-induced periodic surface structures(LIPSS)have been extensively studied over the past few decades.In particular,the period and groove width of high-spatial-frequency LIPSS(HSFL)is much smaller than t...Femtosecond laser-induced periodic surface structures(LIPSS)have been extensively studied over the past few decades.In particular,the period and groove width of high-spatial-frequency LIPSS(HSFL)is much smaller than the diffraction limit,making it a useful method for efficient nanomanufacturing.However,compared with the low-spatial-frequency LIPSS(LSFL),the structure size of the HSFL is smaller,and it is more easily submerged.Therefore,the formation mechanism of HSFL is complex and has always been a research hotspot in this field.In this study,regular LSFL with a period of 760 nm was fabricated in advance on a silicon surface with two-beam interference using an 800 nm,50 fs femtosecond laser.The ultrafast dynamics of HSFL formation on the silicon surface of prefabricated LSFL under single femtosecond laser pulse irradiation were observed and analyzed for the first time using collinear pump-probe imaging method.In general,the evolution of the surface structure undergoes five sequential stages:the LSFL begins to split,becomes uniform HSFL,degenerates into an irregular LSFL,undergoes secondary splitting into a weakly uniform HSFL,and evolves into an irregular LSFL or is submerged.The results indicate that the local enhancement of the submerged nanocavity,or the nanoplasma,in the prefabricated LSFL ridge led to the splitting of the LSFL,and the thermodynamic effect drove the homogenization of the splitting LSFL,which evolved into HSFL.展开更多
Over the past two decades,femtosecond laser-induced periodic structures(femtosecond-LIPSs)have become ubiquitous in a variety of materials,including metals,semiconductors,dielectrics,and polymers.Femtosecond-LIPSs hav...Over the past two decades,femtosecond laser-induced periodic structures(femtosecond-LIPSs)have become ubiquitous in a variety of materials,including metals,semiconductors,dielectrics,and polymers.Femtosecond-LIPSs have become a useful laser processing method,with broad prospects in adjusting material properties such as structural color,data storage,light absorption,and luminescence.This review discusses the formation mechanism of LIPSs,specifically the LIPS formation processes based on the pump-probe imaging method.The pulse shaping of a femtosecond laser in terms of the time/frequency,polarization,and spatial distribution is an efficient method for fabricating high-quality LIPSs.Various LIPS applications are also briefly introduced.The last part of this paper discusses the LIPS formation mechanism,as well as the high-efficiency and high-quality processing of LIPSs using shaped ultrafast lasers and their applications.展开更多
By taking infinite periodic beams as examples,the mutual variational principle for analyzing the free wave propagation in periodic structures is established and demonstrated through the use of the propaga- tion consta...By taking infinite periodic beams as examples,the mutual variational principle for analyzing the free wave propagation in periodic structures is established and demonstrated through the use of the propaga- tion constant in the present paper,and the corresponding hierarchical finite element formulation is then de- rived.Thus,it provides the numerical analysis of that problem with a firm theoretical basis of variational prin- ciples,with which one may conveniently illustrate the mathematical and physical mechanisms of the wave prop- agation in periodic structures and the relationship with the natural vibration.The solution is discussed and ex- amples are given.展开更多
A new computational algorithm is introduced for solving scattering problem in periodic structure. The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is uti...A new computational algorithm is introduced for solving scattering problem in periodic structure. The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is utilized for the spatial discretization. The present study reveals that the method is efficient for solving the problem.展开更多
A simple barotropic potential vorticity equation with the influence of dissipation is applied to investigate the nonlinear Rossby wave in a shear flow in the tropical atmophere. By the reduetive perturbation method, w...A simple barotropic potential vorticity equation with the influence of dissipation is applied to investigate the nonlinear Rossby wave in a shear flow in the tropical atmophere. By the reduetive perturbation method, we derive the rotational KdV （rKdV for short） equation. And then, with the help of Jaeobi elliptie functions, we obtain various periodic structures for these Rossby waves. It is shown that dissipation is very important for these periodic structures of rational form.展开更多
In this study, we designed and fabricated optical materials consisting of alternating ITO and Ag layers. This approach is considered to be a promising way to obtain a light-weight, ultrathin and transparent shielding ...In this study, we designed and fabricated optical materials consisting of alternating ITO and Ag layers. This approach is considered to be a promising way to obtain a light-weight, ultrathin and transparent shielding medium, which not only transmits visible light but also inhibits the transmission of microwaves, despite the fact that the total thickness of the Ag film is much larger than the skin depth in the visible range and less than that in the microwave region. Theoretical results suggest that a high dielectric/metal thickness ratio can enhance the broadband and improve the transmittance in the optical range. Accordingly, the central wavelength was found to be red-shifted with increasing dielectric/metal thickness ratio. A physical mechanism behind the controlling transmission of visible light is also proposed. Meanwhile, the electromagnetic shielding effectiveness of the prepared structures was found to exceed 40 dB in the range from 0.1 GHz to 18 GHz, even reaching up to 70 dB at 0.1 GHz, which is far higher than that of a single ITO film of the same thickness.展开更多
