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.

Sound Transmission Loss Analysis of a Double Plate-Acoustic Cavity Coupling System with In-Plane Functionally Graded Materials

In this paper, the isogeometric analysis (IGA) is employed to develop an acoustic radiation model for a double plate-acoustic cavity coupling system, with a focus on analyzing the sound transmission loss (STL). The functionally graded (FG) plate exhibits a different material properties in-plane, and the power-law rule is adopted as the governing principle for material mixing. To validate the harmonic response and demonstrate the accuracy and convergence of the isogeometric modeling, ANASYS is utilized to compare with numerical examples. A plane wave serves as the acoustic excitation, and the Rayleigh integral is applied to discretize the radiated plate. The STL results are compared with the literature, confirming the reliability of the coupling system. Finally, the investigation is conducted to study impact of cavity depth and power-law parameter on the STL.

The action mechanisms and structures designs of F-containing functional materials for high performance oxygen electrocatalysis

Non-renewable fossil fuels have led to serious problems such as global warming,environmental pollution,etc.Oxygen electrocatalysis including oxygen reduction reaction(ORR)and oxygen evolution reaction(OER)plays a central role in clean energy conversion,enabling a number of sustainable processes for future air battery technologies.Fluorine,as the most electronegative element(4.0)not only can induce more efficient regulation for the electronic structure,but also can bring more abundant defects and other novel effects in materials selection and preparation for favorable catalysis with respect to the other nonmetal elements.However,an individual and comprehensive overview of fluorine-containing functional materials for oxygen electrocatalysis field is still blank.Therefore,it is very meaningful to review the recent progresses of fluorine-containing oxygen electrocatalysts.In this review,we first systematically summarize the controllable preparation methods and their possible development directions based on fluorine-containing materials from four preparation methods.Due to the strong electron-withdrawing properties of fluorine,its control of the electronic structure can effectively enhance the oxygen electrocatalytic activity of the materials.In addition,the catalytic enhancement effect of fluorine on carbonbased materials also includes the prevent oxidation and the layer peeling,and realizes the precise atomic control.And the catalytic improvement mechanism of fluorine containing metal-based compounds also includes the hydration of metal site,the crystal transformation,and the oxygen vacancy induction.Then,based on their various dimensions(0D–3D),we also have summarized the advantages of different morphologies on oxygen electrocatalytic performances.Finally,the prospects and possible future researching direction of F-containing oxygen electrocatalysts are presented(e.g.,novel pathways,advanced methods for measurement and simulation,field assistance and multi-functions).The review is considered valuable and helpful in exploring the novel designs and mechanism analyses of advanced fluorine-containing electrocatalysts.

Review of functionally graded materials processed by additive manufacturing

Additive manufacturing(AM)technology makes parts through layer-by-layer deposition,which can regulate the microstructure and properties of different parts of a single part well.It provides a new idea for the preparation of functionally gradient materials(FGM),and has become a research hotspot at present.By referring to and analyzing the recent research achievements in the additive manufacturing tech-nology of FGM,the latest research progress at domestic and abroad from four aspects were summaried:selective laser melting additive man-ufacturing,electron beam additive manufacturing,arc additive manufacturing,path planning,and material texture.Moreover,the existing problems in the research are pointed out,and the future research direction and focus are prospected.

Complete solutions for elastic fields induced by point load vector in functionally graded material model with transverse isotropy

The paper develops and examines the complete solutions for the elastic field induced by the point load vector in a general functionally graded material(FGM)model with transverse isotropy.The FGMs are approximated with n-layered materials.Each of the n-layered materials is homogeneous and transversely isotropic.The complete solutions of the displacement and stress fields are explicitly expressed in the forms of fifteen classical Hankel transform integrals with ten kernel functions.The ten kernel functions are explicitly expressed in the forms of backward transfer matrices and have clear mathematical properties.The singular terms of the complete solutions are analytically isolated and expressed in exact closed forms in terms of elementary harmonic functions.Numerical results show that the computation of the complete solutions can be achieved with high accuracy and efficiency.

