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Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions
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作者 Xiaoyang SU Tong HU +3 位作者 Wei ZHANG Houjun KANG Yunyue CONG Quan YUAN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第6期983-1000,共18页
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
关键词 transfer matrix method(TMM) free vibration forced vibration functionally graded material(FGM) stepped beam
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Corrigendum to“Atomic-scale electromagnetic theory bridging optics in microscopic world and macroscopic world”
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作者 李志远 陈剑锋 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第2期586-586,共1页
The signs of the electric field markers in Figs.2 and 4 of the paper[Chin.Phys.B 32104211(2023)]have been corrected.These modifications do not affect the results derived in the paper.
关键词 CORRIGENDUM atomic-scale electromagnetic theory two-dimensional materials transfer matrix method
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Transfer matrix method for determination of the natural vibration characteristics of elastically coupled launch vehicle boosters 被引量:6
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作者 Laith K.Abbas Qinbo Zhou +1 位作者 Hossam Hendy Xiaoting Rui 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2015年第4期570-580,共11页
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
关键词 transfer matrix method of linear multibodysystems Free vibration characteristics Coupled launchvehicle boosters
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Discrete time transfer matrix method for dynamics of multibody system with flexible beams moving in space 被引量:4
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作者 Xiao-Ting Rui Edwin Kreuzer +1 位作者 Bao Rong Bin He 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2012年第2期490-504,共15页
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
关键词 Multi-rigid-flexible-body system Spatial mo- tion DYNAMICS Discrete time transfer matrix method
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Dynamics Analysis of a Parallel Mill-turn Tool Spindle Head Driven by Dual-linear Motors Using Extended Transfer Matrix Method 被引量:2
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作者 WU Wenjing LIU Qiang 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2011年第5期859-869,共11页
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
关键词 NC machine tools dynamics modeling transfer matrix method(TMM)
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Forced Axial and Torsional Vibrations of a Shaft Line Using the Transfer Matrix Method Related to Solution Coefficients 被引量:2
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作者 Kandouci Chahr-Eddine Adjal Yassine 《Journal of Marine Science and Application》 2014年第2期200-205,共6页
This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the prop... This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the propeller and intermediate shafts, under the influence of propeller-induced static and variable hydrodynamic excitations are also studied. The transfer matrix method related to the constant coefficients of differential equation solutions is used. The advantage of the latter as compared with a well-known method of transfer matrix associated with state vector is the possibility of reducing the number of multiplied matrices when adjacent shaft segments have the same material properties and diameters. The results show that there is no risk of buckling and confirm that the strength of the shaft line depends on the value of the static tangential stresses which is the most important component of the stress tensor. 展开更多
关键词 shaft line stress tensor vibration axial vibration torsional vibration transfer matrix constant coefficient vector
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Vibration analysis of fluid- structure interaction in water hammer based on transfer matrix method 被引量:1
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作者 GAO Hui TANG Xuelin 《排灌机械工程学报》 EI CSCD 北大核心 2016年第6期518-524,共7页
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
关键词 water hammer fluid-structure interaction transfer matrix method vibration analysis
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Analysis of the flexural vibration of ship's tail shaft by transfer matrix method 被引量:1
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作者 贾小俊 范世东 《Journal of Marine Science and Application》 2008年第3期179-183,共5页
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
关键词 transfer matrix method flexural vibration nature frequency genetic algorithm
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Dynamic Performance Analysis of the Coupling Shaft System in a Carpet Tufting Machine Utilizing the Transfer Matrix Method 被引量:1
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作者 徐洋 孙志军 +1 位作者 黄双 盛晓伟 《Journal of Donghua University(English Edition)》 EI CAS 2016年第1期54-59,共6页
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
关键词 carpet tufting machine coupling shaft system transfer matrix natural frequency mode shape
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The analytical transfer matrix method for quantum reflection
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作者 许田 曹庄琪 方靖淮 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第4期56-61,共6页
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
关键词 analytical transfer matrix method quantum reflection reflection coemcient transmission coefficient reflection time
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PERTURBATION TRANSFER MATRIX METHOD FOR EIGENDATA OF ONE_DIMENSIONAL STRUCTURAL SYSTEM WITH PARAMETER UNCERTAINTIES
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作者 刘保国 殷学纲 +1 位作者 蹇开林 吴永 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第7期801-807,共7页
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
关键词 eigendata PERTURBATION transfer matrix sensitivity derivative
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Energy eigenvalues from an analytical transfer matrix method
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作者 何英 张凡明 +1 位作者 杨艳芳 李春芳 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第4期50-55,共6页
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
关键词 analytical transfer matrix method energy eigenvalues bound state one-dimensional potential
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Dynamic characteristics of a WPC-comparison of transfer matrix method and FE method
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作者 CHEN Guo-long and ME Wu School of Shipbuilding Engineering , Harbin Engineering University, Harbin 150001 , China 《Journal of Marine Science and Application》 2003年第2期25-30,共6页
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
关键词 Wave penetrating catamaran Dynamic characteristics transfer matrix method FEM.
