This paper presents an improved level set method for topology optimization of geometrically nonlinear structures accounting for the effect of thermo-mechanical couplings.It derives a new expression for element couplin...This paper presents an improved level set method for topology optimization of geometrically nonlinear structures accounting for the effect of thermo-mechanical couplings.It derives a new expression for element coupling stress resulting from the combination of mechanical and thermal loading,using geometric nonlinear finite element analysis.A topological model is then developed to minimize compliance while meeting displacement and frequency constraints to fulfill design requirements of structural members.Since the conventional Lagrange multiplier search method is unable to handle convergence instability arising from large deformation,a novel Lagrange multiplier search method is proposed.Additionally,the proposed method can be extended to multi-constrained geometrically nonlinear topology optimization,accommodating multiple physical field couplings.展开更多
Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti- Johnson （G J） hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational ide...Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti- Johnson （G J） hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational identity their ttamiltonian structures are also generated. The approach presented in the paper can also provide nonlinear integrable couplings of other soliton hierarchies of evolution equations.展开更多
An element coupling model (ECM) method was proposed to simulate the global behavior and local damage of a structure.In order to reflect the local damage and improve the computational efficiency,three-dimensional (3D) ...An element coupling model (ECM) method was proposed to simulate the global behavior and local damage of a structure.In order to reflect the local damage and improve the computational efficiency,three-dimensional (3D) solid elements and one-dimensional (1D) beam element were coupled by the multi-point constraint equations.A reduced scale 1?8 model test was simulated by the ECM and a full three dimensional model (3DM) contrastively.The results show that the global behavior and local damages of ECM agree well with the test and 3DM.It is indicated that the proposed method can be used in the structural nonlinear analysis accurately and efficiently.展开更多
The nonlinear dynamical behaviors of artificial neural network (ANN) and their application to science and engineering were summarized. The mechanism of two kinds of dynamical processes, i.e. weight dynamics and activa...The nonlinear dynamical behaviors of artificial neural network (ANN) and their application to science and engineering were summarized. The mechanism of two kinds of dynamical processes, i.e. weight dynamics and activation dynamics in neural networks, and the stability of computing in structural analysis and design were stated briefly. It was successfully applied to nonlinear neural network to evaluate the stability of underground stope structure in a gold mine. With the application of BP network, it is proven that the neuro-com- puting is a practical and advanced tool for solving large-scale underground rock engineering problems.展开更多
Based on the generalized vaxiational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established （see, Analyses on nonlinear coupling of magneto-thermo- elasticity of ferromagnetic thin shell--I...Based on the generalized vaxiational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established （see, Analyses on nonlinear coupling of magneto-thermo- elasticity of ferromagnetic thin shell--I）, the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones.展开更多
Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coup...Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coupled micromechanical resonators,highlighting the latest advancements in four key areas:internal resonance,synchronization,frequency combs,and mode localization.The origin,development,and potential applications of each of these dynamic phenomena within mode-coupled micromechanical systems are investigated,with the goal of inspiring new ideas and directions for researchers in this field.展开更多
We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra.Then its super Hamiltonian structure is furnished by super trace identity.As its r...We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra.Then its super Hamiltonian structure is furnished by super trace identity.As its reduction,we gain the nonlinear integrable couplings of the classical integrable Dirac hierarchy.展开更多
