Revealing the combined influence of interfacial damage and nonlinear factors on the forced vibration is significant for the stability design of fluid-conveying pipes, which are usually assembled in aircraft. The nonli...Revealing the combined influence of interfacial damage and nonlinear factors on the forced vibration is significant for the stability design of fluid-conveying pipes, which are usually assembled in aircraft. The nonlinear forced resonance of fluid-conveying layered pipes with a weak interface and a movable boundary under the external excitation is studied. The pipe is simply supported at both ends, with one end subject to a viscoelastic boundary constraint described by KelvinVoigt model. The weak interface in the pipe is considered in the refined displacement field of the layered pipe employing the interfacial cohesive law. The governing equations are derived by Hamilton's variational principle. Geometric nonlinearities including nonlinear curvature, longitudinal inertia nonlinearity and nonlinear constraint force are comprehensively considered during the theoretical derivation. Amplitude-frequency bifurcation diagrams are obtained utilizing a perturbation-Incremental Harmonic Balance Method(IHBM). Results show that interfacial damage and viscoelastic constraints from boundary and foundation have an important influence on the linear and nonlinear dynamic behavior of the system.展开更多
We study the motion of a spiral wave controlled by a local periodic forcing imposed on a region around the spiral tip in an excitable medium. Three types of trajectories of spiral tip are observed： the epicycloid-lik...We study the motion of a spiral wave controlled by a local periodic forcing imposed on a region around the spiral tip in an excitable medium. Three types of trajectories of spiral tip are observed： the epicycloid-like meandering, the resonant drift, and the hypocycloid-like meandering. The frequency of the spiral is sensitive to the local periodic forcing. The dependency of spiral frequency on the amplitude and size of local periodic forcing are presented. In addition, we show how the drift speed and direction are adjusted by the amplitude and phase of local periodic forcing, which is consistent with a theoretical analysis based on the weak deformation approximation.展开更多
The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engin...The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engineering structures subjected to body forces such as rotational inertia and gravitational loads,additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the domain.In this study,weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are developed.By using divergence theorem or alternatively the radial integration method,the domain integral terms caused by body forces are transformed into boundary integrals.And due to the weak singularity of the formulated boundary integral equations,a simple Gauss-Legendre quadrature with a few integral points is sufficient for numerically evaluating the SGBEM equations.Some numerical examples are presented to verify this approach and results are compared with benchmark solutions.展开更多
The weakly forced vibration of an axially moving viscoelastic beam is inves- tigated. The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved....The weakly forced vibration of an axially moving viscoelastic beam is inves- tigated. The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved. The nonlinear equations governing the transverse vibration are derived from the dynamical, constitutive, and geometrical relations. The method of multiple scales is used to determine the steady-state response. The modulation equation is derived from the solvability condition of eliminating secular terms. Closed-form expressions of the amplitude and existence condition of nontrivial steady-state response are derived from the modulation equation. The stability of non- trivial steady-state response is examined via the Routh-Hurwitz criterion.展开更多
It is presented that there exists approximate inertial manifolds in weakly damped forced Kdv equation with with periodic boundary conditionsIIbns. The approximate inertial manifolds provide approximant of the attractr...It is presented that there exists approximate inertial manifolds in weakly damped forced Kdv equation with with periodic boundary conditionsIIbns. The approximate inertial manifolds provide approximant of the attractror by finite dimensional smooth manifolds which are exphcitly defined And the concepl leads to new numerical schemes which are well adapted to the longtime behavior of dynamical system.展开更多
The existence of local attractors in thin 2D domains far the weakly damped forced KdV equation, whose principal operator is a non-self adjoint and non-sectorial one is given.
