Chiral metamaterials are manmade structures with extraordinary mechanical properties derived from their special geometric design instead of chemical composition.To make the mechanical deformation programmable,the non-...Chiral metamaterials are manmade structures with extraordinary mechanical properties derived from their special geometric design instead of chemical composition.To make the mechanical deformation programmable,the non-uniform rational B-spline(NURBS)curves are taken to replace the traditional ligament boundaries of the chiral structure.The Neural networks are innovatively inserted into the calculation of mechanical properties of the chiral structure instead of finite element methods to improve computational efficiency.For the problem of finding structure configuration with specified mechanical properties,such as Young’s modulus,Poisson’s ratio or deformation,an inverse design method using the Neural network-based proxy model is proposed to build the relationship between mechanical properties and geometric configuration.To satisfy some more complex deformation requirements,a non-homogeneous inverse design method is proposed and verified through simulation and experiments.Numerical and test results reveal the high computational efficiency and accuracy of the proposed method in the design of chiral metamaterials.展开更多
Multibody system dynamics provides a strong tool for the estimation of dynamic performances and the optimization of multisystem robot design. It can be described with differential algebraic equations(DAEs). In this pa...Multibody system dynamics provides a strong tool for the estimation of dynamic performances and the optimization of multisystem robot design. It can be described with differential algebraic equations(DAEs). In this paper, a particle swarm optimization(PSO) method is introduced to solve and control a symplectic multibody system for the first time. It is first combined with the symplectic method to solve problems in uncontrolled and controlled robotic arm systems. It is shown that the results conserve the energy and keep the constraints of the chaotic motion, which demonstrates the efficiency, accuracy, and time-saving ability of the method. To make the system move along the pre-planned path, which is a functional extremum problem, a double-PSO-based instantaneous optimal control is introduced. Examples are performed to test the effectiveness of the double-PSO-based instantaneous optimal control. The results show that the method has high accuracy, a fast convergence speed, and a wide range of applications.All the above verify the immense potential applications of the PSO method in multibody system dynamics.展开更多
In this study,the wave propagation properties of lattice metamaterials with Koch fractal structures are investigated in terms of band structures and directional wave propagation.The analytical models of lattice metama...In this study,the wave propagation properties of lattice metamaterials with Koch fractal structures are investigated in terms of band structures and directional wave propagation.The analytical models of lattice metamaterials are established using the finite element method,and the dispersion relation is solved using the Bloch’s theorem.The band structures of the lattice metamaterials with different numbers of iterations are studied,and the group velocities at a selected frequency are calculated to analyze the directional wave propagation characteristics.Furthermore,dynamic responses of the finite structures are calculated using commercial finite element software to verify the band gaps and directional wave propagation behaviors in the lattice metamaterials.The results show that multiple and low band gaps are present in the lattice materials with various geometric parameters of the Koch fractal,and the position of the lowest band gap decreases as the number of iterations increases.The results indicate the potential applications of lattice metamaterials with Koch fractals for vibration isolation and multi-functional design.展开更多
In this study,multi-resonator coupled metamaterials(MRCMs)with local resonators are proposed to obtain the multiple and wide band gaps.Kinetic models of the MRCMs are established,and the boundary conditions of the uni...In this study,multi-resonator coupled metamaterials(MRCMs)with local resonators are proposed to obtain the multiple and wide band gaps.Kinetic models of the MRCMs are established,and the boundary conditions of the unit cell are obtained with Bloch's theorem.The effects of structural parameters,including the mass of the resonator and the spring stiffness,on the distributions of the band gaps are studied.Furthermore,the frequency domain responses and the time domain responses are calculated for analyzing the structural vibration characteristics and the effects of damping on structural vibration.The results show that the frequency domain response can accurately express the distributions of the band gaps of the MRCMs,and we can increase the number and the width of the band gaps by using the MRCMs for the superior vibration suppression capability.展开更多
The dynamic analysis on the ultra-large spatial structure can be simplified drastically by ignoring the flexibility and damping of the structure.However,these simplifications will result in the erroneous estimate on t...The dynamic analysis on the ultra-large spatial structure can be simplified drastically by ignoring the flexibility and damping of the structure.However,these simplifications will result in the erroneous estimate on the dynamic behaviors of the ultra-large spatial structure.Taking the spatial beam as an example,the minimum control energy defined by the difference between the initial total energy and the final total energy in the assumed stable attitude state of the beam is investigated by the structure-preserving method proposed in our previous studies in two cases:the spatial beam considering the flexibility as well as the damping effect,and the spatial beam ignoring both the flexibility and the damping effect.In the numerical experiments,the assumed simulation interval of three months is evaluated on whether or not it is long enough for the spatial flexible damping beam to arrive at the assumed stable attitude state.And then,taking the initial attitude angle and the initial attitude angle velocity as the independent variables,respectively,the minimum control energies of the mentioned two cases are investigated in detail.From the numerical results,the following conclusions can be obtained.With the fixed initial attitude angle velocity,the minimum control energy of the spatial flexible damping beam is higher than that of the spatial rigid beam when the initial attitude angle is close to or far away from the stable attitude state.With the fixed initial attitude angle,ignoring the flexibility and the damping effect will underestimate the minimum control energy of the spatial beam.展开更多