Considering the dynamic influence of the roll vibration on the lubricant film thickness in the rolling deformation area,nonlinear dynamic rolling forces related to film thickness in the vertical and horizontal directi...Considering the dynamic influence of the roll vibration on the lubricant film thickness in the rolling deformation area,nonlinear dynamic rolling forces related to film thickness in the vertical and horizontal directions were obtained based on the Karman balance theory.Based on these dynamic rolling forces and the mechanical vibration of the rolling mill,a vertical-horizontal coupling nonlinear vibration dynamic model was established.The amplitude-frequency equation of the main resonance was derived by using the multiple-scale method.At last,the parameters of the 1780 rolling mill were used for numerical simulation,and the time-domain response curves of the system’s vibration displacement and lubricating film thickness under the steady and unsteady conditions were analyzed.The influences of parameters such as interface contact ratio,nonlinear parameters and external disturbances on the primary resonance frequency characteristics were obtained,which provided a theoretical reference for the suppression of rolling mill vibration.展开更多
In this paper, the influence of init ial imperfection and coupling between bending and extension on vibration, buckling and nonlinear dynamic stability of laminated plates is studied. The governing e quation is deri...In this paper, the influence of init ial imperfection and coupling between bending and extension on vibration, buckling and nonlinear dynamic stability of laminated plates is studied. The governing e quation is derived. It is a nonlinear modified Mathieu Equation. Numerical solut ions of 5 typical composite materials namely, Glass_epoxy Scotch_1002, Aramid_ep oxy Kevlar_49, Boron_epoxy B4_5505, Graphite_epoxy T300_5208 and AS_3501 are co mputed. Results reveal that the existence of initial imperfection, and also coup ling effect,make the plates much more sensitive to entering parametric resonance with amplitude greater than that of perfect plates. Coupl ing effect for different composite laminates, especially, for that with few laye rs, is different. If coupling effect is neglected, the design of plate structure s for buckling and dynamic stability would unconservatively be for more than 10% .展开更多
A geometrically nonlinear topology optimization(GNTO)method with thermal–mechanical coupling is investigated.Firstly,the new expression of element coupling stress due to superimposed mechanical and thermal loading is...A geometrically nonlinear topology optimization(GNTO)method with thermal–mechanical coupling is investigated.Firstly,the new expression of element coupling stress due to superimposed mechanical and thermal loading is obtained based on the geometrically nonlinear finite element analysis.The lightweight topology optimization(TO)model under stress constraints is established to satisfy the strength requirement.Secondly,the distortion energy theory is introduced to transform themodel into structural strain energy constraints in order to solve the implicit relationship between stress constraints and design variables.Thirdly,the sensitivity analysis of the optimization model is derived,and the model is solved by the method of moving asymptotes(MMA).Numerical examples show that temperature has a significant effect on the optimal configuration,and the TO method considering temperature load is closer to engineering design requirements.The proposed method can be extended to the GNTO design with multiple physical field coupling.展开更多
In this paper, a new nonlinear integrable coupling system of the soliton hierarchy is presented. Prom the Lax pairs, the coupled KdV equations are constructed successfully. Based on the prolongation method of Wahlquis...In this paper, a new nonlinear integrable coupling system of the soliton hierarchy is presented. Prom the Lax pairs, the coupled KdV equations are constructed successfully. Based on the prolongation method of Wahlquist and Estabrook, we study the prolongation structure of the nonlinear integrable couplings of the KdV equation.展开更多
Multimode fiber has a richer spatial dimension than single-mode fiber,and is an ideal platform for studying many novel nonlinear effects.We established a strong linear coupling and short-range fiber model to understan...Multimode fiber has a richer spatial dimension than single-mode fiber,and is an ideal platform for studying many novel nonlinear effects.We established a strong linear coupling and short-range fiber model to understand the interactive effects of linear coupling and nonlinear effects.We find that strong linear coupling can compensate for the group delay between eigenmodes and cause energy fluctuation between modes which weakens the nonlinear effects.In high energy pulses,the interaction of linear coupling and nonlinear effects can help producing weak dispersion waves when the spectrum is broadened.Since linear coupling in a mode group is common and unavoidable,these results may provide a certain theoretical explanation for multi-mode nonlinear phenomena.展开更多