The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear d...The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. Eigen-solutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain, arising from the nonlinear spring stiffness effect, has profound effects on the overall transmission of the chain. The wave propagation characteristics are altered due to nonlinearity, and related to the incident wave intensity, which is a genuine nonlinear effect not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to closing of transmitting gaps. Comparison with the normal recursive approach shows effectiveness and superiority of the symplectic method for the wave propagation problem in nonlinear periodic structures.展开更多
By considering the characteristics of deformation of rotationally periodic structures under rotationally periodic loads, the periodic structure is divided into some identical substructures in this study. The degrees-o...By considering the characteristics of deformation of rotationally periodic structures under rotationally periodic loads, the periodic structure is divided into some identical substructures in this study. The degrees-of-freedom (DOFs) of joint nodes between the neighboring substructures are classified as master and slave ones. The stress and strain conditions of the whole structure are obtained by solving the elastic static equations for only one substructure by introducing the displacement constraints between master and slave DOFs. The complex constraint method is used to get the bifurcation buckling load and mode for the whole rotationally periodic structure by solving the eigenvalue problem for only one substructure without introducing any additional approximation. The finite element (FE) formulation of shell element of relative degrees of freedom (SERDF) in the buckling analysis is derived. Different measures of tackling internal degrees of freedom for different kinds of buckling problems and different stages of numerical analysis are presented. Some numerical examples are given to illustrate the high efficiency and validity of this method.展开更多
With the acceleration of urbanization,environmental vibration and noise pollution have become increasingly severe,and traditional vibration and noise reduction technologies are insufficient to meet current vibration c...With the acceleration of urbanization,environmental vibration and noise pollution have become increasingly severe,and traditional vibration and noise reduction technologies are insufficient to meet current vibration control requirements.This study,based on locally resonant theory,designed a novel local resonance periodic block(LRPB).Using the plane wave expansion method(PWEM)and the finite element method(FEM),this study investigated the bandgap characteristics,formation mechanisms,and vibration and acoustic performance of an LRPB under different periodic structures and material selection.The vibration reduction and noise reduction performance of LRPB has been validated through the Qingdao metro project.The research results show that the LRPB is superior to other periodic structures in terms of wide bandgap.Furthermore,configuring soft scatterer material,increasing the unit size,enhancing the material filling rate,and adopting a honeycomb arrangement can effectively reduce bandgap frequency.In structural design,non-high symmetry demonstrates greater advantages.In a study of a subway tunnel,the LRPB demonstrated superior vibration and noise mitigation performance compared to wave impeding block(WIB),thereby demonstrating potential for use in the field of vibration and noise reduction with regard to structures.展开更多
Periodic isolator is well known for its wave filtering characteristic.While in middle and high frequencies,the internal resonances of the periodic isolator are evident especially when damping is small.This study propo...Periodic isolator is well known for its wave filtering characteristic.While in middle and high frequencies,the internal resonances of the periodic isolator are evident especially when damping is small.This study proposes a novel aperiodic vibration isolation for improving the internal resonances control of the periodic isolator.The mechanism of the internal resonances control by the aperiodic isolator is firstly explained.For comparing the internal resonances suppression effect of the aperiodic isolator with the periodic isolator,a dynamic model combing the rigid machine,the isolator,and the flexible plate is derived through multi subsystem modeling method and transfer matrix method,whose accuracy is verified through the finite element method.The influences of the aperiodicity and damping of the isolator on the vibration isolation performance and internal resonances suppression effect are investigated by numerical analysis.The numerical results demonstrate that vibration attenuation performances of the periodic isolator and aperiodic isolator are greatly over than that of the continuous isolator in middle and high frequencies.The aperiodic isolator opens the stop bandgaps comparing with the periodic isolator where the pass bandgaps are periodically existed.The damping of the isolator has the stop bandgap widening effect on both the periodic isolator and the aperiodic isolator.In addition,a parameter optimization algorithm of the aperiodic isolator is presented for improving the internal resonances control effect.It is shown that the vibration peaks within the target frequency band of the aperiodic isolator are effectively reduced after the optimization.Finally,the experiments of the three different vibration isolation systems are conducted for verifying the analysis work.展开更多