The protagonist, Scarlett, in the book Gone with the Wind, impresses people throughout the world, not only because of her beautiful appearance, but also her brave and strong spirit. However, everyone has his weak poin...The protagonist, Scarlett, in the book Gone with the Wind, impresses people throughout the world, not only because of her beautiful appearance, but also her brave and strong spirit. However, everyone has his weak points, and she is not an exception. So it's sure that she needs some backup forces to support her to get through the tough days. This thesis tries to put forward Scarlett's strong backup forces, which help her pull through the tough life and finally become a real brave person who could face the rest life strongly and fearlessly all by herself.展开更多
The stability of the periodic solution of the Duffing oscillator system in the periodic phase state is proved by using the Yoshizaw theorem, which establishes a theoretical basis for using this kind of chaotic oscilla...The stability of the periodic solution of the Duffing oscillator system in the periodic phase state is proved by using the Yoshizaw theorem, which establishes a theoretical basis for using this kind of chaotic oscillator system to detect weak signals. The restoring force term of the system affects the weak-signal detection ability of the system directly, the quantitative relationship between the coefficients of the linear and nonlinear items of the restoring force of the Duffing oscillator system and the SNR in the detection of weak signals is obtained through a large number of simulation experiments, then a new restoring force function with better detection results is established.展开更多
The present work explores the propagation characteristics of high-power beams in weakly relativistic-ponderomotive thermal quantum plasma.A q-Gaussian laser beam is taken in the present investigation.The quasi-optics ...The present work explores the propagation characteristics of high-power beams in weakly relativistic-ponderomotive thermal quantum plasma.A q-Gaussian laser beam is taken in the present investigation.The quasi-optics equation obtained in the present study is solved through a well-established Wentzel–Kramers–Brillouin approximation and paraxial theory approach for obtaining the second-order differential equation describing the behavior of beam width of the laser beam.Further,a numerical simulation of this second-order differential equation is carried out for determining the behavior of the beam width with dimensionless distance for established laser–plasma parameters.The comparison of the present study is made with ordinary quantum plasma and classical relativistic plasma cases.展开更多
A bottleneck in biomimetic synthesis consists in the full copy of,for example,the hierarchical structure of proteins directed by weak interactions.By contrast with covalent bonds bearing definite orientation and high ...A bottleneck in biomimetic synthesis consists in the full copy of,for example,the hierarchical structure of proteins directed by weak interactions.By contrast with covalent bonds bearing definite orientation and high stability,weak intermolecular forces within a continuous dynamic equilibrium can be hardly tamed for molecular design.In this endeavor,a ligand-dominated strategy that embodies tunable electrostatic repulsion andπ···πstacking was first employed to shape polyoxovanadate-based metal-organic polyhedra(VMOPs).Structural evolution involving transformation,interlock,and discovery of an unprecedented prototype of the Star of David was hence achievable.Not only as a handy tool for the primary structural control over VMOPs,these weak forces allow for an advanced management on the spatial distribution of such manmade macromolecules as well as the associated physicochemical behaviors,representing an ideal model for simulating and interpreting the conformation-function relationship of proteins.展开更多
In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wav...In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.展开更多
微推力器是实现卫星姿态与轨道控制不可或缺的执行机构,精确测量其推力性能至关重要.针对传统微推力测量装置存在的推力力臂难以精确测定,羽流随扭摆转动而偏转以及装配调试复杂等问题,设计并研制了一种基于罗伯威尔平衡结构的新型微推...微推力器是实现卫星姿态与轨道控制不可或缺的执行机构,精确测量其推力性能至关重要.针对传统微推力测量装置存在的推力力臂难以精确测定,羽流随扭摆转动而偏转以及装配调试复杂等问题,设计并研制了一种基于罗伯威尔平衡结构的新型微推力测量装置.该装置的推力力臂长度固定,不受微推力器安装位置的干扰,有效消除了力臂测量引入的不确定度,同时降低了微推力器的装配与调试难度.此外,该装置确保了推力羽流在扭摆转动过程中不发生偏转,便于同步监测推力器羽流信息.本研究利用电磁标准力对其开环和闭环两种测量模式开展了性能测试与评估,并使用该装置对一套冷气微推力器进行了标定.性能测试结果显示,在开环模式下,该装置量程为2 m N,分辨力优于1μN,包含因子为3时的测量不确定度为2.33μN+0.99%T(其中T为实测力值).在闭环模式下,测量量程达到100 mN,分辨力优于5μN,测量不确定度则为18.00μN+0.31%T.该装置可满足多种微牛级至毫牛级微推力器的推力测量需求,为我国商业航天的快速发展提供助力.展开更多
文摘Revealing the combined influence of interfacial damage and nonlinear factors on the forced vibration is significant for the stability design of fluid-conveying pipes, which are usually assembled in aircraft. The nonlinear forced resonance of fluid-conveying layered pipes with a weak interface and a movable boundary under the external excitation is studied. The pipe is simply supported at both ends, with one end subject to a viscoelastic boundary constraint described by KelvinVoigt model. The weak interface in the pipe is considered in the refined displacement field of the layered pipe employing the interfacial cohesive law. The governing equations are derived by Hamilton's variational principle. Geometric nonlinearities including nonlinear curvature, longitudinal inertia nonlinearity and nonlinear constraint force are comprehensively considered during the theoretical derivation. Amplitude-frequency bifurcation diagrams are obtained utilizing a perturbation-Incremental Harmonic Balance Method(IHBM). Results show that interfacial damage and viscoelastic constraints from boundary and foundation have an important influence on the linear and nonlinear dynamic behavior of the system.