Within the linear framework,the Modal Electromechanical Coupling Factor(MEMCF)is an important indicator to quantify the dynamic conversion of mechanical energy and electrical energy of piezoelectric structures.It is a...Within the linear framework,the Modal Electromechanical Coupling Factor(MEMCF)is an important indicator to quantify the dynamic conversion of mechanical energy and electrical energy of piezoelectric structures.It is also an important tool to guide the piezoelectric damping design of linear structures.Advanced aircraft often fly in maneuvers,and the variable working conditions induce drastic changes in the load level on structures.Geometric and contact nonlinearities of thin-walled structures and joint structures are often activated.To achieve a good vibration reduction effect covering all working conditions,one cannot directly use linear electromechanical coupling theory to instruct the piezoelectric damping design for nonlinear structures.Therefore,this paper defines the Nonlinear Modal Electromechanical Coupling Factor(NMEMCF)and proposes the corresponding numerical method for the first time to quantitatively evaluate the electromechanical coupling capability of nonlinear piezoelectric structures.Three candidate definitions of the NMEMCF are given,including two frequency definitions and one energy definition.The energy definition is the most promising one.It is not only applicable to both conservative and dissipative nonlinear structures but also compatible with the linear MEMCF.In addition,based on the energy formula,the NMEMCF can be obtained by only performing one nonlinear modal analysis in the open-circuit state.The analytical findings and the numerical tool are validated against two piezoelectric structures with different types of nonlinearities.A strong correlation among the NMEMCF,geometric parameters,and energy dissipation is observed.The results confirm that the proposed NMEMCF captures the physics of the electromechanical coupling phenomenon associated with nonlinear piezoelectric structures and can be used as an essential design indicator of piezoelectric damping,especially for variable working conditions.展开更多
Both the complex geometrical morphology of rough-walled rock fractures and the nonlinearity of fluid flow contribute to resistance in fluid flow through rock fractures.The interactions of the shear-flow process furthe...Both the complex geometrical morphology of rough-walled rock fractures and the nonlinearity of fluid flow contribute to resistance in fluid flow through rock fractures.The interactions of the shear-flow process further complicate the characterisation of flow behaviours in rock fractures.In this study,an improved friction factor model involving both the effects of viscous and inertial forces is presented based on the Forchheimer equation.The model incorporates two key variables,i.e.Reynolds number and relative roughness,which reflect the effects of flow regimes and fracture roughness,respectively.The changes in geometrical parameters induced by shearing are considered,with the peak asperity height predicted through a correlation with post-peak roughness degradation.The hydraulic aperture during shearing is estimated using a suggested equation that accounts for the mobilised contact area ratio and variable aperture distribution.The parametric sensitivity analysis reveals that shear-induced changes in fracture geometry enhance the flow nonlinearity in rock fractures.The model performs well in predicting the friction factor based on two validation criteria.Then,the proposed friction factor model is incorporated into the three-dimensional distinct element code(3DEC)in the form of the Darcy-Weisbach equation.Coupled with the numerically implemented mechanical model and hydraulic aperture prediction model,numerical simulations of coupled shear-flow processes in single rock fractures are conducted.The simulation outcomes are validated through comparison with the experimental results,showing acceptable agreement and demonstrating that the numerical model is capable of accurately evaluating the hydro-mechanical coupling behaviour during the shearing of rock fractures.展开更多
Understanding the complex flow behavior along a rough rock fracture under high-temperature,high-stress,and high-seepage pressure(HTHM)coupling conditions is of great significance for optimizing deep resource extractio...Understanding the complex flow behavior along a rough rock fracture under high-temperature,high-stress,and high-seepage pressure(HTHM)coupling conditions is of great significance for optimizing deep resource extraction.This study investigates the complex flow behavior of a single rock fracture under coupled HTHM conditions using a self-developed multi-field coupling experimental system,considering real-time high temperatures(20–90℃),confining pressures(30–120 MPa),and seepage pressures(5–60 MPa).Experimental results show that as confining pressure increases,two typical nonlinear flow behaviors are observed,which are Forchheimer flow and low-velocity nonlinear flow.The increase in temperature and decrease in roughness significantly promote the fluid flow and enhance the nonlinear relationship between the volumetric flow rate and the hydraulic gradient at lower confining pressures(30 MPa).However,the change in temperature and fracture surface roughness does not affect the nonlinear type of fluid flow.Under a given hydraulic gradient,the influence of temperature and fracture roughness on the volumetric flow rate varies with changes in confining pressure.Additionally,this study considers both the viscous and inertial terms,and a modified Forchheimer equation is proposed using two parameters:the contact area ratio and the thermal expansion coefficient of the rock.The proposed model can effectively predict the nonlinear flow behavior of fluid along rough fractured rocks under varying temperatures and surface roughness.The experimental results and the proposed model provide valuable data and theoretical guidance for deep oil and gas exploration as well as hydraulic fracturing design.展开更多
