Discrete time transfer matrix method for dynamics of multibody system with flexible beams moving in space

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.

Transfer matrix method for determination of the natural vibration characteristics of elastically coupled launch vehicle boosters

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.

Carbon matrix effects on the micro-structure and performance of Pt nanowire cathode prepared by decal transfer method

High performance cathode for polymer electrolyte membrane fuel cell was prepared by depositing Pt nanowires in a carbon matrix coated on a substrate, and using decal transfer method to fabricate the membrane electrode assembly. The effects of carbon and ionomer contents on the electrode micro-structure and fuel cell performance are investigated by physical characterization and single cell testing. The Pt nanowires are gradient distributed across the cathode thickness, and more Pt exists near the membrane. Both the carbon and ionomer contents can affect the Pt nanowires distribution and aggregation. In addition, the carbon loading dominates the transport distance of gas and proton, and the ionomer content affects the triple phase boundaries and porosity in the cathode. The optimal structure of Pt nanowire cathode is obtained at 0.10 mg·cm^-2 carbon loading and 10 wt% ionomer.

Vibration analysis of fluid- structure interaction in water hammer based on transfer matrix method

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.

Dynamics Analysis of a Parallel Mill-turn Tool Spindle Head Driven by Dual-linear Motors Using Extended Transfer Matrix Method

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.

Analysis of the flexural vibration of ship's tail shaft by transfer matrix method

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.

The analytical transfer matrix method for quantum reflection

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.

Energy eigenvalues from an analytical transfer matrix method

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.

Controlling the Bandgaps of One-Dimensional TiO2/SiO2, TiO2/SnO2, and SiO2/SnO2 Photonic Crystals Using the Transfer Matrix Method

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 TiO2/SiO2, TiO2/SnO2, SiO2/SnO2, 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 TiO2/SiO2 and SiO2/SnO2, the edges became sharper and wider and the photonic bandgap width increased. Moreover, we demonstrated that PhCs with significantly thick TiO2/SiO2 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.

Dynamic characteristics of a WPC-comparison of transfer matrix method and FE method

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.

TRANSFER-MATRIX METHOD FOR SURFACE SPIN WAVES IN A SEMI-INFINITE MAGNETIC SUPERLATTICE WITH A SINGLE-ION ANISOTROPY

Surface spin waves in a semi-infinite magnetre super lattice with a single-ion uniaxial anisotropy are investigated through the transfer mafrix method.The dispersion equations of surface spin wavs are obfained.We find that not all the magnetic superlattice structures can excite the surface spin waves,and that the anisotropy term need not be favorable to the excitation of surface spin wavs,but surely influences the values of the energy of the excited surface spin waves.

Enabling the transfer matrix method to model serial-parallel compliant mechanisms including curved flexure beams

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.

Radiation heat transfer model for complex superalloy turbine blade in directional solidification process based on finite element method

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.

The Effects of Interfaces on Stress Transfer in Short Fiber Reinforced Metal Matrix Composites

In this paper, the effects of interface properties on the stress transfer between matrix and fiber in short fiber reinforced metal matrix composites (SFRMMCs) is studied with the method of the elasto plastic finite element. The interface properties include Young’s modulus, thickness and elasto plastic performances. In the calculation an interfacial layer with given thickness is introduced into the single fiber model. It is shown that, for a soft interface, the variation in interfacial properties influences the stress transfer greatly.

Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions

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.

压电复合材料梯度分布声学特性研究

目前,压电复合材料在吸声降噪领域应用广泛,但其低频吸声性能并不理想。为解决此问题,以0-3型压电复合材料为研究对象,提出使压电陶瓷体积含量呈梯度分布以提高其低频吸声系数的方法。首先,基于声电类比法和传递矩阵法,推导多梯度分布的理论公式,并通过文献构型对其进行验证;其次,将均匀分布与梯度分布的吸声系数进行比较,发现梯度分布会改变材料的声阻抗,从而改变吸声系数。最后,进行梯度分布压电复合材料数值分析,结果表明,同等条件下,当压电陶瓷体积含量呈梯度递减,且梯度差和第一梯度的厚度增加时,可明显提高低频吸声系数。