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The rotating Morse potential energy eigenvalues solved by using the analytical transfer matrix method
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作者 何英 陶求功 杨艳芳 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第10期73-78,共6页
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
关键词 rotating Morse potential analytical transfer matrix(ATM) Pekeris approximation supersymmetry quantum mechanics(SUSY QM)
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Radiation heat transfer model for complex superalloy turbine blade in directional solidification process based on finite element method 被引量:4
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作者 Dun-ming Liao Liu Cao +4 位作者 Tao Chen Fei Sun Yong-zhen Jia Zi-hao Teng Yu-long Tang 《China Foundry》 SCIE 2016年第2期123-132,共10页
For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is develo... For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is developed in this study. Key technologies, such as distinguishing boundaries automatically, local matrix and lumped heat capacity matrix, are also stated. In order to analyze the effect of withdrawing rate on DS process,the solidification processes of a complex superalloy turbine blade in the High Rate Solidification(HRS) process with different withdrawing rates are simulated; and by comparing the simulation results, it is found that the most suitable withdrawing rate is determined to be 5.0 mm·min^(-1). Finally, the accuracy and reliability of the radiation heat transfer model are verified, because of the accordance of simulation results with practical process. 展开更多
关键词 directional solidification radiation heat transfer finite element method numerical simulation local matrix superalloy turbine blade
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Parametrization of Transfer Matrix:for One-Dimensional Anderson Model with Diagonal Disorder
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作者 康凯 覃绍京 王垂林 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第10期735-740,共6页
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
关键词 Anderson localization parametrization of transfer matrix
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Controlling the Bandgaps of One-Dimensional TiO2/SiO2, TiO2/SnO2, and SiO2/SnO2 Photonic Crystals Using the Transfer Matrix Method
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作者 Fatimah Alamrani Edreese Alsharaeh 《Optics and Photonics Journal》 CAS 2022年第7期171-189,共19页
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
关键词 One-Dimensional Photonic Crystal Photonic Bandgap transfer Matrix Method Optical Filter Metal Oxides
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Transfer Matrix Approach for Two-State Scattering Problem with Arbitrary Coupling
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作者 Diwaker Aniruddha Chakraborty 《Chinese Physics Letters》 SCIE CAS CSCD 2015年第7期5-8,共4页
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
关键词 transfer Matrix Approach for Two-State Scattering Problem with Arbitrary Coupling
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Effects of Solid Matrix and Porosity of Porous Medium on Heat Transfer of Marangoni Boundary Layer Flow Saturated with Power-Law Nanofluids
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作者 陈晖 肖天丽 +1 位作者 陈嘉阳 沈明 《Chinese Physics Letters》 SCIE CAS CSCD 2016年第10期80-84,共5页
The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of soli... The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of solid matrix of porous medium including glass balls and aluminum foam are considered. The governing partial differential equations are simplified by dimensionless variables and similarity transformations, and are solved numerically by using a shooting method with the fourth-fifth-order Runge-Kutta integration technique. It is indicated that the increase of the porosity leads to the enhancement of heat transfer in the surface of the Marangoni boundary layer flow. 展开更多
关键词 of is as Effects of Solid Matrix and Porosity of Porous Medium on Heat transfer of Marangoni Boundary Layer Flow Saturated with Power-Law Nanofluids in with on
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Observation and mitigation of image distortion in high-energy electron radiography
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作者 Hao-Qing Li Liang Sheng +22 位作者 Chang-Qing Zhang Ying-Chao Du Zheng Zhou Xiu-Feng Weng Jia-Hao Xiao Hong-Qiao Yin Bin Sun Kun Wei Yang Li Bao-Jun Duan Yong-Tang Liu Yan-Hong Zhang Mei Zhang Yan Song Xiao-Dong Zhang Jun Liu Zhu-Ming Fu Qing Xu Xue Du Jian-Peng Gao Xin-Yi Wang Xin-Jian Tan Dong-Wei Hei 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2023年第6期69-77,共9页
Image distortion caused by the angular misalignment of quadrupole magnets in high-energy electron radiography has been studied systematically.We propose that the distortion originates from the coupling of the electron... Image distortion caused by the angular misalignment of quadrupole magnets in high-energy electron radiography has been studied systematically.We propose that the distortion originates from the coupling of the electron motions in the transverse directions,based on a theoretical analysis and the transfer-matrix method.The relative angular rotation between the second and third magnetic quadrupoles was identified as the main contributor to image distortion.This was verified by both a beam-dynamics simulation and experiments.Different strategies to mitigate this image distortion are also explored,including magnets online tuning,higher beam energy and larger magnification factor.This study provides criteria for designing experiments and paves the way for achieving higher image precision. 展开更多
关键词 MISALIGNMENT Angular rotation Russian quadruplet transfer matrix
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