The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations ...The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.展开更多
Previous work examined the effect of the attached stiffness matrix terms on stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the nonlinear formulations ...Previous work examined the effect of the attached stiffness matrix terms on stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the nonlinear formulations to an elastic beam with free large overall motion. Based on initial stress method, the nonlinear coupling equations of elastic beams are obtained with free large overall motion and the attached stiffness matrix is derived by solving sub-static formulation. The angular velocity and the tip deformation of the elastic pendulum are calculated. The analytical results show that the simulation results of the present model are tabled and coincide with the one-order approximate model. It is shown that the simulation results accord with energy conservation principle.展开更多
In the paper, 3-D analysis method with unitive schemes is set up, which is used to resolve the uplift with multiple moving boundaries and multiple nonlinear coupling for anchored liquid storage tanks. hi it, an algori...In the paper, 3-D analysis method with unitive schemes is set up, which is used to resolve the uplift with multiple moving boundaries and multiple nonlinear coupling for anchored liquid storage tanks. hi it, an algorithm of quasi-harmonious finite elements for arbitrary quadrilateral of thin plates and shells is built up to analyze the multiple coupling problems of general thin plates and shells structures with three dimensions, the complementary equations for analyzing uplifting moving boundary problems are deduced. The axial symmetry and presumption of beam type mode are not used. In it, an algorithm is put forward for analyzing the Navier-Stokes problems of unsteady, three-dimensional, and viscous liquid with sloshing of moving boundary surfaces in large amplitude under ALE frame by scheme of time-split-steps to which linear potential theory is not applied. The algorithms can be used to analyze the solid-liquid multiple nonlinear coupling problems with 3-D moving boundary with friction in multiple places.展开更多
Nonlinear couplings of various Alfvén modes driven by energetic particles in HL-2 A are addressed by employing the Fourier bicoherence and Lissajous-curve technique. Long-lived modes and high-frequency coherent m...Nonlinear couplings of various Alfvén modes driven by energetic particles in HL-2 A are addressed by employing the Fourier bicoherence and Lissajous-curve technique. Long-lived modes and high-frequency coherent modes are presented. Then the squared bicoherence of three waves establishes the existence of three-wave coupling. Lissajous-curves of those waves manifest that their phases are locked, which again confirms that they are nonlinearly coupled to each other. Moreover, coupled modes triggered by supersonic molecular beam injection are investigated. The phase evolution of them is given by the Lissajous-curve. Further details of phase-flip and phase-slip are presented and discussed.展开更多
Coherent perfect absorption provides a method of light-controlling-light and has practical applications in optical communications. Recently, a cavity-based nonlinear perfect photon absorption extends the coherent perf...Coherent perfect absorption provides a method of light-controlling-light and has practical applications in optical communications. Recently, a cavity-based nonlinear perfect photon absorption extends the coherent perfect absorber（CPA）beyond the linear regime. As nanowire-based system is a more competitive candidate for full-optical device, we introduce a nonlinear CPA in the single two-level atom–nanowires coupling system in this work. Nonlinear input–output relations are derived analytically, and three contributions of atomic saturation nonlinearity are explicit. The consociation of optical nonlinearity and destructive interference makes it feasible to fabricate a nonlinear monoatomic CPA. Our results also indicate that a nonlinear system may work linearly even when the incoming lights are not weak any more. Our findings show promising applications in full-optical devices.展开更多
基金supported by grants from the National Natural Science Foundation of China (51478130)the Guangzhou Municipal Education Bureau’s Scientific Research Project, China (2024312217)+1 种基金the China Scholarship Council (201808440070)the 111 Project of China (D21021).