connecting wires are the main manifestations of the coupling dynamic effects on the orbit evolution,the attitude adjusting and the flexible vibration of the tethered satellite system.To investigate attitude evolution ...connecting wires are the main manifestations of the coupling dynamic effects on the orbit evolution,the attitude adjusting and the flexible vibration of the tethered satellite system.To investigate attitude evolution of the tethered system and the mechanical energy transfer/loss characteristics between the bus system and the solar sail via the connecting wires,a structure-preserving method is developed in this paper.Simplifying the tethered satellite system as a composite structure consisting of a particle and a flexible thin panel connected by four special springs,the dynamic model is deduced via the Hamiltonian variational principle firstly.Then,a structure-preserving approach that connects the symplectic Runge-Kutta method and the multi-symplectic method is developed.The excellent structure-preserving property of the numerical scheme constructed is presented to illustrate the credibility of the numerical results obtained by the constructed structure-preserving approach.From the numerical results on the mechanical energy transfer/loss in the composite structure,it can be found that the mechanical energy transfer tendency in the tethered system is dependent of the initial attitude angle of the system while the total mechanical energy loss of the system is almost independent of the initial attitude angle.In addition,the special stiffness range of the spring is found in the attitude angle evolution of the system,which provides a structural parameter design window for the connecting wires,that is,the duration needed to arrive the stable attitude is short when the stiffness of the wire is designed in this special range.展开更多
Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are establi...Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.展开更多
In order to increase the accuracy of turbulence field reconstruction,this paper combines experimental observation and numerical simulation to develop and establish a data assimilation framework,and apply it to the stu...In order to increase the accuracy of turbulence field reconstruction,this paper combines experimental observation and numerical simulation to develop and establish a data assimilation framework,and apply it to the study of S809 low-speed and high-angle airfoil flow.The method is based on the ensemble transform Kalman filter(ETKF)algorithm,which improves the disturbance strategy of the ensemble members and enhances the richness of the initial members by screening high flow field sensitivity constants,increasing the constant disturbance dimensions and designing a fine disturbance interval.The results show that the pressure distribution on the airfoil surface after assimilation is closer to the experimental value than that of the standard Spalart-Allmaras(S-A)model.The separated vortex estimated by filtering is fuller,and the eddy viscosity field information is more abundant,which is physically consistent with the observation information.Therefore,the data assimilation method based on the improved ensemble strategy can more accurately and effectively describe complex turbulence phenomena.展开更多
To reveal some dynamic properties of the deploying process for the solar power satellite via an arbitrarily large phased array （SPS-ALPHA） solar receiver, the symplectic Runge-Kutta method is used to simulate the si...To reveal some dynamic properties of the deploying process for the solar power satellite via an arbitrarily large phased array （SPS-ALPHA） solar receiver, the symplectic Runge-Kutta method is used to simulate the simplified model with the consideration of the Rayleigh damping effect. The system containing the Rayleigh damping can be separated and transformed into the equivalent nondamping system formally to insure the application condition of the symplectic Runge-Kutta method. First, the Lagrange equation with the Rayleigh damping governing the motion of the system is derived via the variational principle. Then, with some reasonable assumptions on the relations among the damping, mass, and stiffness matrices, the Rayleigh damping system is equivalently converted into the nondamping system formally, so that the symplectic Runge-Kutta method can be used to simulate the deploying process for the solar receiver. Finally, some numerical results of the symplectic Runge-Kutta method for the dynamic properties of the solar receiver are reported. The numerical results show that the proposed simplified model is valid for the deploying process for the SPS-ALPHA solar receiver, and the symplectic Runge-Kutta method can preserve the displacement constraints of the system well with excellent long-time numerical stability.展开更多
Wave propagation in two-dimensional hierarchical honeycomb structures with two- order hierarchy is investigated by using the symplectic algorithm. By applying the variational prin- ciple to the dual variables, the wav...Wave propagation in two-dimensional hierarchical honeycomb structures with two- order hierarchy is investigated by using the symplectic algorithm. By applying the variational prin- ciple to the dual variables, the wave propagation problem is transformed into a two-dimensional symplectie eigenvalue problem. The band gaps and spatial filtering phenomena are examined to find the stop bands and directional stop bands. Special attention is directed to the effects of the relative density and the length ratio on the band gaps and phase constant surfaces. This work provides new opportunities for designing hierarchical honeycomb structures in sound insulation applications.展开更多
