Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore th...Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.展开更多
The analysis of natural vibration characteristics has become one of important steps of the manufacture and dynamic design in the aerospace industry. This paper presents a new scenario called virtual cutting in the con...The analysis of natural vibration characteristics has become one of important steps of the manufacture and dynamic design in the aerospace industry. This paper presents a new scenario called virtual cutting in the context of the transfer matrix method of linear multibody systems closed- loop topology for computing the free vibration characteristics of elastically coupled flexible launch vehicle boosters. In this approach, the coupled system is idealized as a triple-beam system-like structure coupled by linear translational springs, where a non-uniform free-free Euler-Bemoulli beam is used. A large thrust-to-weight ratio leads to large axial accelera- tions that result in an axial inertia load distribution from nose to tail. Consequently, it causes the development of significant compressive forces along the length of the launch vehicle. Therefore, it is important to take into account this effect in the transverse vibration model. This scenario does not need the global dynamics equations of a system, and it has high computational efficiency and low memory requirements. The validity of the presented scenario is achieved through com- parison to other approaches published in the literature.展开更多
In this paper, by defining new state vectors and developing new transfer matrices of various elements mov- ing in space, the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to stud...In this paper, by defining new state vectors and developing new transfer matrices of various elements mov- ing in space, the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of multibody system with flexible beams moving in space. Formulations and numerical example of a rigid- flexible-body three pendulums system moving in space are given to validate the method. Using the new method to study the dynamics of multi-rigid-flexible-body system mov- ing in space, the global dynamics equations of system are not needed, the orders of involved matrices of the system are very low and the computational speed is high, irrespec- tive of the size of the system. The new method is simple, straightforward, practical, and provides a powerful tool for multi-rigid-flexible-body system dynamics.展开更多
The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear...The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.展开更多
The structure parameters of 6-degree of freedom(DOF)vibration isolation platform have a significant effect on its performance.To make the designed vibration isolation platform perform well,non-dominanted sorting genet...The structure parameters of 6-degree of freedom(DOF)vibration isolation platform have a significant effect on its performance.To make the designed vibration isolation platform perform well,non-dominanted sorting genetic algorithm version II(NSGA-II)was applied to optimize its structure based on the transfer matrix method for multibody systems.Firstly,the Jacobian matrix of 6-DOF vibration isolation platform was solved based on kinematics.Secondly,the transfer equation of 6-DOF vibration isolation system was established by the linear transfer matrix method for multibody systems.And the formula of its natural frequency was derived according to the boundary conditions of the system.Thirdly,the manipulability index was constructed based on a dimensionless Jacobian matrix.And a new performance index function was established considering the influence of dynamic isotropic and legs mass.Fourthly,genetic algorithm(GA)and NSGA-II were used to optimize the structure of the 6-DOF vibration isolation platform under the same conditions,respectively.It showed that NSGA-II had higher optimization efficiency,better calculation accuracy and shorter optimization time than that of GA.Finally,NSGA-II was adopted for multi-objective optimization design of 6-DOF vibration isolation platform based on the constraint conditions.Optimal Pareto solutions were obtained,which provides structural parameters for subsequent design work.Therefore,the proposed optimization method and the performance index in this paper provide a theoretical basis for the optimal design of relevant vibration isolation mechanism.展开更多
Rotor system supported by nonlinear bearing such as squeeze film damper(SFD)is widely used in practice owing to its wide range of damping capacity and simplicity in structure.In this paper,an improved and effective In...Rotor system supported by nonlinear bearing such as squeeze film damper(SFD)is widely used in practice owing to its wide range of damping capacity and simplicity in structure.In this paper,an improved and effective Incremental transfer matrix method(ITMM)is first presented by combining ITMM and fast Fourier transform(FFT).Afterwards this method is applied to calculate the dynamic characteristics of a Jeffcott rotor system with SFD.The convergence dificulties incurred caused by strong nonlinearities of SFD has been dealt by adopting a control factor.It is found that for the more general boundary problems where the boundary conditions are not at input and output ends of a chain system,the supplementary equation is necessarily added.Additionally,the Floquet theory is used to analyze the stability and bifurcation type of the obtained periodic solution.The semi-analytical results,including the periodic solutions of the system,the bifurcation points and their types,are in good agreement with the numerical method.Furthermore,the involution mechanism of the quasi-periodic and chaotic motions near the first-order translational mode and the second order bending mode of this system is also clarified by this method with the aid of Floquet theory.展开更多