A hybrid method combining simplified sub-entire domain basis function method of moment with finite element method( SSED-MoM /FEM) is accelerated for electromagnetic( EM) scattering analysis of large-scale periodic str...A hybrid method combining simplified sub-entire domain basis function method of moment with finite element method( SSED-MoM /FEM) is accelerated for electromagnetic( EM) scattering analysis of large-scale periodic structures.The unknowns are reduced sharply with non-uniform mesh in FEM. The computational complexity of the hybrid method is dramatically declined by applying conjugate gradient-fast Fourier transform( CG-FFT) to the integral equations of both electric field and magnetic field. The efficiency is further improved by using OpenMP technique. Numerical results demonstrate that the SSED-MoM /FEM method can be accelerated for more than three thousand times with large-scale periodic structures.展开更多
In this paper,the multi-scale computational method for a structure of composite materials with a small periodic configuration under the coupled thermoelasticity condition is presented. The two-scale asymptotic(TSA)exp...In this paper,the multi-scale computational method for a structure of composite materials with a small periodic configuration under the coupled thermoelasticity condition is presented. The two-scale asymptotic(TSA)expression of the displacement and the increment of temperature for composite materials with a small periodic configuration under the condition of thermoelasticity are briefly shown at first,then the multi-scale finite element algorithms based on TSA are discussed.Finally the numerical results evaluated by the multi-scale computational method are shown.It demonstrates that the basic configuration and the increment of temperature strongly influence the local strains and local stresses inside a basic cell.展开更多
Considering the mechnoelectrical coupling, the localization of SH-waves in disordered periodic layered piezoelectric structures is studied. The waves propagating in directions normal and tangential to the layers are c...Considering the mechnoelectrical coupling, the localization of SH-waves in disordered periodic layered piezoelectric structures is studied. The waves propagating in directions normal and tangential to the layers are considered. The transfer matrices between two consecutive unit cells are obtained according to the continuity conditions. The expressions of localization factor and localization length in the disordered periodic structures are presented. For the disordered periodic piezoelectric structures, the numerical results of localization factor and localization length are presented and discussed. It can be seen from the results that the frequency passbands and stopbands appear for the ordered periodic structures and the wave localization phenomenon occurs in the disordered periodic ones, and the larger the coefficient of variation is, the greater the degree of wave localization is. The widths of stopbands in the ordered periodic structures are very narrow when the properties of the consecutive piezoelectric materials are similar and the intervals of stopbands become broader when a certain material parameter has large changes. For the wave propagating in the direction normal to the layers the localization length has less dependence on the frequency, but for the wave propagating in the direction tangential to the layers the localization length is strongly dependent on the frequency.展开更多
Inhomogeneity and low efficiency are two important factors that limit the application of laser-induced periodic surface structures(LIPSSs),especially on glass surfaces.In this study,two-beam interference(TBI)of femtos...Inhomogeneity and low efficiency are two important factors that limit the application of laser-induced periodic surface structures(LIPSSs),especially on glass surfaces.In this study,two-beam interference(TBI)of femtosecond lasers was used to produce large-area straight LIPSSs on fused silica using cylindrical lenses.Compared with those produced us-ing a single circular or cylindrical lens,the LIPSSs produced by TBI are much straighter and more regular.Depending on the laser fluence and scanning velocity,LIPSSs with grating-like or spaced LIPSSs are produced on the fused silica sur-face.Their structural colors are blue,green,and red,and only green and red,respectively.Grating-like LIPSS patterns oriented in different directions are obtained and exhibit bright and vivid colors,indicating potential applications in surface coloring and anti-counterfeiting logos.展开更多
As a promising numerical tool of structural dynamics in mid- and high frequencies, the wave and finite element method（WFEM） is receiving increasingly attention and applications. In this paper, an enhanced WFEM has b...As a promising numerical tool of structural dynamics in mid- and high frequencies, the wave and finite element method（WFEM） is receiving increasingly attention and applications. In this paper, an enhanced WFEM has been developed with a reduced model and a new eigenvalue scheme. The reduced model is applicable for structures with piezoelectric shunts or local dampers;the new eigenvalue scheme can mitigate the ill-conditioning when the wave basis is calculated. The enhanced WFEM is applied to a thin-wall structure with periodically distributed piezoelectric materials（PZT）. Both free wave characteristics and forced response are analyzed and the influences of the suggested enhancements are presented. It is shown that if the control factors are properly chosen, these enhancements can improve the accuracy while accelerating the calculation. Resulting from the complexity of the application, these enhancements are not optional but imperative.展开更多