In view of the complex structure and environment,the dynamic analysis on deoxyribonucleic acid(DNA)is a challenge in the biophysics field.Considering the local interaction with ribonucleic acid(RNA)-polymerase as well...In view of the complex structure and environment,the dynamic analysis on deoxyribonucleic acid(DNA)is a challenge in the biophysics field.Considering the local interaction with ribonucleic acid(RNA)-polymerase as well as the dissipative effect of cellular fluid,a coupling sine-Gordon-type dynamic model is used to describe the rotational motions of the bases in DNA.First,the approximate symmetric form is constructed.Then,the wave form and the wave velocity of the kink solution to the proposed dynamic model are investigated by a Runge-Kutta structure-preserving scheme based on the generalized multi-symplectic idea.The numerical results indicate that,the strengthening of the local interaction between DNA and RNA-polymerase described by the coupling potential makes the form of the kink solution steep,while the appearance of the friction between DNA and cellular fluid makes the form of the kink solution flat.In addition,the appearance of the friction decreases the velocities of both the symplectic configuration and the anti-symplectic configuration with different degrees.The above findings are beneficial to comprehend the DNA transcription mechanism.展开更多
The in-plane dynamic crushing behavior of re-entrant honeycomb is analyzed and compared with the conventional hexagon topology.Detailed deformation modes along two orthogonal directions are examined,where a parametric...The in-plane dynamic crushing behavior of re-entrant honeycomb is analyzed and compared with the conventional hexagon topology.Detailed deformation modes along two orthogonal directions are examined,where a parametric study of the effect of impact velocity and cell wall aspect ratio is performed.An analytical formula of the dynamic crushing strength is then deduced based on the periodic collapse mechanism of cell structures.Comparisons with the finite element results validate the effectiveness of the proposed analytical method.Numerical results also reveal higher plateau stress of re-entrant honeycomb over conventional hexagon topology,implying better energy absorption properties.The underlying physical understanding of the results is emphasized,where the auxetic effect（negative Poisson＇s ratio） induced in the re-entrant topology is believed to be responsible for this superior impact resistance.展开更多
An analytical method,called the symplectic mathematical method,is proposed to study the wave propagation in a spring-mass chain with gradient arranged local resonators and nonlinear ground springs.Combined with the li...An analytical method,called the symplectic mathematical method,is proposed to study the wave propagation in a spring-mass chain with gradient arranged local resonators and nonlinear ground springs.Combined with the linearized perturbation approach,the symplectic transform matrix for a unit cell of the weakly nonlinear graded metamaterial is derived,which only relies on the state vector.The results of the dispersion relation obtained with the symplectic mathematical method agree well with those achieved by the Bloch theory.It is shown that wider and lower frequency bandgaps are formed when the hardening nonlinearity and incident wave intensity increase.Subsequently,the displacement response and transmission performance of nonlinear graded metamaterials with finite length are studied.The dual tunable effects of nonlinearity and gradation on the wave propagation are explored under different excitation frequencies.For small excitation frequencies,the gradient parameter plays a dominant role compared with the nonlinearity.The reason is that the gradient tuning aims at the gradient arrangement of local resonators,which is limited by the critical value of the local resonator mass.In contrast,for larger excitation frequencies,the hardening nonlinearity is dominant and will contribute to the formation of a new bandgap.展开更多
An accurate and straightforward symplectic method is presented for the fracture analysis of fractional two-dimensional(2D)viscoelastic media.The fractional Kelvin-Zener constitutive model is used to describe the time-...An accurate and straightforward symplectic method is presented for the fracture analysis of fractional two-dimensional(2D)viscoelastic media.The fractional Kelvin-Zener constitutive model is used to describe the time-dependent behavior of viscoelastic materials.Within the framework of symplectic elasticity,the governing equations in the Hamiltonian form for the frequency domain(s-domain)can be directly and rigorously calculated.In the s-domain,the analytical solutions of the displacement and stress fields are constructed by superposing the symplectic eigensolutions without any trial function,and the explicit expressions of the intensity factors and J-integral are derived simultaneously.Comparison studies are provided to validate the accuracy and effectiveness of the present solutions.A detailed analysis is made to reveal the effects of viscoelastic parameters and applied loads on the intensity factors and J-integral.展开更多
The placement of pressure taps on the surface of the wind tunnel test model is an important means toobtain the surface pressure distribution.However,limited by space location and experimental cost,it isdifficult to ar...The placement of pressure taps on the surface of the wind tunnel test model is an important means toobtain the surface pressure distribution.However,limited by space location and experimental cost,it isdifficult to arrange enough pressure measuring taps on the surface of complex models to obtain completepressure distribution information,thus it is impossible to obtain accurate lift and moment characteristicsthrough integration.The paper proposes a refined reconstruction method of airfoil surface pressure basedon compressed sensing,which can reconstruct the pressure distribution with high precision with lesspressure measurement data.Tests on typical airfoil subsonic flow around flow show that the accuracyof lift and moment after the pressure integration reconstructed by 4-8 measuring points can meet therequirements of the national military standard.The algorithm is robust to noise,and provides a new ideafor obtaining accurate force data from sparse surface pressure tests in engineering.展开更多