Crystalline framework nanosheets as platforms for functional materials

The integration of organic and inorganic materials has been widely used in various applications to generate novel functional nanomaterials characterized by unique properties.Functional crystalline framework nanosheets and their synergistic effects have been studied recently for possessing the advantages of functional species as well as crystalline framework nanosheets.Hence,we have focused on the preparation methods and applications of functional crystalline framework nanosheets in this review.We introduced crystalline framework nanosheets and discussed the importance of integrating functional species with nanosheets to form functional crystalline framework nanosheets.Then,two aspects of the preparation methods of functional crystalline framework nanosheets were reviewed:in situ synthesis and post-synthesis modification.Subsequently,we discussed the properties of the crystalline framework nanosheets combined with various functional species and summarized their applications in catalysis,sensing,separation,and energy storage.Finally,we have shared our insights on the challenges of functional crystalline framework nanosheets,hoping to contribute to the knowledge base for optimizing the preparation methods,expanding categories,improving stability,and exploring potential applications.

Research progress and application prospect of functional adhesive materials in the field of oil and gas drilling and production

By summarizing the composition,classification,and performance characterization of functional adhesive materials,the adhesion mechanisms of functional adhesive materials,such as adsorption/surface reaction,diffusion,mechanical interlocking,and electrostatic adsorption,are expounded.The research status of these materials in oil and gas drilling and production engineering field such as lost circulation prevention/control,wellbore stabilization,hydraulic fracturing,and profile control and water plugging,and their application challenges and prospects in oil and gas drilling and production are introduced comprehensively.According to the applications of functional adhesive materials in the field of oil and gas drilling and production at this stage,the key research directions of functional adhesive materials in the area of oil and gas drilling and production are proposed:(1)blending and modifying thermoplastic resins or designing curable thermoplastic resins to improve the bonding performance and pressure bearing capacity of adhesive lost circulation materials;(2)introducing low-cost adhesive groups and positive charge structures into polymers to reduce the cost of wellbore strengthening agents and improve their adhesion performance on the wellbore;(3)introducing thermally reversible covalent bond into thermosetting resin to prevent backflow of proppant and improve the compressive strength of adhesive proppant;(4)introducing thermally reversible covalent bonds into thermoplastic polymers to improve the temperature resistance,salt-resistance and water shutoff performance of adhesive water shutoff agents.

Dynamic Characteristics of Functionally Graded Timoshenko Beams by Improved Differential Quadrature Method

This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method(DQM)for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node distribution.Firstly,based on the first-order shear deformation theory,the governing equation of free vibration of a functionally graded beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam axial displacement,transverse displacement,and cross-sectional rotation angle by considering the effects of shear deformation and rotational inertia of the beam cross-section.Then,ignoring the shear deformation of the beam section and only considering the effect of the rotational inertia of the section,the governing equation of the beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam transverse displacement.Based on the differential quadrature method theory,the eigenvalue problem of ordinary differential equations is transformed into the eigenvalue problem of standard generalized algebraic equations.Finally,the first several natural frequencies of the beam can be calculated.The feasibility and accuracy of the improved DQM are verified using the finite element method(FEM)and combined with the results of relevant literature.

Numerical Analysis of Permeability of Functionally Graded Scaffolds

In this work,we numerically study the hydrodynamic permeability of new-generation artificial porous materials used as scaffolds for cell growth in a perfusion bioreactor.We consider two popular solid matrix designs based on triply periodic minimal surfaces,the Schwarz P(primitive)and D(diamond)surfaces,which enable the creation of materials with controlled porosity gradients.The latter property is crucial for regulating the shear stress field in the pores of the scaffold,which makes it possible to control the intensity of cell growth.The permeability of functionally graded materials is studied within the framework of both a microscopic approach based on the Navier-Stokes equation and an averaged description of the liquid filtration through a porous medium based on the equations of the Darcy or Forchheimer models.We calculate the permeability coefficients for both types of solid matrices formed by Schwarz surfaces,study their properties concerning forward and reverse fluid flows,and determine the ranges of Reynolds number for which the description within the Darcy or Forchheimer model is applicable.Finally,we obtain a shear stress field that varies along the sample,demonstrating the ability to tune spatially the rate of tissue growth.

A new electromagnetic functional material composed of metallic hollow micro-spheres

This paper presents a new electromagnetic functional material developed byelectron-less nickel deposition technique, with a single hollow micro-sphere as the core templateand a thin nickel layer as the shell. The micrograph taken by a scanning electron microscope showsthe microstructures of the materials in detail. Scattering parameters of the waveguide sample holderfilled with the materials have been obtained over X band. The electromagnetic parameters computedfrom the measured S parameters show that the material with metallic hollow spheres has as highrelative permeability μ'_r as 19.0 with about 0.6 magnetic loss tangent over the whole bandwidth.Compared to the material with non-metallic spheres, the permeability μ'_r and the magnetic losstangent μ'_r increase greatly, while the permittivity remains lower than 1.8.