The hybrid dynamics of multi-rigid-body and multi-flexible-body system becomes the mainstream of multi-body dynamics.Currently there lacks a compact approach to model the hybrid dynamics,especially in modern machine t...The hybrid dynamics of multi-rigid-body and multi-flexible-body system becomes the mainstream of multi-body dynamics.Currently there lacks a compact approach to model the hybrid dynamics,especially in modern machine tool application,due to the difficulty of solving the hybrid equations or the limitation of current software when dealing with the hybrid dynamics.The extended transfer matrix method（E-TMM）,which extends elements in three-dimensional space with higher matrixes,is proposed to simplify the modeling process of the hybrid dynamics.The E-TMM modeling approaches of 3 basic elements including 3D vibrant rigid body,joint and flexible body are studied in details.A parallel mill-turn tool spindle head unit driven by dual-linear motors is chosen as a plant to demonstrate the E-TMM modeling process.By using E-TMM,the spindle head unit is simplified as a topological network consisting of the three types of element,i.e.,3D vibrant rigid body,joint and flexible body,including 11 rigid bodies,14 joints and 1 3D-Timoshenko beam.Then the dynamic model of the system can be easily obtained by deducing the element-network by means of state vector transformation.The dynamic characteristics of the spindle head,such as natural frequencies,dynamic flexibility,etc.can be predicted by solving the obtained model.Experiment verification indicates that the E-TMM is valid with enough accuracy in the dynamic analysis of the parallel mill-turn tool spindle head.The E-TMM is capable of modeling the dynamics of machine tool structure with no requirements of deducing and solving the sophisticated differential equations.Moreover,the E-TMM provides a simple and elegant tool for hybrid dynamic analysis in future dynamic design of machine tools.展开更多
In consideration of the problem that the effect of conduit structure on water hammer has been ignored in the classical theory,the Poisson coupling between the fluid and the pipeline was studied and a fourteen-equation...In consideration of the problem that the effect of conduit structure on water hammer has been ignored in the classical theory,the Poisson coupling between the fluid and the pipeline was studied and a fourteen-equation mathematical model of fluid-structure interaction(FSI)was developed.Then,the transfer matrix method(TMM)was used to calculate the modal frequency,modal shape and frequency response.The results were compared with that in experiment to verify the correctness of the TMM and the results show that the fluid-structure coupling has a greater impact on the modal frequencies than the modal shape.Finally,the influence on the response spectrum of different damping ratios was studied and the results show that the natural frequency under different damping ratios has changed little but there is a big difference for the pressure spectrum.With the decreasing of damping ratio,the damping of the system on frequency spectrum is more and more significant and the dispersion and dissipation is more and more apparent.Therefore the appropriate damping ratio should be selected to minimize the effects of the vibration of the FSI.The results provide references for the theory research of FSI in the transient process.展开更多
A ship's tail shaft has serious flexural vibration due to the cantilevered nature of the propeller's blades.Analysis of the nature frequency of flexural vibration is vital to be able to provide effective shock...A ship's tail shaft has serious flexural vibration due to the cantilevered nature of the propeller's blades.Analysis of the nature frequency of flexural vibration is vital to be able to provide effective shock absorption for a ship's tail shaft.A mathematic model of tail shaft flexural vibrations was built using the transfer matrix method.The nature frequency of flexural vibration for an electrically propelled ship's tail shaft was then analyzed,and an effective method for calculating it was proposed:a genetic algorithm(GA),which calculates the nature frequency of vibration of a system.Sample calculations,with comparisons by the Prohl method under conditions bearing isotropic support,showed this method to be practical.It should have significant impact on engineering design theory.展开更多
In this paper, the analytical transfer matrix method （ATMM） is applied to study the properties of quantum reflection in three systems： a sech2 barrier, a ramp potential and an inverse harmonic oscillator. Our resul...In this paper, the analytical transfer matrix method （ATMM） is applied to study the properties of quantum reflection in three systems： a sech2 barrier, a ramp potential and an inverse harmonic oscillator. Our results agree with those obtained by Landau and Lifshitz [Landau L D and Lifshitz E M 1977 Quantum Mechanics （Non-relativistic Theory） （New York： Pergamon）], which proves that ATMM is a simple and effective method for quantum reflection.展开更多
A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential c...A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.展开更多
To find the difference in dynamic characteristics between conventional monohull ship and wave penetrating catamaran (WPC), a WPC was taken as an object; its dynamic characteristics were computed by transfer matrix met...To find the difference in dynamic characteristics between conventional monohull ship and wave penetrating catamaran (WPC), a WPC was taken as an object; its dynamic characteristics were computed by transfer matrix method and finite element method respectively. According to the comparison of the nature frequency results and mode shape results, the fact that FEM method is more suitable to dynamic characteristics analysis of a WPC was pointed out, special features on dynamic characteristics of WPC were given, and some beneficial suggestions are proposed to optimize the strength of a WPC in design period.展开更多