文摘This paper presents an improved level set method for topology optimization of geometrically nonlinear structures accounting for the effect of thermo-mechanical couplings.It derives a new expression for element coupling stress resulting from the combination of mechanical and thermal loading,using geometric nonlinear finite element analysis.A topological model is then developed to minimize compliance while meeting displacement and frequency constraints to fulfill design requirements of structural members.Since the conventional Lagrange multiplier search method is unable to handle convergence instability arising from large deformation,a novel Lagrange multiplier search method is proposed.Additionally,the proposed method can be extended to multi-constrained geometrically nonlinear topology optimization,accommodating multiple physical field couplings.
基金Supported by the Fundamental Research Funds of the Central University under Grant No. 2010LKS808the Natural Science Foundation of Shandong Province under Grant No. ZR2009AL021
文摘Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti- Johnson （G J） hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational identity their ttamiltonian structures are also generated. The approach presented in the paper can also provide nonlinear integrable couplings of other soliton hierarchies of evolution equations.
基金Project(2007CB714202) supported by the National Key Basic Research Program of ChinaProject(SLDRCE10-B-07) supported by theMinistry of Science and Technology of China
文摘An element coupling model (ECM) method was proposed to simulate the global behavior and local damage of a structure.In order to reflect the local damage and improve the computational efficiency,three-dimensional (3D) solid elements and one-dimensional (1D) beam element were coupled by the multi-point constraint equations.A reduced scale 1?8 model test was simulated by the ECM and a full three dimensional model (3DM) contrastively.The results show that the global behavior and local damages of ECM agree well with the test and 3DM.It is indicated that the proposed method can be used in the structural nonlinear analysis accurately and efficiently.
基金This work was financially supported by the Key Project for National Science of "9.5" (Reward Ⅱ for National Science and Technol
文摘The nonlinear dynamical behaviors of artificial neural network (ANN) and their application to science and engineering were summarized. The mechanism of two kinds of dynamical processes, i.e. weight dynamics and activation dynamics in neural networks, and the stability of computing in structural analysis and design were stated briefly. It was successfully applied to nonlinear neural network to evaluate the stability of underground stope structure in a gold mine. With the application of BP network, it is proven that the neuro-com- puting is a practical and advanced tool for solving large-scale underground rock engineering problems.
基金supported by he National Natural Science Foundation of China (No.10872081)the Fok Ying-Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (No.111005)
文摘Based on the generalized vaxiational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established （see, Analyses on nonlinear coupling of magneto-thermo- elasticity of ferromagnetic thin shell--I）, the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones.
基金supported by the National Key Research and Development Program of China(No.2022YFB3203600)the National Natural Science Foundation of China(Nos.12202355,12132013,and 12172323)the Zhejiang Provincial Natural Science Foundation of China(No.LZ22A020003)。
文摘Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coupled micromechanical resonators,highlighting the latest advancements in four key areas:internal resonance,synchronization,frequency combs,and mode localization.The origin,development,and potential applications of each of these dynamic phenomena within mode-coupled micromechanical systems are investigated,with the goal of inspiring new ideas and directions for researchers in this field.
基金Supported by the Natural Science Foundation of China under Grant No. 60972164the Program for Liaoning Excellent Talents in University under Grant No. LJQ2011136+2 种基金the Key Technologies R&D Program of Liaoning Province under Grant No. 2011224006the Program for Liaoning Innovative Research Team in University under Grant No. LT2011019the Science and Technology Program of Shenyang under Grant No. F11-264-1-70
文摘We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra.Then its super Hamiltonian structure is furnished by super trace identity.As its reduction,we gain the nonlinear integrable couplings of the classical integrable Dirac hierarchy.
基金This research is supported by the National Natural Science Foundation of China(Grant Nos.61973262 and 51405068)the Natural Science Foundation of Hebei Province of China(Grant No.E2019203146).