The structure-preserving property, in both the time domain and the frequency domain, is an important index for evaluating validity of a numerical method. Even in the known structure-preserving methods such as the symp...The structure-preserving property, in both the time domain and the frequency domain, is an important index for evaluating validity of a numerical method. Even in the known structure-preserving methods such as the symplectic method, the inherent conser- vation law in the frequency domain is hardly conserved. By considering a mathematical pendulum model, a Stormer-Verlet scheme is first constructed in a Hamiltonian frame- work. The conservation law of the StSrmer-Verlet scheme is derived, including the total energy expressed in the time domain and periodicity in the frequency domain. To track the structure-preserving properties of the Stormer-Verlet scheme associated with the con- servation law, the motion of the mathematical pendulum is simulated with different time step lengths. The numerical results illustrate that the StSrmer-Verlet scheme can preserve the total energy of the model but cannot preserve periodicity at all. A phase correction is performed for the StSrmer-Verlet scheme. The results imply that the phase correction can improve the conservative property of periodicity of the Stormer-Verlet scheme.展开更多
In this paper,we report the frequency comb response experimentally and analytically in a rhombic micro-resonator with parametrical modulation.When the electrostatically actuated rhombic micro-resonator is modulated ax...In this paper,we report the frequency comb response experimentally and analytically in a rhombic micro-resonator with parametrical modulation.When the electrostatically actuated rhombic micro-resonator is modulated axially by a low-frequency periodic excitation,a comb-like vibration response with few equidistant positioned fingers in the frequency domain is observed.The finger spacing of frequency comb response is exactly consistent with modulation frequency and the number and amplitude of the fingers can be tuned by modulation strength.A mixed frequency comb with extra comb fingers is further generated when the resonator is modulated simultaneously by two different low-frequency excitation signals.By adjusting the relation of the two modulation frequencies,unequal spacing frequency combs are achieved for the first time,which leads to a more flexible tunability of the comb spacing for different applications.Theoretical analysis based on the dynamic model well explains the corresponding observations.展开更多
Solvent-free nanofluids hold promise for many technologically significant applications.The liquid-like behavior,a typical rheological property of solvent-free nanofluids,has aroused considerable interests.However,ther...Solvent-free nanofluids hold promise for many technologically significant applications.The liquid-like behavior,a typical rheological property of solvent-free nanofluids,has aroused considerable interests.However,there has been still lack of efficient methods to predict and control the liquid-like behavior of solvent-free nanofluids.In this paper,we propose a semi-discrete dynamic system with stochastic excitation describing the temperature change effects on the rheological property of multiwall carbon nanotubes(MWCNTs)modified by grafting sulfonic acid terminated organosilanes as corona and tertiary amine as canopy,which is a typical covalent-type solvent-free nanofluid system.The vibration of the grafting branches is simulated by employing a structure-preserving approach,and the shear force of grafting branches at the fixed end is computed subsequently.By taking the shear forces as an excitation acting on the MWCNTs,the axial motion of the MWCNTs is solved with the 7-point Gauss-Kronrod quadrature rule.The critical temperature associated with the appearance of the liquid-like behavior as well as the upper bound of the moving speed of the modified MWCNTs is determined,which can be used to predict and control the liquid-like behavior of the modified MWCNTs in engineering applications.展开更多
In this study,we propose valley phononic crystals that consist of a hexagonal aluminum plate with six chiral arrangements of ligaments.Valley phononic crystals were introduced into a topological insulator(TI)system to...In this study,we propose valley phononic crystals that consist of a hexagonal aluminum plate with six chiral arrangements of ligaments.Valley phononic crystals were introduced into a topological insulator(TI)system to produce topologically protected edge waves(TPEW s)along the topological interfaces.The implementation of chiral topological edge states is different from the implementation of topological edge states of systems with symmetry.Unlike the conventional breaking of mirror symmetry,a new complete band with topological edge modes gap was opened up at the Dirac point by tuning the difference in lengths of the ligaments in the chiral unit cells.We investigated the dispersion properties in chiral systems and applied the dispersion properties to waveguides on the interfaces to achieve designable route systems.Furthermore,we simulated the robust propagation of TPEWs in different routes and demonstrated their immunity to backscattering at defects.Finally,the existence of the valley Hall effect in chiral systems was demonstrated.The study findings may lead to the further study of the topological states of chiral materials.展开更多
基金supported by the National Natural Science Foundation of China(grant numbers 11972287 and 12072266)the State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment(GZ23106)+1 种基金the National Key Laboratory of Aircraft Configuration Design(No.2023-JCJQ-LB-070)the Fundamental Research Funds for the Central Universities.
文摘Chiral metamaterials are manmade structures with extraordinary mechanical properties derived from their special geometric design instead of chemical composition.To make the mechanical deformation programmable,the non-uniform rational B-spline(NURBS)curves are taken to replace the traditional ligament boundaries of the chiral structure.The Neural networks are innovatively inserted into the calculation of mechanical properties of the chiral structure instead of finite element methods to improve computational efficiency.For the problem of finding structure configuration with specified mechanical properties,such as Young’s modulus,Poisson’s ratio or deformation,an inverse design method using the Neural network-based proxy model is proposed to build the relationship between mechanical properties and geometric configuration.To satisfy some more complex deformation requirements,a non-homogeneous inverse design method is proposed and verified through simulation and experiments.Numerical and test results reveal the high computational efficiency and accuracy of the proposed method in the design of chiral metamaterials.