This paper investigates shear horizontal （SH） waves propagating in a periodically layered structure that consists of piezoelectric （PE） layers perfectly bonded with piezomagnetic （PM） layers alternately. The exp...This paper investigates shear horizontal （SH） waves propagating in a periodically layered structure that consists of piezoelectric （PE） layers perfectly bonded with piezomagnetic （PM） layers alternately. The explicit dispersion relations are derived for the two cases when the propagation directions of SH waves are normal to the interface and parallel to the interface, respectively. The asymptotic expressions for dispersion relations are also given when the wave number is extremely small. Numerical results for stop band effect and phase velocity are presented for a periodic system of alternating BaTiO3 and Terfenol-D layers. The influence of volume fraction on stop band effect and dispersion behaviors is discussed and revealed.展开更多
Femtosecond laser pulses with GHz burst mode that consist of a series of trains of ultrashort laser pulses with a pulse interval of several hundred picoseconds offer distinct features in material processing that canno...Femtosecond laser pulses with GHz burst mode that consist of a series of trains of ultrashort laser pulses with a pulse interval of several hundred picoseconds offer distinct features in material processing that cannot be obtained by the conventional irradiation scheme of femtosecond laser pulses(single-pulse mode).However,most studies using the GHz burst mode femtosecond laser pulses focus on ablation of materials to achieve high-efficiency and high-quality material removal.In this study,we explore the ability of the GHz burst mode femtosecond laser processing to form laser-induced periodic surface structures(LIPSS)on silicon.It is well known that the direction of LIPSS formed by the single-pulse mode with linearly polarized laser pulses is typically perpendicular to the laser polarization direction.In contrast,we find that the GHz burst mode femtosecond laser(wavelength:1030 nm,intra-pulse duration:220 fs,intra-pulse interval time(intra-pulse repetition rate):205 ps(4.88 GHz),burst pulse repetition rate:200 kHz)creates unique two-dimensional(2D)LIPSS.We regard the formation mechanism of 2D LIPSS as the synergetic contribution of the electromagnetic mechanism and the hydrodynamic mechanism.Specifically,generation of hot spots with highly enhanced electric fields by the localized surface plasmon resonance of subsequent pulses in the bursts within the nanogrooves of one-dimensional LIPSS formed by the preceding pulses creates 2D LIPSS.Additionally,hydrodynamic instability including convection flow determines the final structure of 2D LIPSS.展开更多
In this paper, we consider the electromagnetic scattering from periodic chiral structures. The structure is periodic in one direction and invariant in another direction. The electromagnetic fields in the chiral medium...In this paper, we consider the electromagnetic scattering from periodic chiral structures. The structure is periodic in one direction and invariant in another direction. The electromagnetic fields in the chiral medium are governed by the Maxwell equations together with the Drude-Born-Fedorov equations. We simplify the problem to a two-dimensional scattering problem and we show that for all but possibly a discrete set of wave numbers, there is a unique quasi-periodic weak solution to the diffraction problem. The diffraction problem can be solved by finite element method. We also establish uniform error estimates for the finite element method and the error estimates when the truncation of the nonlocal transparent boundary operators takes place.展开更多
Consider an inverse problem that aims to identify key statistical pro-perties of the profile for the unknown random perfectly conducting grating structure by boundary measurements of the diffracted fields in transvers...Consider an inverse problem that aims to identify key statistical pro-perties of the profile for the unknown random perfectly conducting grating structure by boundary measurements of the diffracted fields in transverse mag-netic polarization.The method proposed in this paper is based on a novel combination of the Monte Carlo technique,a continuation method and the Karhunen-Loève expansion for the uncertainty quantification of the random structure.Numerical results are presented to demonstrate the effectiveness of the proposed method.展开更多
Laser induced periodic surface structures(LIPSS)represent a kind of top down approach to produce highly reproducible nano/microstructures without going for any sophisticated process of lithography.This method is much ...Laser induced periodic surface structures(LIPSS)represent a kind of top down approach to produce highly reproducible nano/microstructures without going for any sophisticated process of lithography.This method is much simpler and cost effective.In this work,LIPSS on Si surfaces were generated using femtosecond laser pulses of 800 nm wavelength.Photocatalytic substrates were prepared by depositing TiO2 thin films on top of the structured and unstructured Si wafer.The coatings were produced by sputtering from a Ti target in two different types of oxygen atmospheres.In first case,the oxygen pressure within the sputtering chamber was chosen to be high(3×10^–2 mbar)whereas it was one order of magnitude lower in second case(2.1×10^–3 mbar).In photocatalytic dye decomposition study of Methylene blue dye it was found that in the presence of LIPSS the activity can be enhanced by 2.1 and 3.3 times with high pressure and low pressure grown TiO2 thin films,respectively.The increase in photocatalytic activity is attributed to the enlargement of effective surface area.In comparative study,the dye decomposition rates of TiO2 thin films grown on LIPSS are found to be much higher than the value for standard reference thin film material Pilkington Activ^TM.展开更多
基金supports from the National Natural Science Foundation of China(12074123,12174108)the Foundation of‘Manufacturing beyond limits’of Shanghai‘Talent Program'of Henan Academy of Sciences.
