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 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
The dynamic performance of the coupling shaft system in a carpet tufting machine is the most critical factor affecting the carpet tufting machine's efficiency,and the product quality of the tufted carpet. To deter...The dynamic performance of the coupling shaft system in a carpet tufting machine is the most critical factor affecting the carpet tufting machine's efficiency,and the product quality of the tufted carpet. To determine how to avoid resonance produced by the coupling shaft system's vibration during the weaving process,the dynamic performance of a coupling shaft system in a carpet tufting machine was analyzed. Focusing on a DHGN801D-400 carpet tufting machine,a dynamic model of coupling shaft system was established by utilizing transfer matrix methodology. On the basis of this model,the natural frequencies and mode shapes of the coupling shaft system were obtained through simulations. The correctness of the theoretical model and the dynamic performance of the coupling shaft system were validated by experiments. The first order natural frequency of the coupling shaft system was close to 600 r / min. A conclusion can thus be drawn that operating the carpet tufting machine near this speed should be avoided as much as possible.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 general method based on Riccati transfer matrix is presented to calculate the 2nd order perturbations of eigendatas for one_dimensional structural system with parameter uncertainties. The method is applicable to bot...A general method based on Riccati transfer matrix is presented to calculate the 2nd order perturbations of eigendatas for one_dimensional structural system with parameter uncertainties. The method is applicable to both real and complex eigendatas of any one_dimensional structural system. The formulas for calculating the sensitivity derivatives of eigendatas based on this method are also presented. The method is applied to the perturbation analysis for the eigendatas of a rotor with gyroscopic moment, and the differences between the perturbation results and the accurate calculating results are small.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
We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix(ATM) method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris ...We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix(ATM) method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris approximation,which can be used to calculate the energies of higher rotational states from the energies of lower states.The energies of rotational states of the hydrogen molecule are calculated by the ATM condition,and comparison of the results with those from the hypervirial perturbation method reveals that the accuracy of the approximate expression of Pekeris for the eigenvalues of the rotating Morse potential can be improved substantially in the framework of supersymmetric quantum mechanics.展开更多
The present work deals with the calculation of transition probability between two diabatic potentials coupled by any arbitrary coupling. The method presented in this work is applicable to any type of coupling while fo...The present work deals with the calculation of transition probability between two diabatic potentials coupled by any arbitrary coupling. The method presented in this work is applicable to any type of coupling while for numerical calculations we have assumed the arbitrary coupling as Gaussian coupling. This arbitrary coupling is expressed as a collection of Dirac delta functions and by the use of the transfer matrix technique the transition probability from one diabatic potential to another diabatic potential is calculated. We examine our approach by considering the case of two constant potentials coupled by Gaussian coupling as an arbitrary coupling.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
The dynamic stiffness method and Transfer method is applied to study the vibration characteristics of the Euler-Bernoulli pipe conveying fluid in this paper. According to the dynamics equation of the pipe conveying fl...The dynamic stiffness method and Transfer method is applied to study the vibration characteristics of the Euler-Bernoulli pipe conveying fluid in this paper. According to the dynamics equation of the pipe conveying fluid, the element dynamic stiffness is established. The vibration characteristic of the single-span pipe is analyzed under two kinds of boundary conditions. The results compared with the literature, which has a good consistency. Based on this method, natural frequency and the critical speed of the two types of multi-span pipe are deserved. This paper shows that the dynamic stiffness method and transfer matrix is an effective method to deal with the vibration problem of pipe conveying fluid.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, we developed a new parametrization method to calculate the localization length in one-dimensionalAnderson model with diagonal disorder.This method can avoid the divergence difficulty encountered in thec...In this paper, we developed a new parametrization method to calculate the localization length in one-dimensionalAnderson model with diagonal disorder.This method can avoid the divergence difficulty encountered in theconventional methods, and significantly save computing time as well.展开更多
The transfer matrix of wrist force sensor is important for decoupling theoutput signals and enhancing the precision of wrist force sensor.This paper solves thetransfer matrix from the realization of optimal approximat...The transfer matrix of wrist force sensor is important for decoupling theoutput signals and enhancing the precision of wrist force sensor.This paper solves thetransfer matrix from the realization of optimal approximation of polynomial.First,thegeneral transfer matrix algorithm in the sense of L^2 and two kinds of modified algorithmare proposed.Then,starting from uniform approximation,the optimal transfer matrixalgorithm is offered and solved by the use of linear programming.The results of experi-ment and computation prove that these algorithms are effective.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
A combination of Riccati transfer matrix method and finite element method is proposed for obtaining vibration frequencies of structures. This method reduces the propagation of round-off errors produced in the standar...A combination of Riccati transfer matrix method and finite element method is proposed for obtaining vibration frequencies of structures. This method reduces the propagation of round-off errors produced in the standard transfer matrix method and finds out the values of the frquency by Newton-raphson method. As the application of this method, a numerical example is given for the case of vibration of a cantilever plate. By the result obtained, the method is shown to be more effective.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
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 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National Natural Science Foundation of China(No.51175075)the Research and Innovation Project of Shanghai Municipal Education Commission,China(No.15ZZ034)
文摘The dynamic performance of the coupling shaft system in a carpet tufting machine is the most critical factor affecting the carpet tufting machine's efficiency,and the product quality of the tufted carpet. To determine how to avoid resonance produced by the coupling shaft system's vibration during the weaving process,the dynamic performance of a coupling shaft system in a carpet tufting machine was analyzed. Focusing on a DHGN801D-400 carpet tufting machine,a dynamic model of coupling shaft system was established by utilizing transfer matrix methodology. On the basis of this model,the natural frequencies and mode shapes of the coupling shaft system were obtained through simulations. The correctness of the theoretical model and the dynamic performance of the coupling shaft system were validated by experiments. The first order natural frequency of the coupling shaft system was close to 600 r / min. A conclusion can thus be drawn that operating the carpet tufting machine near this speed should be avoided as much as possible.