基金Project supported by the National Natural Science Foundation of China(Grant No.11274271)the Scientific Research Foundation of Education Bureau of Zhejiang Province,China(Grant No.Y201224250)
文摘We study the motion of a spiral wave controlled by a local periodic forcing imposed on a region around the spiral tip in an excitable medium. Three types of trajectories of spiral tip are observed： the epicycloid-like meandering, the resonant drift, and the hypocycloid-like meandering. The frequency of the spiral is sensitive to the local periodic forcing. The dependency of spiral frequency on the amplitude and size of local periodic forcing are presented. In addition, we show how the drift speed and direction are adjusted by the amplitude and phase of local periodic forcing, which is consistent with a theoretical analysis based on the weak deformation approximation.
基金support of the National Natural Science Foundation of China(12072011).
文摘The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engineering structures subjected to body forces such as rotational inertia and gravitational loads,additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the domain.In this study,weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are developed.By using divergence theorem or alternatively the radial integration method,the domain integral terms caused by body forces are transformed into boundary integrals.And due to the weak singularity of the formulated boundary integral equations,a simple Gauss-Legendre quadrature with a few integral points is sufficient for numerically evaluating the SGBEM equations.Some numerical examples are presented to verify this approach and results are compared with benchmark solutions.
基金Project supported by the National Natural Science Foundation of China (No.10972143)the Shanghai Municipal Education Commission (No.YYY11040)+2 种基金the Shanghai Leading Academic Discipline Project (No.J51501)the Leading Academic Discipline Project of Shanghai Institute of Technology(No.1020Q121001)the Start Foundation for Introducing Talents of Shanghai Institute of Technology (No.YJ2011-26)
文摘The weakly forced vibration of an axially moving viscoelastic beam is inves- tigated. The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved. The nonlinear equations governing the transverse vibration are derived from the dynamical, constitutive, and geometrical relations. The method of multiple scales is used to determine the steady-state response. The modulation equation is derived from the solvability condition of eliminating secular terms. Closed-form expressions of the amplitude and existence condition of nontrivial steady-state response are derived from the modulation equation. The stability of non- trivial steady-state response is examined via the Routh-Hurwitz criterion.
文摘It is presented that there exists approximate inertial manifolds in weakly damped forced Kdv equation with with periodic boundary conditionsIIbns. The approximate inertial manifolds provide approximant of the attractror by finite dimensional smooth manifolds which are exphcitly defined And the concepl leads to new numerical schemes which are well adapted to the longtime behavior of dynamical system.
文摘The existence of local attractors in thin 2D domains far the weakly damped forced KdV equation, whose principal operator is a non-self adjoint and non-sectorial one is given.