文摘Femtosecond laser-induced periodic surface structures(LIPSS)have been extensively studied over the past few decades.In particular,the period and groove width of high-spatial-frequency LIPSS(HSFL)is much smaller than the diffraction limit,making it a useful method for efficient nanomanufacturing.However,compared with the low-spatial-frequency LIPSS(LSFL),the structure size of the HSFL is smaller,and it is more easily submerged.Therefore,the formation mechanism of HSFL is complex and has always been a research hotspot in this field.In this study,regular LSFL with a period of 760 nm was fabricated in advance on a silicon surface with two-beam interference using an 800 nm,50 fs femtosecond laser.The ultrafast dynamics of HSFL formation on the silicon surface of prefabricated LSFL under single femtosecond laser pulse irradiation were observed and analyzed for the first time using collinear pump-probe imaging method.In general,the evolution of the surface structure undergoes five sequential stages:the LSFL begins to split,becomes uniform HSFL,degenerates into an irregular LSFL,undergoes secondary splitting into a weakly uniform HSFL,and evolves into an irregular LSFL or is submerged.The results indicate that the local enhancement of the submerged nanocavity,or the nanoplasma,in the prefabricated LSFL ridge led to the splitting of the LSFL,and the thermodynamic effect drove the homogenization of the splitting LSFL,which evolved into HSFL.
基金This work was supported by the National Natural Science Foundation of China(12074123,11804227,91950112)the Ministry of Science and Technology of China(Grant No.2021YFA1401100)the Foundation of‘Manufacturing beyond limits’of Shanghai.
文摘Over the past two decades,femtosecond laser-induced periodic structures(femtosecond-LIPSs)have become ubiquitous in a variety of materials,including metals,semiconductors,dielectrics,and polymers.Femtosecond-LIPSs have become a useful laser processing method,with broad prospects in adjusting material properties such as structural color,data storage,light absorption,and luminescence.This review discusses the formation mechanism of LIPSs,specifically the LIPS formation processes based on the pump-probe imaging method.The pulse shaping of a femtosecond laser in terms of the time/frequency,polarization,and spatial distribution is an efficient method for fabricating high-quality LIPSs.Various LIPS applications are also briefly introduced.The last part of this paper discusses the LIPS formation mechanism,as well as the high-efficiency and high-quality processing of LIPSs using shaped ultrafast lasers and their applications.
基金Supported by Doctorate Training Fund of National Education Commission of China
文摘By taking infinite periodic beams as examples,the mutual variational principle for analyzing the free wave propagation in periodic structures is established and demonstrated through the use of the propaga- tion constant in the present paper,and the corresponding hierarchical finite element formulation is then de- rived.Thus,it provides the numerical analysis of that problem with a firm theoretical basis of variational prin- ciples,with which one may conveniently illustrate the mathematical and physical mechanisms of the wave prop- agation in periodic structures and the relationship with the natural vibration.The solution is discussed and ex- amples are given.
基金Supported by the NNSF of China(10626017)the Science Foundation of the Education Committee of Heilongjiang Province(11511276)the Foundation of Heilongjiang Province(LBH-Q05114).
文摘A new computational algorithm is introduced for solving scattering problem in periodic structure. The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is utilized for the spatial discretization. The present study reveals that the method is efficient for solving the problem.
基金The project supports by National Natural Science Foundation of China under Grant No. 40233033
文摘A simple barotropic potential vorticity equation with the influence of dissipation is applied to investigate the nonlinear Rossby wave in a shear flow in the tropical atmophere. By the reduetive perturbation method, we derive the rotational KdV （rKdV for short） equation. And then, with the help of Jaeobi elliptie functions, we obtain various periodic structures for these Rossby waves. It is shown that dissipation is very important for these periodic structures of rational form.
