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.

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.

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.

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.

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.

Preparation of CH_3NH_3PbI_3 thin films for solar cells via Vapor Transfer Method

Organometal halide perovskite based solar cells have emerged as one of the most promising candidates for low-cost and high-efficiency solar cell technologies. Here a Vapor Transfer Method （VTM） is used to fabricate high quality perovskite thin films in a balanced vacuum capsule. By adjusting the reaction tem- perature, CH_3NHl_3 saturated vapor which then reacts with Pbl_2 films can be controlled and the formation process of CH_3NH_3Pbl_3 perovskite films can be further influenced. Prepared perovskite films which ex- hibit pure phase, smooth surface and high crystallinity are assembled into planar heterojunction inverted solar cells. The whole fabrication process of solar cell devices is organic solution free. Finally, the cham- pion cell achieved power conversion efficiency （PCE） of 13.08% with negligible current-voltage hysteresis under fully open-air conditions. The photovoltaic performance could be further enhanced by optimizing perovskite composition and the device structure.

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.

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.

Grey GM(1,1) Model with Function-Transfer Method for Wear Trend Prediction and its Application

Trend forecasting is an important aspect in fault diagnosis and work state supervision. The principle, where Grey theory is applied in fault forecasting, is that the forecast system is considered as a Grey system; the existing known information is used to infer the unknown information's character, state and development trend in a fault pattern, and to make possible forecasting and decisions for future development. It involves the whitenization of a Grey process. But the traditional equal time interval Grey GM (1,1) model requires equal interval data and needs to bring about accumulating addition generation and reversion calculations. Its calculation is very complex. However, the non equal interval Grey GM (1,1) model decreases the condition of the primitive data when establishing a model, but its requirement is still higher and the data were pre processed. The abrasion primitive data of plant could not always satisfy these modeling requirements. Therefore, it establishes a division method suited for general data modeling and estimating parameters of GM (1,1), the standard error coefficient that was applied to judge accuracy height of the model was put forward; further, the function transform to forecast plant abrasion trend and assess GM (1,1) parameter was established. These two models need not pre process the primitive data. It is not only suited for equal interval data modeling, but also for non equal interval data modeling. Its calculation is simple and convenient to use. The oil spectrum analysis acted as an example. The two GM (1,1) models put forward in this paper and the new information model and its comprehensive usage were investigated. The example shows that the two models are simple and practical, and worth expanding and applying in plant fault diagnosis.

Simulation of oxygen transfer in liquid lead under influence of nanoparticles by using lattice Boltzmann method

Oxygen transfer presents a serious challenge in the application of liquid lead as a nuclear coolant in advanced reactors. To mitigate corrosion by liquid lead in contact with steel, carefully controlling the oxygen concentration has been used as an effective way. Oxygen needs to mix in liquid lead uniformly and quickly. To enhance oxygen transport in liquid lead, nanoparticles are added to the liquid metal. In the current study, a lattice Boltzmann method is applied to investigate natural convection of copper/lead and aluminum oxide/lead in two-dimensional simplified container. Two thermal boundary cases are evaluated in order to check the effect of different natural convection flow patterns on oxygen transport. Some useful information are obtained such as improvement in natural convection and reduction in oxygen equilibrium time.

Streamline upwind finite element method for conjugate heat transfer problems

This paper presents a combined finite element method for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow. The streamline upwind finite element method is used for the analysis of thermal viscous flow in the fluid region, whereas the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the proposed method is to consistently couple heat transfer along the fluid-solid interface. Three test cases, i.e. conjugate Couette flow problem in parallel plate channel, counter-flow in heat exchanger, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the present method.

Nodeless variable finite element method for heat transfer analysis by means of flux-based formulation and mesh adaptation

Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method, The solution accuracy is further improved by implementing an adaptive meshing technique to generaie finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems tire： （a） a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and （b） a transient heat conduction analysis in a long plate subjected to moving heat source.

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.

Regularization Method to the Parameter Identification of Interfacial Heat Transfer Coefficient and Properties during Casting Solidification

The accurate material physical properties, initial and boundary conditions are indispensable to the numerical simulation in the casting process, and they are related to the simulation accuracy directly. The inverse heat conduction method can be used to identify the mentioned above parameters based on the temperature measurement data. This paper presented a new inverse method according to Tikhonov regularization theory. A regularization functional was established and the regularization parameter was deduced, the Newton-Raphson iteration method was used to solve the equations. One detailed case was solved to identify the thermal conductivity and specific heat of sand mold and interfacial heat transfer coefficient (IHTC) at the meantime. This indicates that the regularization method is very efficient in decreasing the sensitivity to the temperature measurement data, overcoming the ill-posedness of the inverse heat conduction problem (IHCP) and improving the stability and accuracy of the results. As a general inverse method, it can be used to identify not only the material physical properties but also the initial and boundary conditions' parameters.

ANALYSIS OF THE HEAT TRANSFER IN FIN ASSEMBLIES BY THE BOUNDARY ELEMENT METHOD

The special formulation that allows an accurate and efficient solution to the heat transfer problems within fin assemblies with very large aspect ratios has been developed in this paper Numerically,it consists of the boundary element method in the wall region and the analytical solution in the fin region This modified BEM makes tractable a large class of heat transfer problems in the long and thin domains which are frequently encountered in practice.

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.

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.

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.

Fighting Poor Quality Medicines: Development, Transfer and Validation of Generic HPLC Methods for Analyzing Two WHO Recommended Antimalarial Tablets

As serious but neglected public health problems, poor quality medicines, i.e. for antimalarial medicines, urged to be fought. One of the approaches is to consider the analytical chemistry and separative techniques. In this study, a generic liquid chromatographic method was firstly developed for the purpose of screening 8 antimalarial active ingredients, namely amodiaquine (AQ), piperaquine (PPQ), sulfalene (SL), pyrimethamine (PM), lumefantrine (LF), artesunate (AS), artemether (AM) and dihydroartemisinine (DHA) by applying DoE/DS optimization strategy. Since the method was not totally satisfying in terms of peak separation, further experiments were undergone applying the same development strategy while splitting the 8 ingredients into five groups. Excellent prediction was observed prior to correlation between retention times of predicted and observed separation conditions. Then, a successful geometric transfer was realized to reduce the analysis time focusing on the simultaneous quantification of two WHO’s recommended ACTs in anti-malarial fixed-dose combination (AM-LF and AS-AQ) in tablets. The optimal separation was achieved using an isocratic elution of methanol-ammonium formate buffer (pH 2.8;10 mM) (82.5:17.5, v/v) at 0.6 ml/min through a C18 column (100 mm × 3.5 mm, 3.5 μm) thermostated at 25℃. After a successful validation stage based on the total error approach, the method was applied to determine the content of AM/LF or AS/AQ in seven brands of antimalarial tablets currently marketed in West, Central and East Africa. Satisfying results were obtained compared to the claimed contents.

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.