One-dimensional photonic crystals (1D PhCs) have a unique ability to control the propagation of light waves, however certain classes of 1D oxides remain relatively unexplored for use as PhCs. Specifically, there has n...One-dimensional photonic crystals (1D PhCs) have a unique ability to control the propagation of light waves, however certain classes of 1D oxides remain relatively unexplored for use as PhCs. Specifically, there has not been a comparative study of the three different 1D PhC structures to compare the influence of layer thickness, number, and refractive index on the ability of the PhCs to control light transmission. Herein, we use the transfer matrix method (TMM) to theoretically examine the transmission of 1D PhCs composed of layers of TiO<sub>2</sub>/SiO<sub>2</sub>, TiO<sub>2</sub>/SnO<sub>2</sub>, SiO<sub>2</sub>/SnO<sub>2</sub>, and combinations of the three with various top and bottom layer thicknesses to cover a substantial region of the electromagnetic spectrum (UV to NIR). With increasing layer numbers for TiO<sub>2</sub>/SiO<sub>2</sub> and SiO<sub>2</sub>/SnO<sub>2</sub>, the edges became sharper and wider and the photonic bandgap width increased. Moreover, we demonstrated that PhCs with significantly thick TiO<sub>2</sub>/SiO<sub>2</sub> layers had a high transmittance for a wide bandgap, allowing for wide-band optical filter applications. These different PhC architectures could enable a variety of applications, depending on the properties needed.展开更多
Efficient transient analysis is critical in rotor dynamics.This study proposes the super-element(SE)differential-quadraturediscrete-time transfer matrix method(DQ-DT-TMM),a novel approach that eliminates the requireme...Efficient transient analysis is critical in rotor dynamics.This study proposes the super-element(SE)differential-quadraturediscrete-time transfer matrix method(DQ-DT-TMM),a novel approach that eliminates the requirement for initial componentaccelerations and effectively handles beam and solid finite element(FE)models with high-dimensional degrees of freedom(DOFs)in rotor systems.The primary methodologies of this approach include:(1)For the beam substructure FE dynamicequation,the Craig-Bampton method is employed for the order reduction of internal coordinates,followed by the differentialquadraturemethod for temporal discretization.Using SE technology,the internal accelerations are condensed into theboundary accelerations,and the transfer equation and matrix for beam SEs are derived.(2)For the solid substructureFE dynamic equation formulated in the rotating reference frame,in addition to applying the procedures used for beamsubstructures,rigid multipoint constraints are introduced to condense the boundary coordinates for hybrid modeling withlumped parameter components.The transfer equation is subsequently formulated in the inertial reference frame,enabling thederivation of the transfer matrix for solid SEs.Comparative analysis with full-order FE models in commercial softwaredemonstrates the advantages of the SE DQ-DT-TMM for linear rotor systems:(i)Accurately captures system dynamics usingonly a few primary modes.(ii)Achieves a 99.68%reduction in computational time for a beam model with 1120 elements and a99.98%reduction for a solid model with 75361 elements.(iii)Effectively recovers dynamic responses at any system node usingrecovery techniques.This research develops a computationally efficient framework for the transient analysis of large-scale rotorsystems,effectively addressing the challenges associated with high-dimensional DOF models in conventional DT-TMMs.展开更多
Compliant mechanisms with curved flexure hinges/beams have potential advantages of small spaces,low stress levels,and flexible design parameters,which have attracted considerable attention in precision engineering,met...Compliant mechanisms with curved flexure hinges/beams have potential advantages of small spaces,low stress levels,and flexible design parameters,which have attracted considerable attention in precision engineering,metamaterials,robotics,and so forth.However,serial-parallel configurations with curved flexure hinges/beams often lead to a complicated parametric design.Here,the transfer matrix method is enabled for analysis of both the kinetostatics and dynamics of general serial-parallel compliant mechanisms without deriving laborious formulas or combining other modeling methods.Consequently,serial-parallel compliant mechanisms with curved flexure hinges/beams can be modeled in a straightforward manner based on a single transfer matrix of Timoshenko straight beams using a step-by-step procedure.Theoretical and numerical validations on two customized XY nanopositioners comprised of straight and corrugated flexure units confirm the concise modeling process and high prediction accuracy of the presented approach.In conclusion,the present study provides an enhanced transfer matrix modeling approach to streamline the kinetostatic and dynamic analyses of general serial-parallel compliant mechanisms and beam structures,including curved flexure hinges and irregular-shaped rigid bodies.展开更多
The multibody system transfer matrix method(MSTMM),a novel dynamics approach developed during the past three decades,has several advantages compared to conventional dynamics methods.Some of these advantages include av...The multibody system transfer matrix method(MSTMM),a novel dynamics approach developed during the past three decades,has several advantages compared to conventional dynamics methods.Some of these advantages include avoiding global dynamics equations with a system inertia matrix,utilizing low‐order matrices independent of system degree of freedom,high computational speed,and simplicity of computer implementation.MSTMM has been widely used in computer modeling,simulations,and performance evaluation of approximately 150 different complex mechanical systems.In this paper,the following aspects regarding MSTMM are reviewed:basic theory,algorithms,simulation and design software,and applications.Future research directions and generalization to more applications in various fields of science,technology,and engineering are discussed.展开更多