基金Project supported by the International Science&Technology Cooperation Program of China(Grant No.2014DFR10020)the Science Foundation of Shanxi Province,China(Grant Nos.201701D121050 and 201701D121007)
文摘In this study, we designed and fabricated optical materials consisting of alternating ITO and Ag layers. This approach is considered to be a promising way to obtain a light-weight, ultrathin and transparent shielding medium, which not only transmits visible light but also inhibits the transmission of microwaves, despite the fact that the total thickness of the Ag film is much larger than the skin depth in the visible range and less than that in the microwave region. Theoretical results suggest that a high dielectric/metal thickness ratio can enhance the broadband and improve the transmittance in the optical range. Accordingly, the central wavelength was found to be red-shifted with increasing dielectric/metal thickness ratio. A physical mechanism behind the controlling transmission of visible light is also proposed. Meanwhile, the electromagnetic shielding effectiveness of the prepared structures was found to exceed 40 dB in the range from 0.1 GHz to 18 GHz, even reaching up to 70 dB at 0.1 GHz, which is far higher than that of a single ITO film of the same thickness.
基金Project supported by the National Natural Science Foundation of China (Nos. 10972182,10772147,and 10632030)the National Basic Research Program of China (No. 2006CB 601202)+4 种基金the National 111 Project of China (No. B07050)the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment (No. GZ0802)the Doctoral Foundation of Northwestern Polytechnical University (No. CX200908)the China Postdoctoral Science Foundation (No. 20090450170)the Northwestern Polytechnical University Foundation for Fundamental Research (No. JC200938)
文摘The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. Eigen-solutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain, arising from the nonlinear spring stiffness effect, has profound effects on the overall transmission of the chain. The wave propagation characteristics are altered due to nonlinearity, and related to the incident wave intensity, which is a genuine nonlinear effect not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to closing of transmitting gaps. Comparison with the normal recursive approach shows effectiveness and superiority of the symplectic method for the wave propagation problem in nonlinear periodic structures.
文摘By considering the characteristics of deformation of rotationally periodic structures under rotationally periodic loads, the periodic structure is divided into some identical substructures in this study. The degrees-of-freedom (DOFs) of joint nodes between the neighboring substructures are classified as master and slave ones. The stress and strain conditions of the whole structure are obtained by solving the elastic static equations for only one substructure by introducing the displacement constraints between master and slave DOFs. The complex constraint method is used to get the bifurcation buckling load and mode for the whole rotationally periodic structure by solving the eigenvalue problem for only one substructure without introducing any additional approximation. The finite element (FE) formulation of shell element of relative degrees of freedom (SERDF) in the buckling analysis is derived. Different measures of tackling internal degrees of freedom for different kinds of buckling problems and different stages of numerical analysis are presented. Some numerical examples are given to illustrate the high efficiency and validity of this method.
基金Natural Science Foundation of China under Grant No.42277130Natural Science Foundation of Shandong Province under Grant No.ZR2021ME144。
文摘With the acceleration of urbanization,environmental vibration and noise pollution have become increasingly severe,and traditional vibration and noise reduction technologies are insufficient to meet current vibration control requirements.This study,based on locally resonant theory,designed a novel local resonance periodic block(LRPB).Using the plane wave expansion method(PWEM)and the finite element method(FEM),this study investigated the bandgap characteristics,formation mechanisms,and vibration and acoustic performance of an LRPB under different periodic structures and material selection.The vibration reduction and noise reduction performance of LRPB has been validated through the Qingdao metro project.The research results show that the LRPB is superior to other periodic structures in terms of wide bandgap.Furthermore,configuring soft scatterer material,increasing the unit size,enhancing the material filling rate,and adopting a honeycomb arrangement can effectively reduce bandgap frequency.In structural design,non-high symmetry demonstrates greater advantages.In a study of a subway tunnel,the LRPB demonstrated superior vibration and noise mitigation performance compared to wave impeding block(WIB),thereby demonstrating potential for use in the field of vibration and noise reduction with regard to structures.
基金supported by the National Key Research and Development Plan of China (Grant No.2023YFB3406302)Guangdong Basic and Applied Basic Research Foundation (Grant No.2024A1515011126)the Key Research and Development Plan of Shanxi (Grant No.2024GH-ZDXM-29)。
文摘Periodic isolator is well known for its wave filtering characteristic.While in middle and high frequencies,the internal resonances of the periodic isolator are evident especially when damping is small.This study proposes a novel aperiodic vibration isolation for improving the internal resonances control of the periodic isolator.The mechanism of the internal resonances control by the aperiodic isolator is firstly explained.For comparing the internal resonances suppression effect of the aperiodic isolator with the periodic isolator,a dynamic model combing the rigid machine,the isolator,and the flexible plate is derived through multi subsystem modeling method and transfer matrix method,whose accuracy is verified through the finite element method.The influences of the aperiodicity and damping of the isolator on the vibration isolation performance and internal resonances suppression effect are investigated by numerical analysis.The numerical results demonstrate that vibration attenuation performances of the periodic isolator and aperiodic isolator are greatly over than that of the continuous isolator in middle and high frequencies.The aperiodic isolator opens the stop bandgaps comparing with the periodic isolator where the pass bandgaps are periodically existed.The damping of the isolator has the stop bandgap widening effect on both the periodic isolator and the aperiodic isolator.In addition,a parameter optimization algorithm of the aperiodic isolator is presented for improving the internal resonances control effect.It is shown that the vibration peaks within the target frequency band of the aperiodic isolator are effectively reduced after the optimization.Finally,the experiments of the three different vibration isolation systems are conducted for verifying the analysis work.
