The motional payloads on stabilized platform must be linked by some cable harnesses with other immobile apparatus.During the operation of stabilized platform,these cable harnesses can create spring disturbance torque ...The motional payloads on stabilized platform must be linked by some cable harnesses with other immobile apparatus.During the operation of stabilized platform,these cable harnesses can create spring disturbance torque which is exerted on the stabilized platform and then reduce the stabilizing precision.None of current studies can deal with the spring disturbance torque problem.To analyze the spring disturbance toque,a dynamic thin rod model is presented for simulating the motional cable harness which is based on the Kirchhoff rod theorem and can consider the geometrically non-linear effects.The internal bending and torsion restoring torques are simulated and then a predictive analysis of the disturbance torque can be performed in motional cable routing design.This model is solved with differential quadrature method（DQM）.By using zeros of the Chebyshev polynomial as the grid points,the arc-coordinate is discretized to obtain a set of ordinary differential equations in time domain which is solved by implied method to obtain the profile and internal force of cable harness.The accuracy of this model is validated by comparing the simulation results and the experiment results（both the spring force and the deformed profile of the motional cable harness）.In the experiment,a special optical measuring instrument based on binocular vision is developed.The comparison of experimental and simulated results shows that the simulation model can represent the real motional cable harness well,and the spring disturbance force simulation results are precise enough for spring disturbance torque analysis.This study will be helpful to obtain an optimized motional cable harness layout design with small spring disturbance torque.展开更多
Recently the Kirchhoff rod and the methods of dynamical analogue have been widely used in modeling DNA.The features of a DNA such as its super slender and super large deformation raise new challenges in modeling and n...Recently the Kirchhoff rod and the methods of dynamical analogue have been widely used in modeling DNA.The features of a DNA such as its super slender and super large deformation raise new challenges in modeling and numerical simulations of a Kirchhoff rod.In this paper,Euler parameters are introduced to set up the quasi-Hamilton system of an elastic rod,then a symplectic algorithm is applied in its numerical simulations.Finally,a simplified surface model of the rod is given based on the hypothesis of rigid cross-section.展开更多
Biological growth is a common phenomenon in nature,and some organisms such as DNA molecules and bacterial filaments grow in viscous media.The growth induced instability of morphoelastic rod in a viscous medium is stud...Biological growth is a common phenomenon in nature,and some organisms such as DNA molecules and bacterial filaments grow in viscous media.The growth induced instability of morphoelastic rod in a viscous medium is studied in this paper.Based on the Kirchhoff kinetic analogy method,the mechanical model for growing elastic thin rod in the viscous medium is established.A perturbation analysis is used to analyze the stability of the growing elastic rod in the viscous medium.We apply the results into planar growing ring and get its criterion of instability.Take the criterion into DNA ring to discuss the influence of viscous resistance on its instability.展开更多
Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff＇s kinetic analogy is an effective approach to the stability analysis of e...Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff＇s kinetic analogy is an effective approach to the stability analysis of equilibrium of a thin elastic rod. The main hypotheses of Kirchhoff＇s theory without the extension of the centerline and the shear deformation of the cross section are not adoptable to real soft materials of biological fibers. In this paper, the dynamic equations of a rod with a circular cross section are established on the basis of the exact Cosserat model by considering the tension and the shear deformations. Euler＇s angles are applied as the attitude representation of the cross section. The deviation of the normal axis of the cross section from the tangent of the centerline is considered as the result of the shear deformation. Lyapunov＇s stability of the helical equilibrium is discussed in static category. Euler＇s critical values of axial force and torque are obtained. Lyapunov＇s and Euler＇s stability conditions in the space domain are the necessary conditions of Lyapunov＇s stability of the helical rod in the time domain.展开更多
Geometric phases have natural manifestations in large deformations of geometrically exact rods. The primary concerns of this article are the physical implications and observable consequences of geometric phases arisin...Geometric phases have natural manifestations in large deformations of geometrically exact rods. The primary concerns of this article are the physical implications and observable consequences of geometric phases arising from the deformed patterns exhibited by a rod subjected to end moments. This mechanical problem is classical and has a long tradition dating back to Kirchhoff. However, the perspective from geometric phases seems to go more deeply into relations between local strain states and global geometry of shapes, and infuses genuinely new insights and better understanding, which enable one to describe this kind of deformation in a neat and elegant way. On the other hand, visual representations of these deformations provide beautiful illustrations of geometric phases and render the meaning of the abstract concept of holonomy more direct and transparent.展开更多
DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural mod...DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. This paper studies the structural properties of a super-long elastic slender rod as a structural model of DNA by using Kirchhoff＇s analogue technique and presents the Noether symmetries of the model by using the method of infinitesimal transformation. Baaed on Kirchhoff＇s analogue it analyses the generalized Hamilton canonical equations. The infinitesimal transfornaationa with rcspect to the radial coordinnte, the gonarnlizod coordinates, and the Cluasi-momenta of 5he model are introduced. The Noether gymmetries and conserved qugntities of the model are obtained.展开更多
The design work of motional cable in products is vital due to the difficulty in estimating the potential issues in current researches.In this paper,a physics-based modeling and simulation method for the motional cable...The design work of motional cable in products is vital due to the difficulty in estimating the potential issues in current researches.In this paper,a physics-based modeling and simulation method for the motional cable harness design is presented.The model,based on continuum mechanics,is established by analyzing the force of microelement in equilibrium.During the analysis procedure,three coordinate systems：inertial,Frenet and main-axis coordinate systems are used.By variable substitution and dimensionless processing,the equation set is discretized by differential quadrature method and subsequently becomes an overdetermined nonlinear equation set with boundary conditions solved by Levenberg-Marquardt method.With the profile of motional cable harness obtained from the integral of arithmetic solution,a motion simulation system based on＂path＂and＂profile＂as well as the experimental equipments is built.Using the same parameters as input for the simulation and the real cable harness correspondingly,the issue in designing,such as collision,can be easily found by the simulation system.This research obtains a better result which has no potential collisions by redesign,and the proposed method can be used as an accurate and efficient way in motional cable harness design work.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 50805009)
文摘The motional payloads on stabilized platform must be linked by some cable harnesses with other immobile apparatus.During the operation of stabilized platform,these cable harnesses can create spring disturbance torque which is exerted on the stabilized platform and then reduce the stabilizing precision.None of current studies can deal with the spring disturbance torque problem.To analyze the spring disturbance toque,a dynamic thin rod model is presented for simulating the motional cable harness which is based on the Kirchhoff rod theorem and can consider the geometrically non-linear effects.The internal bending and torsion restoring torques are simulated and then a predictive analysis of the disturbance torque can be performed in motional cable routing design.This model is solved with differential quadrature method（DQM）.By using zeros of the Chebyshev polynomial as the grid points,the arc-coordinate is discretized to obtain a set of ordinary differential equations in time domain which is solved by implied method to obtain the profile and internal force of cable harness.The accuracy of this model is validated by comparing the simulation results and the experiment results（both the spring force and the deformed profile of the motional cable harness）.In the experiment,a special optical measuring instrument based on binocular vision is developed.The comparison of experimental and simulated results shows that the simulation model can represent the real motional cable harness well,and the spring disturbance force simulation results are precise enough for spring disturbance torque analysis.This study will be helpful to obtain an optimized motional cable harness layout design with small spring disturbance torque.
基金Jiangsu Overseas Research or Training Program for University Prominent Young Faculty and PresidentsNational Natural Science Foundation of China(Grant Nos.11426141,11571136 and 11072120).
文摘Recently the Kirchhoff rod and the methods of dynamical analogue have been widely used in modeling DNA.The features of a DNA such as its super slender and super large deformation raise new challenges in modeling and numerical simulations of a Kirchhoff rod.In this paper,Euler parameters are introduced to set up the quasi-Hamilton system of an elastic rod,then a symplectic algorithm is applied in its numerical simulations.Finally,a simplified surface model of the rod is given based on the hypothesis of rigid cross-section.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11772141 and 11262019)the State Scholarship Fund of China Scholarship Council(Grant No.201708370030).