文摘The protagonist, Scarlett, in the book Gone with the Wind, impresses people throughout the world, not only because of her beautiful appearance, but also her brave and strong spirit. However, everyone has his weak points, and she is not an exception. So it's sure that she needs some backup forces to support her to get through the tough days. This thesis tries to put forward Scarlett's strong backup forces, which help her pull through the tough life and finally become a real brave person who could face the rest life strongly and fearlessly all by herself.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 40374045 and 40574051）, and by the Jilin Technology Development Plan （Grant No 20050526）,
文摘The stability of the periodic solution of the Duffing oscillator system in the periodic phase state is proved by using the Yoshizaw theorem, which establishes a theoretical basis for using this kind of chaotic oscillator system to detect weak signals. The restoring force term of the system affects the weak-signal detection ability of the system directly, the quantitative relationship between the coefficients of the linear and nonlinear items of the restoring force of the Duffing oscillator system and the SNR in the detection of weak signals is obtained through a large number of simulation experiments, then a new restoring force function with better detection results is established.
文摘The present work explores the propagation characteristics of high-power beams in weakly relativistic-ponderomotive thermal quantum plasma.A q-Gaussian laser beam is taken in the present investigation.The quasi-optics equation obtained in the present study is solved through a well-established Wentzel–Kramers–Brillouin approximation and paraxial theory approach for obtaining the second-order differential equation describing the behavior of beam width of the laser beam.Further,a numerical simulation of this second-order differential equation is carried out for determining the behavior of the beam width with dimensionless distance for established laser–plasma parameters.The comparison of the present study is made with ordinary quantum plasma and classical relativistic plasma cases.
基金financially supported by the National Natural Science Foundation of China(No.22001066)the Natural Science Foundation of Hunan Province(Nos.2021JJ40049 and 2022JJ20007)+3 种基金the Science and Technology Innovation Program of Hunan Province(No.2022RC1115)J.Du acknowledges the Science and Technology Project of Hebei Education Department(No.QN2023049)Science Foundation of Hebei Normal University(No.L2023B51)TianHe-2(LvLiang,China)Cloud Computing Center for support。
文摘A bottleneck in biomimetic synthesis consists in the full copy of,for example,the hierarchical structure of proteins directed by weak interactions.By contrast with covalent bonds bearing definite orientation and high stability,weak intermolecular forces within a continuous dynamic equilibrium can be hardly tamed for molecular design.In this endeavor,a ligand-dominated strategy that embodies tunable electrostatic repulsion andπ···πstacking was first employed to shape polyoxovanadate-based metal-organic polyhedra(VMOPs).Structural evolution involving transformation,interlock,and discovery of an unprecedented prototype of the Star of David was hence achievable.Not only as a handy tool for the primary structural control over VMOPs,these weak forces allow for an advanced management on the spatial distribution of such manmade macromolecules as well as the associated physicochemical behaviors,representing an ideal model for simulating and interpreting the conformation-function relationship of proteins.
基金Project supported by the National Natural Science Foundation of China (Nos. 19772063, 19772068)the Doctoral Research Fund of the Ministry of Education (No.20010141024)
文摘In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.
文摘微推力器是实现卫星姿态与轨道控制不可或缺的执行机构,精确测量其推力性能至关重要.针对传统微推力测量装置存在的推力力臂难以精确测定,羽流随扭摆转动而偏转以及装配调试复杂等问题,设计并研制了一种基于罗伯威尔平衡结构的新型微推力测量装置.该装置的推力力臂长度固定,不受微推力器安装位置的干扰,有效消除了力臂测量引入的不确定度,同时降低了微推力器的装配与调试难度.此外,该装置确保了推力羽流在扭摆转动过程中不发生偏转,便于同步监测推力器羽流信息.本研究利用电磁标准力对其开环和闭环两种测量模式开展了性能测试与评估,并使用该装置对一套冷气微推力器进行了标定.性能测试结果显示,在开环模式下,该装置量程为2 m N,分辨力优于1μN,包含因子为3时的测量不确定度为2.33μN+0.99%T(其中T为实测力值).在闭环模式下,测量量程达到100 mN,分辨力优于5μN,测量不确定度则为18.00μN+0.31%T.该装置可满足多种微牛级至毫牛级微推力器的推力测量需求,为我国商业航天的快速发展提供助力.