DESIGN AND PROPERTIES OF A FUNCTIONALLY GRADIENT CERAMIC TOOL MATERIAL

Based on the analyses of the severity of cutting process as well as the failure mechanisms of ceramic tools, a model for designing functionally gradient ceramic tool materials with symmetrical distribution is presented, by which a Al 2O 3/(W,Ti)C ceramic tool material FG 2 was developed. Multi objective optimization method was employed in designing the compositional distribution of this ceramic tool material. The results of both continuous and intermittent cutting tests are indicative of the much better cutting behavior of the functionally gradient ceramic tool FG 2 than that of the common ceramic tool SG 4.

Optimum Weight Design of Functionally Graded Material Gears

Traditional gear weight optimization methods consider gear tooth number, module, face width or other dimension parameters of gear as design variables. However, due to the complicated form and geometric features peculiar to the gear, there will be large amounts of design parameters in gear design, and the influences of gear parameters changing on gear trains, transmission system and the whole equipment have to be taken into account, which increases the complexity of optimization problem. This paper puts forward to apply functionally graded materials（FGMs） to gears and then conduct the optimization. According to the force situation of gears, the material distribution form of FGM gears is determined. Then based on the performance parameters analysis of FGMs and the practical working demands for gears, a multi-objective optimization model is formed. Finally by using the goal driven optimization（GDO） method, the optimal material distribution is achieved, which makes gear weight and the maximum deformation be minimum and the maximum bending stress do not exceed the allowable stress. As an example, the applying of FGM to automotive transmission gear is conducted to illustrate the optimization design process and the result shows that under the condition of keeping the normal working performance of gear, the method achieves in greatly reducing the gear weight. This research proposes a FGM gears design method that is able to largely reduce the weight of gears by optimizing the microscopic material parameters instead of changing the macroscopic dimension parameters of gears, which reduces the complexity of gear weight optimization problem.

Functional porous carbon-based composite electrode materials for lithium secondary batteries

The synthetic routes of porous carbons and the applications of the functional porous carbon-based composite electrode materials for lithium secondary batteries are reviewed. The synthetic methods have made great breakthroughs to control the pore size and volume, wall thickness, surface area, and connectivity of porous carbons, which result in the development of functional porous carbon-based composite electrode materials. The effects of porous carbons on the electrochemical properties are further discussed. The porous carbons as ideal matrixes to incorporate active materials make a great improvement on the electrochemical properties because of high surface area and pore volume, excellent electronic conductivity, and strong adsorption capacity. Large numbers of the composite electrode materials have been used for the devices of electrochemical energy conversion and storage, such as lithium-ion batteries （LIBs）, Li-S batteries, and Li-O2 batteries. It is believed that functional porous carbon-based composite electrode materials will continuously contribute to the field of lithium secondary batteries.

Intercalation Assembly Method and Intercalation Process Control of Layered Intercalated Functional Materials

Layered intercalated functional materials of layered double hydroxide type are an important class of functional materials developed in recent years. Based on long term studies on these materials in the State Key Laboratory of Chemical Resource Engineering in Beiiing University of Chemical Technology, the orinciole for the design of controlled intercalation processes in the light of tuture production processing requirements has been developed. Intercalation assembly methods and technologies have been invented to control the intercalation process for preparing layered intercalated materials with various structures and functions.

Pure bending of simply supported circular plate of transversely isotropic functionally graded material

This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogenous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM).

Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment

Free vibration of statically thermal postbuckled functionally graded material （FGM） beams with surface-bonded piezoelectric layers subject to both temperature rise and voltage is studied. By accurately considering the axial extension and based on the Euler-Bernoulli beam theory, geometrically nonlinear dynamic governing equations for FGM beams with surface-bonded piezoelectric layers subject to thermo-electro- mechanical loadings are formulated. It is assumed that the material properties of the middle FGM layer vary continuously as a power law function of the thickness coordinate, and the piezoelectric layers are isotropic and homogenous. By assuming that the amplitude of the beam vibration is small and its response is harmonic, the above mentioned non-linear partial differential equations are reduced to two sets of coupled ordinary differential equations. One is for the postbuckling, and the other is for the linear vibration of the beam superimposed upon the postbuckled configuration. Using a shooting method to solve the two sets of ordinary differential equations with fixed-fixed boundary conditions numerically, the response of postbuckling and free vibration in the vicinity of the postbuckled configuration of the beam with fixed-fixed ends and subject to transversely nonuniform heating and uniform electric field is obtained. Thermo-electric postbuckling equilibrium paths and characteristic curves of the first three natural frequencies versus the temperature, the electricity, and the material gradient parameters are plotted. It is found that the three lowest frequencies of the prebuckled beam decrease with the increase of the temperature, but those of a buckled beam increase monotonically with the temperature rise. The results also show that the tensional force produced in the piezoelectric layers by the voltage can efficiently increase the critical buckling temperature and the natural frequency.