基金Project supported by the National Natural Science Foundation of China(Nos.91648101 and11672233)the Northwestern Polytechnical University(NPU)Foundation for Fundamental Research(No.3102017AX008)the National Training Program of Innovation and Entrepreneurship for Undergraduates(No.S201710699033)
文摘Multibody system dynamics provides a strong tool for the estimation of dynamic performances and the optimization of multisystem robot design. It can be described with differential algebraic equations(DAEs). In this paper, a particle swarm optimization(PSO) method is introduced to solve and control a symplectic multibody system for the first time. It is first combined with the symplectic method to solve problems in uncontrolled and controlled robotic arm systems. It is shown that the results conserve the energy and keep the constraints of the chaotic motion, which demonstrates the efficiency, accuracy, and time-saving ability of the method. To make the system move along the pre-planned path, which is a functional extremum problem, a double-PSO-based instantaneous optimal control is introduced. Examples are performed to test the effectiveness of the double-PSO-based instantaneous optimal control. The results show that the method has high accuracy, a fast convergence speed, and a wide range of applications.All the above verify the immense potential applications of the PSO method in multibody system dynamics.
基金Funding for this work has been provided by the National Natural Science Foundation of China(Nos.11872313 and 11502202)National Key R&D Program of China(2017YFB1102801)Fundamental Research Funds for the Central Universities and Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University(CX2020107).
文摘In this study,the wave propagation properties of lattice metamaterials with Koch fractal structures are investigated in terms of band structures and directional wave propagation.The analytical models of lattice metamaterials are established using the finite element method,and the dispersion relation is solved using the Bloch’s theorem.The band structures of the lattice metamaterials with different numbers of iterations are studied,and the group velocities at a selected frequency are calculated to analyze the directional wave propagation characteristics.Furthermore,dynamic responses of the finite structures are calculated using commercial finite element software to verify the band gaps and directional wave propagation behaviors in the lattice metamaterials.The results show that multiple and low band gaps are present in the lattice materials with various geometric parameters of the Koch fractal,and the position of the lowest band gap decreases as the number of iterations increases.The results indicate the potential applications of lattice metamaterials with Koch fractals for vibration isolation and multi-functional design.
基金Project supported by the National Natural Science Foundation of China(Nos.11872313 and11902045)the National Key R&D Program of China(No.2017YFB1102801)+1 种基金the Fundamental Research Fund for the Central Universitiesthe Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University(No.CX2020107)。
文摘In this study,multi-resonator coupled metamaterials(MRCMs)with local resonators are proposed to obtain the multiple and wide band gaps.Kinetic models of the MRCMs are established,and the boundary conditions of the unit cell are obtained with Bloch's theorem.The effects of structural parameters,including the mass of the resonator and the spring stiffness,on the distributions of the band gaps are studied.Furthermore,the frequency domain responses and the time domain responses are calculated for analyzing the structural vibration characteristics and the effects of damping on structural vibration.The results show that the frequency domain response can accurately express the distributions of the band gaps of the MRCMs,and we can increase the number and the width of the band gaps by using the MRCMs for the superior vibration suppression capability.
基金The research is supported by the National Natural Science Foundation of China(11672241,11972284,11432010)Fund for Distinguished Young Scholars of Shaanxi Province(2019JC-29)Fund of the Youth Innovation Team of Shaanxi Universities,the Seed Foundation of Qian Xuesen Laboratory of Space Technology,and the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment(GZ1605).
文摘The dynamic analysis on the ultra-large spatial structure can be simplified drastically by ignoring the flexibility and damping of the structure.However,these simplifications will result in the erroneous estimate on the dynamic behaviors of the ultra-large spatial structure.Taking the spatial beam as an example,the minimum control energy defined by the difference between the initial total energy and the final total energy in the assumed stable attitude state of the beam is investigated by the structure-preserving method proposed in our previous studies in two cases:the spatial beam considering the flexibility as well as the damping effect,and the spatial beam ignoring both the flexibility and the damping effect.In the numerical experiments,the assumed simulation interval of three months is evaluated on whether or not it is long enough for the spatial flexible damping beam to arrive at the assumed stable attitude state.And then,taking the initial attitude angle and the initial attitude angle velocity as the independent variables,respectively,the minimum control energies of the mentioned two cases are investigated in detail.From the numerical results,the following conclusions can be obtained.With the fixed initial attitude angle velocity,the minimum control energy of the spatial flexible damping beam is higher than that of the spatial rigid beam when the initial attitude angle is close to or far away from the stable attitude state.With the fixed initial attitude angle,ignoring the flexibility and the damping effect will underestimate the minimum control energy of the spatial beam.
基金was supported by the National Natural Science Foundation of China(Grants 11972284,11872303)the Fund for Distinguished Young Scholars of Shaanxi Province(2019JC-29)the Fund of the Youth Innovation Team of Shaanxi Universities,and the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment(Grant GZ19103).