Efficient, precise dynamic modeling and analysis for complex weapon systems have become more and more important in their dynamic design and performance optimizing. As a new method developed in recent years, the discre...Efficient, precise dynamic modeling and analysis for complex weapon systems have become more and more important in their dynamic design and performance optimizing. As a new method developed in recent years, the discrete time transfer matrix method of multibody system is highly efficient for multibody system dynamics. In this paper, taking a shipboard gun system as an example, by deducing some new transfer equations of elements, the discrete time transfer matrix method of multibody sys- tem is used to solve the dynamics problems of complex rigid-flexible coupling weapon systems successfully. This method does not need the global dynamic equations of system and has the low order of system matrix, high computational efficiency. The proposed method has advantages for dynamic design of complex weapon systems, and can be carried over straightforwardly to other complex mechanical systems.展开更多
Analytical expressions of electron transmittance and tunneling current in an anisotropic TiNx/HfO2/SiO2/p-Si（100） metal-oxide-semiconductor （MOS） capacitor were derived by considering the coupling of transverse an...Analytical expressions of electron transmittance and tunneling current in an anisotropic TiNx/HfO2/SiO2/p-Si（100） metal-oxide-semiconductor （MOS） capacitor were derived by considering the coupling of transverse and longitudinal energies of an electron. Exponential and Airy wavefunctions were utilized to obtain the electron transmittance and the electron tunneling current. A transfer matrix method, as a numerical approach, was used as a benchmark to assess the analytical approaches. It was found that there is a similarity in the transmittances calculated among exponential- and Airy-wavefimction approaches and the TMM at low electron energies. However, for high energies, only the transmit- tance calculated by using the Airy-wavefunction approach is the same as that evaluated by the TMM. It was also found that only the tunneling currents calculated by using the Airy-wavefunction approach are the same as those obtained under the TMM for all range of oxide voltages. Therefore, a better analytical description for the tunneling phenomenon in the MOS capacitor is given by the Airy-wavefunction approach. Moreover, the tunneling current density decreases as the titanium concentration of the TiNx metal gate increases because the electron effective mass of TiNx decreases with increasing nitrogen concentration. In addition, the mass anisotropy cannot be neglected because the tunneling currents obtained under the isotropic and anisotropic masses are very different.展开更多
In the multibody system transfer matrix method(MSTMM),the transfer matrix of body elements may be directly obtained from kinematic and kinetic equations.However,regarding the transfer matrices of hinge elements,typica...In the multibody system transfer matrix method(MSTMM),the transfer matrix of body elements may be directly obtained from kinematic and kinetic equations.However,regarding the transfer matrices of hinge elements,typically information of their outboard body is involved complicating modeling and even resulting in combinatorial problems w.r.t.various types of outboard body's output links.This problem may be resolved by formulating decoupled hinge equations and introducing the Riccati transformation in the new version of MSTMM called the reduced multibody system transfer matrix method in this paper.Systematic procedures for chain,tree,closed-loop,and arbitrary general systems are defined,respectively,to generate the overall system equations satisfying the boundary conditions of the system during the entire computational process.As a result,accumulation errors are avoided and computational stability is guaranteed even for huge systems with long chains as demonstrated by examples and comparison with commercial software automatic dynamic analysis of the mechanical system.展开更多
For linear mechanical systems,the transfer matrix method is one of the most efficient modeling and analysis methods.However,in contrast to classical mod-eling strategies,the final eigenvalue problem is based on a matr...For linear mechanical systems,the transfer matrix method is one of the most efficient modeling and analysis methods.However,in contrast to classical mod-eling strategies,the final eigenvalue problem is based on a matrix which is a highly nonlinear function of the eigenvalues.Therefore,classical strategies for sensitivity analysis of eigenvalues w.r.t.system parameters cannot be applied.The paper develops two specific strategies for this situation,a direct differentiation strategy and an adjoint variable method,where especially the latter is easy to use and applicable to arbitrarily complex chain or branched multibody systems.Like the system analysis itself,it is able to break down the sensitivity analysis of the overall system to analytically determinable derivatives of element transfer matrices and recursive formula which can be applied along the transfer path of the topology figure.Several examples of different complexity validate the proposed approach by comparing results to analytical calculations and numerical differentiation.The obtained procedure may support gradient‐based optimization and robust design by delivering exact sensitivities.展开更多
基金the National Natural Science Foundation of China(Nos.12302007,12372006,and 12202109)the Specific Research Project of Guangxi for Research Bases and Talents(No.AD23026051)。
文摘Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.