文摘Considering the dynamic influence of the roll vibration on the lubricant film thickness in the rolling deformation area,nonlinear dynamic rolling forces related to film thickness in the vertical and horizontal directions were obtained based on the Karman balance theory.Based on these dynamic rolling forces and the mechanical vibration of the rolling mill,a vertical-horizontal coupling nonlinear vibration dynamic model was established.The amplitude-frequency equation of the main resonance was derived by using the multiple-scale method.At last,the parameters of the 1780 rolling mill were used for numerical simulation,and the time-domain response curves of the system’s vibration displacement and lubricating film thickness under the steady and unsteady conditions were analyzed.The influences of parameters such as interface contact ratio,nonlinear parameters and external disturbances on the primary resonance frequency characteristics were obtained,which provided a theoretical reference for the suppression of rolling mill vibration.
文摘In this paper, the influence of init ial imperfection and coupling between bending and extension on vibration, buckling and nonlinear dynamic stability of laminated plates is studied. The governing e quation is derived. It is a nonlinear modified Mathieu Equation. Numerical solut ions of 5 typical composite materials namely, Glass_epoxy Scotch_1002, Aramid_ep oxy Kevlar_49, Boron_epoxy B4_5505, Graphite_epoxy T300_5208 and AS_3501 are co mputed. Results reveal that the existence of initial imperfection, and also coup ling effect,make the plates much more sensitive to entering parametric resonance with amplitude greater than that of perfect plates. Coupl ing effect for different composite laminates, especially, for that with few laye rs, is different. If coupling effect is neglected, the design of plate structure s for buckling and dynamic stability would unconservatively be for more than 10% .
基金provided by the National Natural Science Foundation ofChina(Grant No.11872080)Beijing Natural Science Foundation(Grant No.3192005).
文摘A geometrically nonlinear topology optimization(GNTO)method with thermal–mechanical coupling is investigated.Firstly,the new expression of element coupling stress due to superimposed mechanical and thermal loading is obtained based on the geometrically nonlinear finite element analysis.The lightweight topology optimization(TO)model under stress constraints is established to satisfy the strength requirement.Secondly,the distortion energy theory is introduced to transform themodel into structural strain energy constraints in order to solve the implicit relationship between stress constraints and design variables.Thirdly,the sensitivity analysis of the optimization model is derived,and the model is solved by the method of moving asymptotes(MMA).Numerical examples show that temperature has a significant effect on the optimal configuration,and the TO method considering temperature load is closer to engineering design requirements.The proposed method can be extended to the GNTO design with multiple physical field coupling.
基金Project supported by the Scientific Research Fundation of the Education Department of Liaoning Province,China(GrantNo.L2010513)the China Postdoctoral Science Foundation(Grant No.2011M500404)
文摘In this paper, a new nonlinear integrable coupling system of the soliton hierarchy is presented. Prom the Lax pairs, the coupled KdV equations are constructed successfully. Based on the prolongation method of Wahlquist and Estabrook, we study the prolongation structure of the nonlinear integrable couplings of the KdV equation.
基金This work has been supported by the National Key Research and Development Program of China(No.2018YFB0504400)the National Natural Science Foundation of China(Nos.61775107,61322510 and 11674177)the Tianjin Natural Science Foundation(No.19JCZDJC31200).
文摘Multimode fiber has a richer spatial dimension than single-mode fiber,and is an ideal platform for studying many novel nonlinear effects.We established a strong linear coupling and short-range fiber model to understand the interactive effects of linear coupling and nonlinear effects.We find that strong linear coupling can compensate for the group delay between eigenmodes and cause energy fluctuation between modes which weakens the nonlinear effects.In high energy pulses,the interaction of linear coupling and nonlinear effects can help producing weak dispersion waves when the spectrum is broadened.Since linear coupling in a mode group is common and unavoidable,these results may provide a certain theoretical explanation for multi-mode nonlinear phenomena.