文摘connecting wires are the main manifestations of the coupling dynamic effects on the orbit evolution,the attitude adjusting and the flexible vibration of the tethered satellite system.To investigate attitude evolution of the tethered system and the mechanical energy transfer/loss characteristics between the bus system and the solar sail via the connecting wires,a structure-preserving method is developed in this paper.Simplifying the tethered satellite system as a composite structure consisting of a particle and a flexible thin panel connected by four special springs,the dynamic model is deduced via the Hamiltonian variational principle firstly.Then,a structure-preserving approach that connects the symplectic Runge-Kutta method and the multi-symplectic method is developed.The excellent structure-preserving property of the numerical scheme constructed is presented to illustrate the credibility of the numerical results obtained by the constructed structure-preserving approach.From the numerical results on the mechanical energy transfer/loss in the composite structure,it can be found that the mechanical energy transfer tendency in the tethered system is dependent of the initial attitude angle of the system while the total mechanical energy loss of the system is almost independent of the initial attitude angle.In addition,the special stiffness range of the spring is found in the attitude angle evolution of the system,which provides a structural parameter design window for the connecting wires,that is,the duration needed to arrive the stable attitude is short when the stiffness of the wire is designed in this special range.
基金Project supported by the National Natural Science Foundation of China(No.11432010)the Doctoral Program Foundation of Education Ministry of China(No.20126102110023)+2 种基金the 111Project of China(No.B07050)the Fundamental Research Funds for the Central Universities(No.310201401JCQ01001)the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University(No.CX201517)
文摘Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.
基金Project supported by the Foundation of National Key Laboratory of Science and Technology on Aerodynamic Design and Research of China(No.614220119040101)the National Natural Science Foundation of China(No.91852115)。
文摘In order to increase the accuracy of turbulence field reconstruction,this paper combines experimental observation and numerical simulation to develop and establish a data assimilation framework,and apply it to the study of S809 low-speed and high-angle airfoil flow.The method is based on the ensemble transform Kalman filter(ETKF)algorithm,which improves the disturbance strategy of the ensemble members and enhances the richness of the initial members by screening high flow field sensitivity constants,increasing the constant disturbance dimensions and designing a fine disturbance interval.The results show that the pressure distribution on the airfoil surface after assimilation is closer to the experimental value than that of the standard Spalart-Allmaras(S-A)model.The separated vortex estimated by filtering is fuller,and the eddy viscosity field information is more abundant,which is physically consistent with the observation information.Therefore,the data assimilation method based on the improved ensemble strategy can more accurately and effectively describe complex turbulence phenomena.
基金supported by the National Natural Science Foundation of China(Nos.11432010,11672241,and 11502202)the Open Foundation of the State Key Laboratory of Structural Analysis of Industrial Equipment of China(No.GZ1605)
文摘To reveal some dynamic properties of the deploying process for the solar power satellite via an arbitrarily large phased array （SPS-ALPHA） solar receiver, the symplectic Runge-Kutta method is used to simulate the simplified model with the consideration of the Rayleigh damping effect. The system containing the Rayleigh damping can be separated and transformed into the equivalent nondamping system formally to insure the application condition of the symplectic Runge-Kutta method. First, the Lagrange equation with the Rayleigh damping governing the motion of the system is derived via the variational principle. Then, with some reasonable assumptions on the relations among the damping, mass, and stiffness matrices, the Rayleigh damping system is equivalently converted into the nondamping system formally, so that the symplectic Runge-Kutta method can be used to simulate the deploying process for the solar receiver. Finally, some numerical results of the symplectic Runge-Kutta method for the dynamic properties of the solar receiver are reported. The numerical results show that the proposed simplified model is valid for the deploying process for the SPS-ALPHA solar receiver, and the symplectic Runge-Kutta method can preserve the displacement constraints of the system well with excellent long-time numerical stability.
基金Project supported by the National Basic Research Program of China(No.2011CB610300)the National Natural Science Foundation of China(Nos.11172239 and 11372252)+3 种基金the Doctoral Program Foundation of Education Ministry of China(No.20126102110023)the Fundamental Research Funds for the Central Universities(Nos.310201401JCQ01001 and 3102015ZY036)China Postdoctoral Science Foundation(No.2013M540724)Shaanxi postdoctoral research projects
文摘Wave propagation in two-dimensional hierarchical honeycomb structures with two- order hierarchy is investigated by using the symplectic algorithm. By applying the variational prin- ciple to the dual variables, the wave propagation problem is transformed into a two-dimensional symplectie eigenvalue problem. The band gaps and spatial filtering phenomena are examined to find the stop bands and directional stop bands. Special attention is directed to the effects of the relative density and the length ratio on the band gaps and phase constant surfaces. This work provides new opportunities for designing hierarchical honeycomb structures in sound insulation applications.