文摘Biological growth is a common phenomenon in nature,and some organisms such as DNA molecules and bacterial filaments grow in viscous media.The growth induced instability of morphoelastic rod in a viscous medium is studied in this paper.Based on the Kirchhoff kinetic analogy method,the mechanical model for growing elastic thin rod in the viscous medium is established.A perturbation analysis is used to analyze the stability of the growing elastic rod in the viscous medium.We apply the results into planar growing ring and get its criterion of instability.Take the criterion into DNA ring to discuss the influence of viscous resistance on its instability.
基金supported by the National Natural Science Fundation of China(No.10972143)
文摘Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff＇s kinetic analogy is an effective approach to the stability analysis of equilibrium of a thin elastic rod. The main hypotheses of Kirchhoff＇s theory without the extension of the centerline and the shear deformation of the cross section are not adoptable to real soft materials of biological fibers. In this paper, the dynamic equations of a rod with a circular cross section are established on the basis of the exact Cosserat model by considering the tension and the shear deformations. Euler＇s angles are applied as the attitude representation of the cross section. The deviation of the normal axis of the cross section from the tangent of the centerline is considered as the result of the shear deformation. Lyapunov＇s stability of the helical equilibrium is discussed in static category. Euler＇s critical values of axial force and torque are obtained. Lyapunov＇s and Euler＇s stability conditions in the space domain are the necessary conditions of Lyapunov＇s stability of the helical rod in the time domain.
文摘Geometric phases have natural manifestations in large deformations of geometrically exact rods. The primary concerns of this article are the physical implications and observable consequences of geometric phases arising from the deformed patterns exhibited by a rod subjected to end moments. This mechanical problem is classical and has a long tradition dating back to Kirchhoff. However, the perspective from geometric phases seems to go more deeply into relations between local strain states and global geometry of shapes, and infuses genuinely new insights and better understanding, which enable one to describe this kind of deformation in a neat and elegant way. On the other hand, visual representations of these deformations provide beautiful illustrations of geometric phases and render the meaning of the abstract concept of holonomy more direct and transparent.
基金supported by the National Natural Science Foundation of China (Grant Nos 10672143 and 60575055)the State Key Laboratory of Scientific and Engineering ComputingChinese Academy of Sciences and the Natural Science Foundation of Henan Province Government of China (Grant No 0511022200)
文摘DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. This paper studies the structural properties of a super-long elastic slender rod as a structural model of DNA by using Kirchhoff＇s analogue technique and presents the Noether symmetries of the model by using the method of infinitesimal transformation. Baaed on Kirchhoff＇s analogue it analyses the generalized Hamilton canonical equations. The infinitesimal transfornaationa with rcspect to the radial coordinnte, the gonarnlizod coordinates, and the Cluasi-momenta of 5he model are introduced. The Noether gymmetries and conserved qugntities of the model are obtained.
基金Supported by National Natural Science Foundation of China(Grant No.51275047)
文摘The design work of motional cable in products is vital due to the difficulty in estimating the potential issues in current researches.In this paper,a physics-based modeling and simulation method for the motional cable harness design is presented.The model,based on continuum mechanics,is established by analyzing the force of microelement in equilibrium.During the analysis procedure,three coordinate systems：inertial,Frenet and main-axis coordinate systems are used.By variable substitution and dimensionless processing,the equation set is discretized by differential quadrature method and subsequently becomes an overdetermined nonlinear equation set with boundary conditions solved by Levenberg-Marquardt method.With the profile of motional cable harness obtained from the integral of arithmetic solution,a motion simulation system based on＂path＂and＂profile＂as well as the experimental equipments is built.Using the same parameters as input for the simulation and the real cable harness correspondingly,the issue in designing,such as collision,can be easily found by the simulation system.This research obtains a better result which has no potential collisions by redesign,and the proposed method can be used as an accurate and efficient way in motional cable harness design work.