基金funded by Major Projects of Aero-Engines and Gas Turbines(J2019-Ⅳ-0023-0091 and J2019-Ⅳ-0005-0073)Aeronautical Science Foundation of China(2019ZB051002)+1 种基金China Postdoctoral Science Foundation(2021M700326)Advanced Jet Propulsion Creativity Center(Projects HKCX2020-02-013,HKCX2020-02-016 and HKCX2022-01009)。
文摘Within the linear framework,the Modal Electromechanical Coupling Factor(MEMCF)is an important indicator to quantify the dynamic conversion of mechanical energy and electrical energy of piezoelectric structures.It is also an important tool to guide the piezoelectric damping design of linear structures.Advanced aircraft often fly in maneuvers,and the variable working conditions induce drastic changes in the load level on structures.Geometric and contact nonlinearities of thin-walled structures and joint structures are often activated.To achieve a good vibration reduction effect covering all working conditions,one cannot directly use linear electromechanical coupling theory to instruct the piezoelectric damping design for nonlinear structures.Therefore,this paper defines the Nonlinear Modal Electromechanical Coupling Factor(NMEMCF)and proposes the corresponding numerical method for the first time to quantitatively evaluate the electromechanical coupling capability of nonlinear piezoelectric structures.Three candidate definitions of the NMEMCF are given,including two frequency definitions and one energy definition.The energy definition is the most promising one.It is not only applicable to both conservative and dissipative nonlinear structures but also compatible with the linear MEMCF.In addition,based on the energy formula,the NMEMCF can be obtained by only performing one nonlinear modal analysis in the open-circuit state.The analytical findings and the numerical tool are validated against two piezoelectric structures with different types of nonlinearities.A strong correlation among the NMEMCF,geometric parameters,and energy dissipation is observed.The results confirm that the proposed NMEMCF captures the physics of the electromechanical coupling phenomenon associated with nonlinear piezoelectric structures and can be used as an essential design indicator of piezoelectric damping,especially for variable working conditions.
基金supported by the China Scholarship Council(CSC)(Grant No.202006060033).
文摘Both the complex geometrical morphology of rough-walled rock fractures and the nonlinearity of fluid flow contribute to resistance in fluid flow through rock fractures.The interactions of the shear-flow process further complicate the characterisation of flow behaviours in rock fractures.In this study,an improved friction factor model involving both the effects of viscous and inertial forces is presented based on the Forchheimer equation.The model incorporates two key variables,i.e.Reynolds number and relative roughness,which reflect the effects of flow regimes and fracture roughness,respectively.The changes in geometrical parameters induced by shearing are considered,with the peak asperity height predicted through a correlation with post-peak roughness degradation.The hydraulic aperture during shearing is estimated using a suggested equation that accounts for the mobilised contact area ratio and variable aperture distribution.The parametric sensitivity analysis reveals that shear-induced changes in fracture geometry enhance the flow nonlinearity in rock fractures.The model performs well in predicting the friction factor based on two validation criteria.Then,the proposed friction factor model is incorporated into the three-dimensional distinct element code(3DEC)in the form of the Darcy-Weisbach equation.Coupled with the numerically implemented mechanical model and hydraulic aperture prediction model,numerical simulations of coupled shear-flow processes in single rock fractures are conducted.The simulation outcomes are validated through comparison with the experimental results,showing acceptable agreement and demonstrating that the numerical model is capable of accurately evaluating the hydro-mechanical coupling behaviour during the shearing of rock fractures.
基金supported by the National Natural Science Foundation of China(Nos.52034010 and 52479113)the Natural Science Foundation of Shandong Province,China(No.ZR2024ME165)the Postgraduate Education and Teaching Reform Project of China University of Petroleum(East China)(No.YJG2024005).