基金Supported by the Aeronautical Science Foundation of China(20121852031)
文摘A hybrid method combining simplified sub-entire domain basis function method of moment with finite element method( SSED-MoM /FEM) is accelerated for electromagnetic( EM) scattering analysis of large-scale periodic structures.The unknowns are reduced sharply with non-uniform mesh in FEM. The computational complexity of the hybrid method is dramatically declined by applying conjugate gradient-fast Fourier transform( CG-FFT) to the integral equations of both electric field and magnetic field. The efficiency is further improved by using OpenMP technique. Numerical results demonstrate that the SSED-MoM /FEM method can be accelerated for more than three thousand times with large-scale periodic structures.
基金The project supported by the National Natural Science Foundation of China(19932030)Special Funds for Major State Basic Research Projects
文摘In this paper,the multi-scale computational method for a structure of composite materials with a small periodic configuration under the coupled thermoelasticity condition is presented. The two-scale asymptotic(TSA)expression of the displacement and the increment of temperature for composite materials with a small periodic configuration under the condition of thermoelasticity are briefly shown at first,then the multi-scale finite element algorithms based on TSA are discussed.Finally the numerical results evaluated by the multi-scale computational method are shown.It demonstrates that the basic configuration and the increment of temperature strongly influence the local strains and local stresses inside a basic cell.
基金The project supported by National Natural Science Foundation of China (10632020, 10672017 and 20451057)
文摘Considering the mechnoelectrical coupling, the localization of SH-waves in disordered periodic layered piezoelectric structures is studied. The waves propagating in directions normal and tangential to the layers are considered. The transfer matrices between two consecutive unit cells are obtained according to the continuity conditions. The expressions of localization factor and localization length in the disordered periodic structures are presented. For the disordered periodic piezoelectric structures, the numerical results of localization factor and localization length are presented and discussed. It can be seen from the results that the frequency passbands and stopbands appear for the ordered periodic structures and the wave localization phenomenon occurs in the disordered periodic ones, and the larger the coefficient of variation is, the greater the degree of wave localization is. The widths of stopbands in the ordered periodic structures are very narrow when the properties of the consecutive piezoelectric materials are similar and the intervals of stopbands become broader when a certain material parameter has large changes. For the wave propagating in the direction normal to the layers the localization length has less dependence on the frequency, but for the wave propagating in the direction tangential to the layers the localization length is strongly dependent on the frequency.
文摘Inhomogeneity and low efficiency are two important factors that limit the application of laser-induced periodic surface structures(LIPSSs),especially on glass surfaces.In this study,two-beam interference(TBI)of femtosecond lasers was used to produce large-area straight LIPSSs on fused silica using cylindrical lenses.Compared with those produced us-ing a single circular or cylindrical lens,the LIPSSs produced by TBI are much straighter and more regular.Depending on the laser fluence and scanning velocity,LIPSSs with grating-like or spaced LIPSSs are produced on the fused silica sur-face.Their structural colors are blue,green,and red,and only green and red,respectively.Grating-like LIPSS patterns oriented in different directions are obtained and exhibit bright and vivid colors,indicating potential applications in surface coloring and anti-counterfeiting logos.
基金the company PSA Peugeot Citroёn for the financial support
文摘As a promising numerical tool of structural dynamics in mid- and high frequencies, the wave and finite element method（WFEM） is receiving increasingly attention and applications. In this paper, an enhanced WFEM has been developed with a reduced model and a new eigenvalue scheme. The reduced model is applicable for structures with piezoelectric shunts or local dampers;the new eigenvalue scheme can mitigate the ill-conditioning when the wave basis is calculated. The enhanced WFEM is applied to a thin-wall structure with periodically distributed piezoelectric materials（PZT）. Both free wave characteristics and forced response are analyzed and the influences of the suggested enhancements are presented. It is shown that if the control factors are properly chosen, these enhancements can improve the accuracy while accelerating the calculation. Resulting from the complexity of the application, these enhancements are not optional but imperative.