基于声电类比的低频消音结构优化设计

基于声电类比,设计了与电滤波器性能相似的低频消音结构,并结合传递矩阵法和模拟退火法,构造了声学结构的优化设计策略。首先,采用归一化方法,以四阶切比雪夫高通电滤波器为基准,设计了电学带阻滤波器;然后,基于声电类比,将电路中的电感电容转换为声学结构中的细管和圆柱腔,构造了消音结构原型,并利用传递矩阵法,建立其数学模型,推导声波传递损失表达式;最后,结合声学结构的数学模型和模拟退火法,以有效衰减带宽最大为目标,以消音结构的尺寸参数为变量,对原型结构进行优化设计。结果表明:基于声电类比,能获得合理的消音结构原型,克服了仅依靠经典消音结构进行设计的局限;结合推导的传递损失数学模型和模拟退火法,对消音结构原型进行参数优化,能显著提高其消音效果,表现在传递损失超过20 dB的带宽拓宽至410~2 165 Hz,是优化前带宽的202%,特别是优化后的结构克服了原型结构在466~537 Hz频率内不能实现有效消音的缺陷,获得了连续的大跨度有效带宽,且传递损失曲线平均增幅达22.8%。

双功能梯度石墨烯片增强金属-陶瓷基圆柱壳的行波振动分析

采用Halpin-Tsai微观力学模型和传递矩阵方法,开展了旋转态双功能梯度石墨烯片增强复合材料圆柱壳体的行波振动特性研究。描述了金属-陶瓷功能梯度基体和5种石墨烯片分布模式的材料属性,基于Love壳理论和传递矩阵方法,考虑转速影响推导了任一截面状态向量的常微分方程和整体传递矩阵关系。以固支-自由(悬臂)边界条件为主,对动力学微分方程进行求解计算,验证了分析方法的合理性。结果表明:低阶模态以轴向半波数为1和周向模态的振动为主,转速引起的科氏力使行波曲线出现分离现象;行波频率随着石墨烯质量分数的增加而增大,分布模式对振型顺序的影响较小,基体体积分数指数对振动特性的影响较大,而石墨烯片层数对振动特性的影响很小,不同倍频激励对共振特性的影响不同。

基于混合FTMM-SEA法的高速列车真空玻璃车窗隔声特性预测与分析

真空玻璃在轻质高隔声方面的性能优势尤为突出,将其用于高速列车车窗是轻量化高速列车车内噪声控制的新型解决方案。将声波在真空玻璃中的传播分解为沿真空层和沿声桥结构的两条独立传播路径,分别使用有限传递矩阵法(FTMM)和统计能量分析法(SEA)计算两条路径的声功率传递系数,建立基于混合FTMM-SEA法的真空玻璃车窗结构隔声量预测模型,并通过实测真空玻璃混响隔声量验证模型的准确性。进一步调查分析声桥结构刚度对耦合板间能量传递、真空玻璃隔声特性的影响。结果表明:减小声桥结构刚度是提高真空玻璃车窗隔声性能的一种有效的方法。与刚性声桥相比,柔性声桥具备更好的能量吸收能力与隔振特性。

基于传递矩阵法的足式机器人四连杆腿部机构正向与逆向动力学分析

为了保证足式机器人腿部机构的控制准确性与实时性,利用向量代数方法,对足式机器人四连杆腿部机构进行几何运动学分析;根据有限元形函数理论,建立足式机器人四连杆腿部机构典型构件的质量离散方法;在几何运动学分析的基础上,基于力矩平衡原理,分别进行正向与逆向动力学分析;利用线性变换原理并结合传递矩阵法,建立足式机器人四连杆腿部机构正-逆向动力学统一模型,并利用Adams软件建立足式机器人四连杆腿部机构虚拟样机模型,进行正向与逆向动力学仿真实例分析。结果表明,所建立的足式机器人四连杆腿部机构正-逆向动力学统一模型与虚拟样机模型3个油缸力与3个方向足底力的误差分别小于1%与3%,验证了所建立的足式机器人四连杆腿部机构正-逆向动力学统一模型能够精确地求解油缸力与足底力。