文摘Understanding the complex flow behavior along a rough rock fracture under high-temperature,high-stress,and high-seepage pressure(HTHM)coupling conditions is of great significance for optimizing deep resource extraction.This study investigates the complex flow behavior of a single rock fracture under coupled HTHM conditions using a self-developed multi-field coupling experimental system,considering real-time high temperatures(20–90℃),confining pressures(30–120 MPa),and seepage pressures(5–60 MPa).Experimental results show that as confining pressure increases,two typical nonlinear flow behaviors are observed,which are Forchheimer flow and low-velocity nonlinear flow.The increase in temperature and decrease in roughness significantly promote the fluid flow and enhance the nonlinear relationship between the volumetric flow rate and the hydraulic gradient at lower confining pressures(30 MPa).However,the change in temperature and fracture surface roughness does not affect the nonlinear type of fluid flow.Under a given hydraulic gradient,the influence of temperature and fracture roughness on the volumetric flow rate varies with changes in confining pressure.Additionally,this study considers both the viscous and inertial terms,and a modified Forchheimer equation is proposed using two parameters:the contact area ratio and the thermal expansion coefficient of the rock.The proposed model can effectively predict the nonlinear flow behavior of fluid along rough fractured rocks under varying temperatures and surface roughness.The experimental results and the proposed model provide valuable data and theoretical guidance for deep oil and gas exploration as well as hydraulic fracturing design.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1604200)the National Natural Science Foundation of China(Grant No.12261131495)Institute of Systems Science,Beijing Wuzi University(Grant No.BWUISS21).
文摘The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.
基金supported by the National Natural Science Foundation of China (11132007)
文摘Previous work examined the effect of the attached stiffness matrix terms on stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the nonlinear formulations to an elastic beam with free large overall motion. Based on initial stress method, the nonlinear coupling equations of elastic beams are obtained with free large overall motion and the attached stiffness matrix is derived by solving sub-static formulation. The angular velocity and the tip deformation of the elastic pendulum are calculated. The analytical results show that the simulation results of the present model are tabled and coincide with the one-order approximate model. It is shown that the simulation results accord with energy conservation principle.
文摘In the paper, 3-D analysis method with unitive schemes is set up, which is used to resolve the uplift with multiple moving boundaries and multiple nonlinear coupling for anchored liquid storage tanks. hi it, an algorithm of quasi-harmonious finite elements for arbitrary quadrilateral of thin plates and shells is built up to analyze the multiple coupling problems of general thin plates and shells structures with three dimensions, the complementary equations for analyzing uplifting moving boundary problems are deduced. The axial symmetry and presumption of beam type mode are not used. In it, an algorithm is put forward for analyzing the Navier-Stokes problems of unsteady, three-dimensional, and viscous liquid with sloshing of moving boundary surfaces in large amplitude under ALE frame by scheme of time-split-steps to which linear potential theory is not applied. The algorithms can be used to analyze the solid-liquid multiple nonlinear coupling problems with 3-D moving boundary with friction in multiple places.
基金supported in part by National Natural Science Foundation of China (Nos. 11875021, 11835010, 11875024, 11775072, 11505053, 11475058)by the ITER-CN (Nos. 2017YFE0300501, 2017YFE0300405, 2017YFE0301202 and 2017YFE030168)
文摘Nonlinear couplings of various Alfvén modes driven by energetic particles in HL-2 A are addressed by employing the Fourier bicoherence and Lissajous-curve technique. Long-lived modes and high-frequency coherent modes are presented. Then the squared bicoherence of three waves establishes the existence of three-wave coupling. Lissajous-curves of those waves manifest that their phases are locked, which again confirms that they are nonlinearly coupled to each other. Moreover, coupled modes triggered by supersonic molecular beam injection are investigated. The phase evolution of them is given by the Lissajous-curve. Further details of phase-flip and phase-slip are presented and discussed.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11864018 and 11574229)Scientific Research Foundation of the Education Department of Jiangxi Province of China(Grant No.GJJ170645)Doctor Startup Fund of the Natural Science of Jinggangshan University,China(Grant No.JZB16003)
文摘Coherent perfect absorption provides a method of light-controlling-light and has practical applications in optical communications. Recently, a cavity-based nonlinear perfect photon absorption extends the coherent perfect absorber（CPA）beyond the linear regime. As nanowire-based system is a more competitive candidate for full-optical device, we introduce a nonlinear CPA in the single two-level atom–nanowires coupling system in this work. Nonlinear input–output relations are derived analytically, and three contributions of atomic saturation nonlinearity are explicit. The consociation of optical nonlinearity and destructive interference makes it feasible to fabricate a nonlinear monoatomic CPA. Our results also indicate that a nonlinear system may work linearly even when the incoming lights are not weak any more. Our findings show promising applications in full-optical devices.