The nonlocal solution of two parallel cracks in functionally graded materials subjected to harmonic anti-plane shear waves

In this paper, the dynamic interaction of two parallel cracks in functionally graded materials （FGMs） is investigated by means of the non-local theory. To make the analysis tractable, the shear modulus and the material density are assumed to vary exponentially with the coordinate vertical to the crack. To reduce mathematical difficulties, a one-dimensional non-local kernel is used instead of a twodimensional one for the dynamic problem to obtain stress fields near the crack tips. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present at the crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tips. The present result provides theoretical references helpful for evaluating relevant strength and preventing material failure of FGMs with initial cracks. The magnitude of the finite stress field depends on relevant parameters, such as the crack length, the distance between two parallel cracks, the parameter describing the FGMs, the frequency of the incident waves and the lattice parameter of materials.

Solution-based Chemical Strategies to Purposely Control the Microstructure of Functional Materials

Micro/nanostructured crystals with controlled architectures are desirable for many applications in optics, electronics, biology, medicine, and energy conversions. Low-temperature, aqueous chemical routes have been widely investigated for the synthesis of particles, and arrays of oriented nanorods and nanotubes. In this paper, based on the ideal crystal shapes predicted by the chemical bonding theory, we have developed some potential chemical strategies to tune the microstructure of functional materials, ZnS and Nb205 nanotube arrays, MgO wiskers and nestlike spheres, and cubic phase Cu2O microcrystals were synthesized here to elucidate these strategies. We describe their controlled crystallization processes and illustrate the detailed key factors controlling their growth by examining various reaction parameters. Current results demonstrate that our designed chemical strategies for tuning microstructure of functional materials are applicable to several technologically important materials, and therefore may be used as a versatile and effective route to the controllable synthesis of other inorganic functional materials.

NVESTIGATION OF PRODUCTOPN OF FUNCTIONALLY GRADIENT MATERIAL BY ELECTROLESS PLATING

Thispaper proposed a new methodof producing Ceramic/ Metalfunctionally gradient mate rialby electroless platingtechnique. The experimentof producing SiC/ Ni PFGM wascar ried out with self made electroless plating facilities. The results show that the thickness of FGMcoating andthegradientdistribution ofcompositioncanbecontrolled byoptimizingelec trolessplating technology and changing the parameters such as plating time, the additionspeed and concentration of SiCparticles. Analysisdemonstratesthatthereisastrongrelation ship amongthe SiCcontent,the microstructureandthe mechanicalproperty ofthe FGM.

Interface microstructure and mechanical properties of selective laser melted multilayer functionally graded materials

Functionally graded material(FGM)can tailor properties of components such as wear resistance,corrosion resistance,and functionality to enhance the overall performance.The selective laser melting(SLM)additive manufacturing highlights the capability in manufacturing FGMs with a high geometrical complexity and manufacture flexibility.In this work,the 316L/CuSn10/18Ni300/CoCr four-type materials FGMs were fabricated using SLM.The microstructure and properties of the FGMs were investigated to reveal the effects of SLM processing parameters on the defects.A large number of microcracks were found at the 316L/CuSn10 interface,which initiated from the fusion boundary of 316L region and extended along the building direction.The elastic modulus and nano-hardness in the 18Ni300/CoCr fusion zone decreased significantly,less than those in the 18Ni300 region or the CoCr region.The iron and copper elements were well diffused in the 316L/CuSn10 fusion zone,while elements in the CuSn10/18Ni300 and the 18Ni300/CoCr fusion zones showed significantly gradient transitions.Compared with other regions,the width of the CuSn10/18Ni300 interface and the CuSn10 region expand significantly.The mechanisms of materials fusion and crack generation at the 316L/CuSn10 interface were discussed.In addition,FGM structures without macro-crack were built by only altering the deposition subsequence of 316L and CuSn10,which provides a guide for the additive manufacturing of FGM structures.