基金supported by the Research Fund for the Doctoral Program of Higher Education of China(Grants 20113219110025,20133219110037)the National Natural Science Foundation of China(Grants 11102089,61304137)the Program for New Century Excellent Talents in University(NCET-10-0075)
文摘The analysis of natural vibration characteristics has become one of important steps of the manufacture and dynamic design in the aerospace industry. This paper presents a new scenario called virtual cutting in the context of the transfer matrix method of linear multibody systems closed- loop topology for computing the free vibration characteristics of elastically coupled flexible launch vehicle boosters. In this approach, the coupled system is idealized as a triple-beam system-like structure coupled by linear translational springs, where a non-uniform free-free Euler-Bemoulli beam is used. A large thrust-to-weight ratio leads to large axial accelera- tions that result in an axial inertia load distribution from nose to tail. Consequently, it causes the development of significant compressive forces along the length of the launch vehicle. Therefore, it is important to take into account this effect in the transverse vibration model. This scenario does not need the global dynamics equations of a system, and it has high computational efficiency and low memory requirements. The validity of the presented scenario is achieved through com- parison to other approaches published in the literature.
基金supported by the Natural Science Foundation of China Government (10902051)the Natural Science Foundation of Jiangsu Province (BK2008046)the German Science Foundation
文摘In this paper, by defining new state vectors and developing new transfer matrices of various elements mov- ing in space, the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of multibody system with flexible beams moving in space. Formulations and numerical example of a rigid- flexible-body three pendulums system moving in space are given to validate the method. Using the new method to study the dynamics of multi-rigid-flexible-body system mov- ing in space, the global dynamics equations of system are not needed, the orders of involved matrices of the system are very low and the computational speed is high, irrespec- tive of the size of the system. The new method is simple, straightforward, practical, and provides a powerful tool for multi-rigid-flexible-body system dynamics.
基金supported by the National Natural Science Foundation of China (No.10662003)Educational Commission of Guangxi Province of China (No.200807MS109)
文摘The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.
基金supported by the National Natural Science Foundation of China(Grant 51975298)the Natural Science Foundation of Jiangsu Province(Grant BK20181301)the National Science Foundation of China(Grant 11874303).
文摘The structure parameters of 6-degree of freedom(DOF)vibration isolation platform have a significant effect on its performance.To make the designed vibration isolation platform perform well,non-dominanted sorting genetic algorithm version II(NSGA-II)was applied to optimize its structure based on the transfer matrix method for multibody systems.Firstly,the Jacobian matrix of 6-DOF vibration isolation platform was solved based on kinematics.Secondly,the transfer equation of 6-DOF vibration isolation system was established by the linear transfer matrix method for multibody systems.And the formula of its natural frequency was derived according to the boundary conditions of the system.Thirdly,the manipulability index was constructed based on a dimensionless Jacobian matrix.And a new performance index function was established considering the influence of dynamic isotropic and legs mass.Fourthly,genetic algorithm(GA)and NSGA-II were used to optimize the structure of the 6-DOF vibration isolation platform under the same conditions,respectively.It showed that NSGA-II had higher optimization efficiency,better calculation accuracy and shorter optimization time than that of GA.Finally,NSGA-II was adopted for multi-objective optimization design of 6-DOF vibration isolation platform based on the constraint conditions.Optimal Pareto solutions were obtained,which provides structural parameters for subsequent design work.Therefore,the proposed optimization method and the performance index in this paper provide a theoretical basis for the optimal design of relevant vibration isolation mechanism.
文摘Rotor system supported by nonlinear bearing such as squeeze film damper(SFD)is widely used in practice owing to its wide range of damping capacity and simplicity in structure.In this paper,an improved and effective Incremental transfer matrix method(ITMM)is first presented by combining ITMM and fast Fourier transform(FFT).Afterwards this method is applied to calculate the dynamic characteristics of a Jeffcott rotor system with SFD.The convergence dificulties incurred caused by strong nonlinearities of SFD has been dealt by adopting a control factor.It is found that for the more general boundary problems where the boundary conditions are not at input and output ends of a chain system,the supplementary equation is necessarily added.Additionally,the Floquet theory is used to analyze the stability and bifurcation type of the obtained periodic solution.The semi-analytical results,including the periodic solutions of the system,the bifurcation points and their types,are in good agreement with the numerical method.Furthermore,the involution mechanism of the quasi-periodic and chaotic motions near the first-order translational mode and the second order bending mode of this system is also clarified by this method with the aid of Floquet theory.