基金the National Natural Science Foundation of China(Nos.11972284 and11672241)the Fund for Distinguished Young Scholars of Shaanxi Province of China(No.2019JC-29)the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment of China(No.GZ19103)。
文摘In view of the complex structure and environment,the dynamic analysis on deoxyribonucleic acid(DNA)is a challenge in the biophysics field.Considering the local interaction with ribonucleic acid(RNA)-polymerase as well as the dissipative effect of cellular fluid,a coupling sine-Gordon-type dynamic model is used to describe the rotational motions of the bases in DNA.First,the approximate symmetric form is constructed.Then,the wave form and the wave velocity of the kink solution to the proposed dynamic model are investigated by a Runge-Kutta structure-preserving scheme based on the generalized multi-symplectic idea.The numerical results indicate that,the strengthening of the local interaction between DNA and RNA-polymerase described by the coupling potential makes the form of the kink solution steep,while the appearance of the friction between DNA and cellular fluid makes the form of the kink solution flat.In addition,the appearance of the friction decreases the velocities of both the symplectic configuration and the anti-symplectic configuration with different degrees.The above findings are beneficial to comprehend the DNA transcription mechanism.
基金Project supported by the National Natural Science Foundation of China(Nos.11372252 and 11402035)
文摘The in-plane dynamic crushing behavior of re-entrant honeycomb is analyzed and compared with the conventional hexagon topology.Detailed deformation modes along two orthogonal directions are examined,where a parametric study of the effect of impact velocity and cell wall aspect ratio is performed.An analytical formula of the dynamic crushing strength is then deduced based on the periodic collapse mechanism of cell structures.Comparisons with the finite element results validate the effectiveness of the proposed analytical method.Numerical results also reveal higher plateau stress of re-entrant honeycomb over conventional hexagon topology,implying better energy absorption properties.The underlying physical understanding of the results is emphasized,where the auxetic effect（negative Poisson＇s ratio） induced in the re-entrant topology is believed to be responsible for this superior impact resistance.
基金Project supported by the National Natural Science Foundation of China(Nos.12072266,12172297,11972287,and 12072262)the Open Foundation of the State Key Laboratory of Structural Analysis for Industrial Equipment of China(No.GZ22106)。
文摘An analytical method,called the symplectic mathematical method,is proposed to study the wave propagation in a spring-mass chain with gradient arranged local resonators and nonlinear ground springs.Combined with the linearized perturbation approach,the symplectic transform matrix for a unit cell of the weakly nonlinear graded metamaterial is derived,which only relies on the state vector.The results of the dispersion relation obtained with the symplectic mathematical method agree well with those achieved by the Bloch theory.It is shown that wider and lower frequency bandgaps are formed when the hardening nonlinearity and incident wave intensity increase.Subsequently,the displacement response and transmission performance of nonlinear graded metamaterials with finite length are studied.The dual tunable effects of nonlinearity and gradation on the wave propagation are explored under different excitation frequencies.For small excitation frequencies,the gradient parameter plays a dominant role compared with the nonlinearity.The reason is that the gradient tuning aims at the gradient arrangement of local resonators,which is limited by the critical value of the local resonator mass.In contrast,for larger excitation frequencies,the hardening nonlinearity is dominant and will contribute to the formation of a new bandgap.
基金Project supported by the National Natural Science Foundation of China(Nos.11872303 and 11702221)the China Postdoctoral Science Foundation(No.2017M613198)the Fundamental Research Funds for the Central Universities of China(No.G2020KY05402)
文摘An accurate and straightforward symplectic method is presented for the fracture analysis of fractional two-dimensional(2D)viscoelastic media.The fractional Kelvin-Zener constitutive model is used to describe the time-dependent behavior of viscoelastic materials.Within the framework of symplectic elasticity,the governing equations in the Hamiltonian form for the frequency domain(s-domain)can be directly and rigorously calculated.In the s-domain,the analytical solutions of the displacement and stress fields are constructed by superposing the symplectic eigensolutions without any trial function,and the explicit expressions of the intensity factors and J-integral are derived simultaneously.Comparison studies are provided to validate the accuracy and effectiveness of the present solutions.A detailed analysis is made to reveal the effects of viscoelastic parameters and applied loads on the intensity factors and J-integral.
基金by the foundation of National Key Laboratory of Science and Technology on Aerodynamic Design and Research(Grant 614220119040101)the National Natural Science Foundation of China(Grants 91852115 and 12072282)+1 种基金the National Numerical Wind tunnel Project(Grant NNW2018-ZT1B01)the Seed Foundation of Innovation and Creation for Graduate Student in Northwestern Polytechnical University(Grant CX2020195).
文摘The placement of pressure taps on the surface of the wind tunnel test model is an important means toobtain the surface pressure distribution.However,limited by space location and experimental cost,it isdifficult to arrange enough pressure measuring taps on the surface of complex models to obtain completepressure distribution information,thus it is impossible to obtain accurate lift and moment characteristicsthrough integration.The paper proposes a refined reconstruction method of airfoil surface pressure basedon compressed sensing,which can reconstruct the pressure distribution with high precision with lesspressure measurement data.Tests on typical airfoil subsonic flow around flow show that the accuracyof lift and moment after the pressure integration reconstructed by 4-8 measuring points can meet therequirements of the national military standard.The algorithm is robust to noise,and provides a new ideafor obtaining accurate force data from sparse surface pressure tests in engineering.