基金supported by the National Natural Science Foundation of China (Nos.10672108,10572069 and 10820101048)
文摘This paper investigates shear horizontal （SH） waves propagating in a periodically layered structure that consists of piezoelectric （PE） layers perfectly bonded with piezomagnetic （PM） layers alternately. The explicit dispersion relations are derived for the two cases when the propagation directions of SH waves are normal to the interface and parallel to the interface, respectively. The asymptotic expressions for dispersion relations are also given when the wave number is extremely small. Numerical results for stop band effect and phase velocity are presented for a periodic system of alternating BaTiO3 and Terfenol-D layers. The influence of volume fraction on stop band effect and dispersion behaviors is discussed and revealed.
基金supported by MEXT Quantum Leap Flagship Program(MEXT Q-LEAP)Grant Number JPMXS0118067246.
文摘Femtosecond laser pulses with GHz burst mode that consist of a series of trains of ultrashort laser pulses with a pulse interval of several hundred picoseconds offer distinct features in material processing that cannot be obtained by the conventional irradiation scheme of femtosecond laser pulses(single-pulse mode).However,most studies using the GHz burst mode femtosecond laser pulses focus on ablation of materials to achieve high-efficiency and high-quality material removal.In this study,we explore the ability of the GHz burst mode femtosecond laser processing to form laser-induced periodic surface structures(LIPSS)on silicon.It is well known that the direction of LIPSS formed by the single-pulse mode with linearly polarized laser pulses is typically perpendicular to the laser polarization direction.In contrast,we find that the GHz burst mode femtosecond laser(wavelength:1030 nm,intra-pulse duration:220 fs,intra-pulse interval time(intra-pulse repetition rate):205 ps(4.88 GHz),burst pulse repetition rate:200 kHz)creates unique two-dimensional(2D)LIPSS.We regard the formation mechanism of 2D LIPSS as the synergetic contribution of the electromagnetic mechanism and the hydrodynamic mechanism.Specifically,generation of hot spots with highly enhanced electric fields by the localized surface plasmon resonance of subsequent pulses in the bursts within the nanogrooves of one-dimensional LIPSS formed by the preceding pulses creates 2D LIPSS.Additionally,hydrodynamic instability including convection flow determines the final structure of 2D LIPSS.
基金The Special Funds for Major State Basic Research Projects (G1999032802) in China the NNSF (10076006) of China.
文摘In this paper, we consider the electromagnetic scattering from periodic chiral structures. The structure is periodic in one direction and invariant in another direction. The electromagnetic fields in the chiral medium are governed by the Maxwell equations together with the Drude-Born-Fedorov equations. We simplify the problem to a two-dimensional scattering problem and we show that for all but possibly a discrete set of wave numbers, there is a unique quasi-periodic weak solution to the diffraction problem. The diffraction problem can be solved by finite element method. We also establish uniform error estimates for the finite element method and the error estimates when the truncation of the nonlocal transparent boundary operators takes place.
基金supported in part by National Natural Science Foundation of China Innovative Group Fund(Grant No.11621101)
文摘Consider an inverse problem that aims to identify key statistical pro-perties of the profile for the unknown random perfectly conducting grating structure by boundary measurements of the diffracted fields in transverse mag-netic polarization.The method proposed in this paper is based on a novel combination of the Monte Carlo technique,a continuation method and the Karhunen-Loève expansion for the uncertainty quantification of the random structure.Numerical results are presented to demonstrate the effectiveness of the proposed method.
基金Deutsche Forschungsgemeinschaft (DFG), Germany (Grant number GR 1782/12)Science and Engineering Research Board (SERB), India (Grant number EMR/2015/001175)
文摘Laser induced periodic surface structures(LIPSS)represent a kind of top down approach to produce highly reproducible nano/microstructures without going for any sophisticated process of lithography.This method is much simpler and cost effective.In this work,LIPSS on Si surfaces were generated using femtosecond laser pulses of 800 nm wavelength.Photocatalytic substrates were prepared by depositing TiO2 thin films on top of the structured and unstructured Si wafer.The coatings were produced by sputtering from a Ti target in two different types of oxygen atmospheres.In first case,the oxygen pressure within the sputtering chamber was chosen to be high(3×10^–2 mbar)whereas it was one order of magnitude lower in second case(2.1×10^–3 mbar).In photocatalytic dye decomposition study of Methylene blue dye it was found that in the presence of LIPSS the activity can be enhanced by 2.1 and 3.3 times with high pressure and low pressure grown TiO2 thin films,respectively.The increase in photocatalytic activity is attributed to the enlargement of effective surface area.In comparative study,the dye decomposition rates of TiO2 thin films grown on LIPSS are found to be much higher than the value for standard reference thin film material Pilkington Activ^TM.