基金supported by National Key Technology R&D Program of China (Grant No. 2006BAF01B09)the Research Fund for Doctoral Program of Higher Education of China (Grant No. 200800060010)
文摘The hybrid dynamics of multi-rigid-body and multi-flexible-body system becomes the mainstream of multi-body dynamics.Currently there lacks a compact approach to model the hybrid dynamics,especially in modern machine tool application,due to the difficulty of solving the hybrid equations or the limitation of current software when dealing with the hybrid dynamics.The extended transfer matrix method（E-TMM）,which extends elements in three-dimensional space with higher matrixes,is proposed to simplify the modeling process of the hybrid dynamics.The E-TMM modeling approaches of 3 basic elements including 3D vibrant rigid body,joint and flexible body are studied in details.A parallel mill-turn tool spindle head unit driven by dual-linear motors is chosen as a plant to demonstrate the E-TMM modeling process.By using E-TMM,the spindle head unit is simplified as a topological network consisting of the three types of element,i.e.,3D vibrant rigid body,joint and flexible body,including 11 rigid bodies,14 joints and 1 3D-Timoshenko beam.Then the dynamic model of the system can be easily obtained by deducing the element-network by means of state vector transformation.The dynamic characteristics of the spindle head,such as natural frequencies,dynamic flexibility,etc.can be predicted by solving the obtained model.Experiment verification indicates that the E-TMM is valid with enough accuracy in the dynamic analysis of the parallel mill-turn tool spindle head.The E-TMM is capable of modeling the dynamics of machine tool structure with no requirements of deducing and solving the sophisticated differential equations.Moreover,the E-TMM provides a simple and elegant tool for hybrid dynamic analysis in future dynamic design of machine tools.
文摘In consideration of the problem that the effect of conduit structure on water hammer has been ignored in the classical theory,the Poisson coupling between the fluid and the pipeline was studied and a fourteen-equation mathematical model of fluid-structure interaction(FSI)was developed.Then,the transfer matrix method(TMM)was used to calculate the modal frequency,modal shape and frequency response.The results were compared with that in experiment to verify the correctness of the TMM and the results show that the fluid-structure coupling has a greater impact on the modal frequencies than the modal shape.Finally,the influence on the response spectrum of different damping ratios was studied and the results show that the natural frequency under different damping ratios has changed little but there is a big difference for the pressure spectrum.With the decreasing of damping ratio,the damping of the system on frequency spectrum is more and more significant and the dispersion and dissipation is more and more apparent.Therefore the appropriate damping ratio should be selected to minimize the effects of the vibration of the FSI.The results provide references for the theory research of FSI in the transient process.
基金the National Natural Science Foundation under Grant No.50675162
文摘A ship's tail shaft has serious flexural vibration due to the cantilevered nature of the propeller's blades.Analysis of the nature frequency of flexural vibration is vital to be able to provide effective shock absorption for a ship's tail shaft.A mathematic model of tail shaft flexural vibrations was built using the transfer matrix method.The nature frequency of flexural vibration for an electrically propelled ship's tail shaft was then analyzed,and an effective method for calculating it was proposed:a genetic algorithm(GA),which calculates the nature frequency of vibration of a system.Sample calculations,with comparisons by the Prohl method under conditions bearing isotropic support,showed this method to be practical.It should have significant impact on engineering design theory.
基金Project supported by Science Foundation of Nantong University (Grant Nos. 03080122 and 09ZY001)
文摘In this paper, the analytical transfer matrix method （ATMM） is applied to study the properties of quantum reflection in three systems： a sech2 barrier, a ramp potential and an inverse harmonic oscillator. Our results agree with those obtained by Landau and Lifshitz [Landau L D and Lifshitz E M 1977 Quantum Mechanics （Non-relativistic Theory） （New York： Pergamon）], which proves that ATMM is a simple and effective method for quantum reflection.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60877055 and 60806041)the Shanghai Rising-Star Program,China (Grant No. 08QA14030)+1 种基金the Innovation Funds for Graduates of Shanghai University,China (Grant No. SHUCX092021)the Foundation of the Science and Technology Commission of Shanghai Municipality,China (Grant No. 08JC14097)
文摘A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.
文摘To find the difference in dynamic characteristics between conventional monohull ship and wave penetrating catamaran (WPC), a WPC was taken as an object; its dynamic characteristics were computed by transfer matrix method and finite element method respectively. According to the comparison of the nature frequency results and mode shape results, the fact that FEM method is more suitable to dynamic characteristics analysis of a WPC was pointed out, special features on dynamic characteristics of WPC were given, and some beneficial suggestions are proposed to optimize the strength of a WPC in design period.