基金the National Natural Science Foundation of China(Nos.11672241,11372253,and 11432010)the Astronautics Supporting Technology Foundation of China(No.2015-HT-XGD)the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment(Nos.GZ1312 and GZ1605)
文摘The structure-preserving property, in both the time domain and the frequency domain, is an important index for evaluating validity of a numerical method. Even in the known structure-preserving methods such as the symplectic method, the inherent conser- vation law in the frequency domain is hardly conserved. By considering a mathematical pendulum model, a Stormer-Verlet scheme is first constructed in a Hamiltonian frame- work. The conservation law of the StSrmer-Verlet scheme is derived, including the total energy expressed in the time domain and periodicity in the frequency domain. To track the structure-preserving properties of the Stormer-Verlet scheme associated with the con- servation law, the motion of the mathematical pendulum is simulated with different time step lengths. The numerical results illustrate that the StSrmer-Verlet scheme can preserve the total energy of the model but cannot preserve periodicity at all. A phase correction is performed for the StSrmer-Verlet scheme. The results imply that the phase correction can improve the conservative property of periodicity of the Stormer-Verlet scheme.
基金the National Natural Science Foundation of China(Grant Nos.12172323 and 52075432)Zhejiang Provincial Natural Science Foundation of China(Grant No.LZ22A020003)+1 种基金Fundamental Research Funds for the Central Universities(Grant No.G2022KY05104)Program for Innovation Team of Shaanxi Province(Grant No.2021TD-23).
文摘In this paper,we report the frequency comb response experimentally and analytically in a rhombic micro-resonator with parametrical modulation.When the electrostatically actuated rhombic micro-resonator is modulated axially by a low-frequency periodic excitation,a comb-like vibration response with few equidistant positioned fingers in the frequency domain is observed.The finger spacing of frequency comb response is exactly consistent with modulation frequency and the number and amplitude of the fingers can be tuned by modulation strength.A mixed frequency comb with extra comb fingers is further generated when the resonator is modulated simultaneously by two different low-frequency excitation signals.By adjusting the relation of the two modulation frequencies,unequal spacing frequency combs are achieved for the first time,which leads to a more flexible tunability of the comb spacing for different applications.Theoretical analysis based on the dynamic model well explains the corresponding observations.
基金supported by the National Natural Science Foundation of China(Nos.12172281 and 11972284)the Distinguished Young Scholars of Shaanxi Province of China(No.2019JC-29)+2 种基金the Foundation Strengthening Programme Technical Area Fund of Shaanxi Province of China(No.2021-JCJQ-JJ-0565)the Science and Technology Innovation Team of Shaanxi Province of China(No.2022TD-61)the Youth Innovation Team of Shaanxi Universities and Doctoral Dissertation Innovation Fund of Xi’an University of Technology of China(Nos.252072016 and 252072115)。
文摘Solvent-free nanofluids hold promise for many technologically significant applications.The liquid-like behavior,a typical rheological property of solvent-free nanofluids,has aroused considerable interests.However,there has been still lack of efficient methods to predict and control the liquid-like behavior of solvent-free nanofluids.In this paper,we propose a semi-discrete dynamic system with stochastic excitation describing the temperature change effects on the rheological property of multiwall carbon nanotubes(MWCNTs)modified by grafting sulfonic acid terminated organosilanes as corona and tertiary amine as canopy,which is a typical covalent-type solvent-free nanofluid system.The vibration of the grafting branches is simulated by employing a structure-preserving approach,and the shear force of grafting branches at the fixed end is computed subsequently.By taking the shear forces as an excitation acting on the MWCNTs,the axial motion of the MWCNTs is solved with the 7-point Gauss-Kronrod quadrature rule.The critical temperature associated with the appearance of the liquid-like behavior as well as the upper bound of the moving speed of the modified MWCNTs is determined,which can be used to predict and control the liquid-like behavior of the modified MWCNTs in engineering applications.
基金supported by the National Natural Science Foundation of China(Grant Nos.11872313 and 12172297).
文摘In this study,we propose valley phononic crystals that consist of a hexagonal aluminum plate with six chiral arrangements of ligaments.Valley phononic crystals were introduced into a topological insulator(TI)system to produce topologically protected edge waves(TPEW s)along the topological interfaces.The implementation of chiral topological edge states is different from the implementation of topological edge states of systems with symmetry.Unlike the conventional breaking of mirror symmetry,a new complete band with topological edge modes gap was opened up at the Dirac point by tuning the difference in lengths of the ligaments in the chiral unit cells.We investigated the dispersion properties in chiral systems and applied the dispersion properties to waveguides on the interfaces to achieve designable route systems.Furthermore,we simulated the robust propagation of TPEWs in different routes and demonstrated their immunity to backscattering at defects.Finally,the existence of the valley Hall effect in chiral systems was demonstrated.The study findings may lead to the further study of the topological states of chiral materials.