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.
文摘A general method based on Riccati transfer matrix is presented to calculate the 2nd order perturbations of eigendatas for one_dimensional structural system with parameter uncertainties. The method is applicable to both real and complex eigendatas of any one_dimensional structural system. The formulas for calculating the sensitivity derivatives of eigendatas based on this method are also presented. The method is applied to the perturbation analysis for the eigendatas of a rotor with gyroscopic moment, and the differences between the perturbation results and the accurate calculating results are small.
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.
基金Project supported by the Fund from the Science and Technology Committee of Shanghai Municipality,China (Grant No. 11ZR1412300)the National Natural Science Foundation of China (Grant No. 61108010)
文摘We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix(ATM) method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris approximation,which can be used to calculate the energies of higher rotational states from the energies of lower states.The energies of rotational states of the hydrogen molecule are calculated by the ATM condition,and comparison of the results with those from the hypervirial perturbation method reveals that the accuracy of the approximate expression of Pekeris for the eigenvalues of the rotating Morse potential can be improved substantially in the framework of supersymmetric quantum mechanics.
文摘The present work deals with the calculation of transition probability between two diabatic potentials coupled by any arbitrary coupling. The method presented in this work is applicable to any type of coupling while for numerical calculations we have assumed the arbitrary coupling as Gaussian coupling. This arbitrary coupling is expressed as a collection of Dirac delta functions and by the use of the transfer matrix technique the transition probability from one diabatic potential to another diabatic potential is calculated. We examine our approach by considering the case of two constant potentials coupled by Gaussian coupling as an arbitrary coupling.
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.
文摘The dynamic stiffness method and Transfer method is applied to study the vibration characteristics of the Euler-Bernoulli pipe conveying fluid in this paper. According to the dynamics equation of the pipe conveying fluid, the element dynamic stiffness is established. The vibration characteristic of the single-span pipe is analyzed under two kinds of boundary conditions. The results compared with the literature, which has a good consistency. Based on this method, natural frequency and the critical speed of the two types of multi-span pipe are deserved. This paper shows that the dynamic stiffness method and transfer matrix is an effective method to deal with the vibration problem of pipe conveying fluid.
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Supported by National Natural Science Foundation of China under Grant No.10374093the National Program for Basic Research of MOST of Chinathe Knowledge Innovation Project of Chinese Academy of Sciences
文摘In this paper, we developed a new parametrization method to calculate the localization length in one-dimensionalAnderson model with diagonal disorder.This method can avoid the divergence difficulty encountered in theconventional methods, and significantly save computing time as well.
文摘The transfer matrix of wrist force sensor is important for decoupling theoutput signals and enhancing the precision of wrist force sensor.This paper solves thetransfer matrix from the realization of optimal approximation of polynomial.First,thegeneral transfer matrix algorithm in the sense of L^2 and two kinds of modified algorithmare proposed.Then,starting from uniform approximation,the optimal transfer matrixalgorithm is offered and solved by the use of linear programming.The results of experi-ment and computation prove that these algorithms are effective.
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A combination of Riccati transfer matrix method and finite element method is proposed for obtaining vibration frequencies of structures. This method reduces the propagation of round-off errors produced in the standard transfer matrix method and finds out the values of the frquency by Newton-raphson method. As the application of this method, a numerical example is given for the case of vibration of a cantilever plate. By the result obtained, the method is shown to be more effective.
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.