文摘One-dimensional photonic crystals (1D PhCs) have a unique ability to control the propagation of light waves, however certain classes of 1D oxides remain relatively unexplored for use as PhCs. Specifically, there has not been a comparative study of the three different 1D PhC structures to compare the influence of layer thickness, number, and refractive index on the ability of the PhCs to control light transmission. Herein, we use the transfer matrix method (TMM) to theoretically examine the transmission of 1D PhCs composed of layers of TiO<sub>2</sub>/SiO<sub>2</sub>, TiO<sub>2</sub>/SnO<sub>2</sub>, SiO<sub>2</sub>/SnO<sub>2</sub>, and combinations of the three with various top and bottom layer thicknesses to cover a substantial region of the electromagnetic spectrum (UV to NIR). With increasing layer numbers for TiO<sub>2</sub>/SiO<sub>2</sub> and SiO<sub>2</sub>/SnO<sub>2</sub>, the edges became sharper and wider and the photonic bandgap width increased. Moreover, we demonstrated that PhCs with significantly thick TiO<sub>2</sub>/SiO<sub>2</sub> layers had a high transmittance for a wide bandgap, allowing for wide-band optical filter applications. These different PhC architectures could enable a variety of applications, depending on the properties needed.
基金supported by the National Natural Science Foundation of China(Grant/Award No.92266201).
文摘Efficient transient analysis is critical in rotor dynamics.This study proposes the super-element(SE)differential-quadraturediscrete-time transfer matrix method(DQ-DT-TMM),a novel approach that eliminates the requirement for initial componentaccelerations and effectively handles beam and solid finite element(FE)models with high-dimensional degrees of freedom(DOFs)in rotor systems.The primary methodologies of this approach include:(1)For the beam substructure FE dynamicequation,the Craig-Bampton method is employed for the order reduction of internal coordinates,followed by the differentialquadraturemethod for temporal discretization.Using SE technology,the internal accelerations are condensed into theboundary accelerations,and the transfer equation and matrix for beam SEs are derived.(2)For the solid substructureFE dynamic equation formulated in the rotating reference frame,in addition to applying the procedures used for beamsubstructures,rigid multipoint constraints are introduced to condense the boundary coordinates for hybrid modeling withlumped parameter components.The transfer equation is subsequently formulated in the inertial reference frame,enabling thederivation of the transfer matrix for solid SEs.Comparative analysis with full-order FE models in commercial softwaredemonstrates the advantages of the SE DQ-DT-TMM for linear rotor systems:(i)Accurately captures system dynamics usingonly a few primary modes.(ii)Achieves a 99.68%reduction in computational time for a beam model with 1120 elements and a99.98%reduction for a solid model with 75361 elements.(iii)Effectively recovers dynamic responses at any system node usingrecovery techniques.This research develops a computationally efficient framework for the transient analysis of large-scale rotorsystems,effectively addressing the challenges associated with high-dimensional DOF models in conventional DT-TMMs.
基金funded by the National Natural Science Foundation of China(Grant/Award Numbers:52075179 and 52130508)Jiangsu Policy Guidance Program(International Science and Technology Cooperation)the Belt and Road Initiative Innovative Cooperation Projects:BZ2021016.
文摘Compliant mechanisms with curved flexure hinges/beams have potential advantages of small spaces,low stress levels,and flexible design parameters,which have attracted considerable attention in precision engineering,metamaterials,robotics,and so forth.However,serial-parallel configurations with curved flexure hinges/beams often lead to a complicated parametric design.Here,the transfer matrix method is enabled for analysis of both the kinetostatics and dynamics of general serial-parallel compliant mechanisms without deriving laborious formulas or combining other modeling methods.Consequently,serial-parallel compliant mechanisms with curved flexure hinges/beams can be modeled in a straightforward manner based on a single transfer matrix of Timoshenko straight beams using a step-by-step procedure.Theoretical and numerical validations on two customized XY nanopositioners comprised of straight and corrugated flexure units confirm the concise modeling process and high prediction accuracy of the presented approach.In conclusion,the present study provides an enhanced transfer matrix modeling approach to streamline the kinetostatic and dynamic analyses of general serial-parallel compliant mechanisms and beam structures,including curved flexure hinges and irregular-shaped rigid bodies.
基金National Program on Key Basic Research Project of China,Grant/Award Number:613308Science Challenge Project,Grant/Award Number:TZ2016006‐0104+3 种基金Natural Science Foundation of China Government,Grant/Award Number:11472135supported by the National Program on Key Basic Research Project of China(973 Program,No.613308)the Science Challenge Project(No.TZ2016006‐0104)the Natural Science Foundation of China Government(No.11472135).
文摘The multibody system transfer matrix method(MSTMM),a novel dynamics approach developed during the past three decades,has several advantages compared to conventional dynamics methods.Some of these advantages include avoiding global dynamics equations with a system inertia matrix,utilizing low‐order matrices independent of system degree of freedom,high computational speed,and simplicity of computer implementation.MSTMM has been widely used in computer modeling,simulations,and performance evaluation of approximately 150 different complex mechanical systems.In this paper,the following aspects regarding MSTMM are reviewed:basic theory,algorithms,simulation and design software,and applications.Future research directions and generalization to more applications in various fields of science,technology,and engineering are discussed.
基金supported by the National Natural Science Foundation of China (Grant No: 10902051)the Natural Science Foundation of Jiangsu Province (Grant No: BK2008046)
文摘Efficient, precise dynamic modeling and analysis for complex weapon systems have become more and more important in their dynamic design and performance optimizing. As a new method developed in recent years, the discrete time transfer matrix method of multibody system is highly efficient for multibody system dynamics. In this paper, taking a shipboard gun system as an example, by deducing some new transfer equations of elements, the discrete time transfer matrix method of multibody sys- tem is used to solve the dynamics problems of complex rigid-flexible coupling weapon systems successfully. This method does not need the global dynamic equations of system and has the low order of system matrix, high computational efficiency. The proposed method has advantages for dynamic design of complex weapon systems, and can be carried over straightforwardly to other complex mechanical systems.
文摘Analytical expressions of electron transmittance and tunneling current in an anisotropic TiNx/HfO2/SiO2/p-Si（100） metal-oxide-semiconductor （MOS） capacitor were derived by considering the coupling of transverse and longitudinal energies of an electron. Exponential and Airy wavefunctions were utilized to obtain the electron transmittance and the electron tunneling current. A transfer matrix method, as a numerical approach, was used as a benchmark to assess the analytical approaches. It was found that there is a similarity in the transmittances calculated among exponential- and Airy-wavefimction approaches and the TMM at low electron energies. However, for high energies, only the transmit- tance calculated by using the Airy-wavefunction approach is the same as that evaluated by the TMM. It was also found that only the tunneling currents calculated by using the Airy-wavefunction approach are the same as those obtained under the TMM for all range of oxide voltages. Therefore, a better analytical description for the tunneling phenomenon in the MOS capacitor is given by the Airy-wavefunction approach. Moreover, the tunneling current density decreases as the titanium concentration of the TiNx metal gate increases because the electron effective mass of TiNx decreases with increasing nitrogen concentration. In addition, the mass anisotropy cannot be neglected because the tunneling currents obtained under the isotropic and anisotropic masses are very different.
基金This work was performed at the Brandenburg University of Technology(BTU Cottbus-Senftenberg)and supported by the National Major Project of the Chinese Government(No.2017JCJQ-ZD-005)the National Natural Science Foundation of China(No.11472135)+1 种基金a Scholarship by the Chinese Scholarship Council of the Ministry of Education of China(No.201708080083)the Nanjing University of Science and Technology International Joint Training Scholarship.
文摘In the multibody system transfer matrix method(MSTMM),the transfer matrix of body elements may be directly obtained from kinematic and kinetic equations.However,regarding the transfer matrices of hinge elements,typically information of their outboard body is involved complicating modeling and even resulting in combinatorial problems w.r.t.various types of outboard body's output links.This problem may be resolved by formulating decoupled hinge equations and introducing the Riccati transformation in the new version of MSTMM called the reduced multibody system transfer matrix method in this paper.Systematic procedures for chain,tree,closed-loop,and arbitrary general systems are defined,respectively,to generate the overall system equations satisfying the boundary conditions of the system during the entire computational process.As a result,accumulation errors are avoided and computational stability is guaranteed even for huge systems with long chains as demonstrated by examples and comparison with commercial software automatic dynamic analysis of the mechanical system.
文摘For linear mechanical systems,the transfer matrix method is one of the most efficient modeling and analysis methods.However,in contrast to classical mod-eling strategies,the final eigenvalue problem is based on a matrix which is a highly nonlinear function of the eigenvalues.Therefore,classical strategies for sensitivity analysis of eigenvalues w.r.t.system parameters cannot be applied.The paper develops two specific strategies for this situation,a direct differentiation strategy and an adjoint variable method,where especially the latter is easy to use and applicable to arbitrarily complex chain or branched multibody systems.Like the system analysis itself,it is able to break down the sensitivity analysis of the overall system to analytically determinable derivatives of element transfer matrices and recursive formula which can be applied along the transfer path of the topology figure.Several examples of different complexity validate the proposed approach by comparing results to analytical calculations and numerical differentiation.The obtained procedure may support gradient‐based optimization and robust design by delivering exact sensitivities.
