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.

Wrinkling in graded core/shell systems using symplectic formulation

Wrinkles in flat graded elastic layers have been recently described as a timevarying Hamiltonian system by the energy method.Cylindrical core/shell structures can also undergo surface instabilities under the external pressure.In this study,we show that by treating the radial direction as a pseudo-time variable,the graded core/shell system with radially decaying elastic properties can also be described within the symplectic framework.In combination with the shell buckling equation,the present paper addresses the surface wrinkling of graded core/shell structures subjected to the uniform external pressure by solving a series of ordinary differential equations with varying coefficients.Three representative gradient distributions are showcased,and the predicted critical pressure and critical wave number are verified by finite element simulations.The symplectic framework provides an efficient and accurate approach to understand the surface instability and morphological evolution in curved biological tissues and engineered structures.

Parametric resonance of axially functionally graded pipes conveying pulsating fluid

Based on the generalized Hamilton's principle,the nonlinear governing equation of an axially functionally graded(AFG)pipe is established.The non-trivial equilibrium configuration is superposed by the modal functions of a simply supported beam.Via the direct multi-scale method,the response and stability boundary to the pulsating fluid velocity are solved analytically and verified by the differential quadrature element method(DQEM).The influence of Young's modulus gradient on the parametric resonance is investigated in the subcritical and supercritical regions.In general,the pipe in the supercritical region is more sensitive to the pulsating excitation.The nonlinearity changes from hard to soft,and the non-trivial equilibrium configuration introduces more frequency components to the vibration.Besides,the increasing Young's modulus gradient improves the critical pulsating flow velocity of the parametric resonance,and further enhances the stability of the system.In addition,when the temperature increases along the axial direction,reducing the gradient parameter can enhance the response asymmetry.This work further complements the theoretical analysis of pipes conveying pulsating fluid.

Thermal transport in composition graded silicene/germanene heterostructures

Through equilibrium and non-equilibrium molecular dynamics simulations,we have demonstrated the inhibitory effect of composition graded interface on thermal transport behavior in lateral heterostructures.Specifically,we investigated the influence of composition gradient length and heterogeneous particles at the silicene/germanene(SIL/GER)heterostructure interface on heat conduction.Our results indicate that composition graded interface at the interface diminishes the thermal conductivity of the heterostructure,with a further reduction observed as the length increases,while the effect of the heterogeneous particles can be considered negligible.To unveil the influence of composition graded interface on thermal transport,we conducted phonon analysis and identified the presence of phonon localization within the interface composition graded region.Through these analyses,we have determined that the decrease in thermal conductivity is correlated with phonon localization within the heterostructure,where a stronger degree of phonon localization signifies poorer thermal conductivity in the material.Our research findings not only contribute to understanding the impact of interface gradient-induced phonon localization on thermal transport but also offer insights into the modulation of thermal conductivity in heterostructures.

Biomimetic MXene membranes with negatively thermo-responsive switchable 2D nanochannels for graded molecular sieving

Negatively thermo-responsive 2D membranes,which mimic the stomatal opening/closing of plants,have drawn substantial interest for tunable molecular separation processes.However,these membranes are still restricted significantly on account of low water permeability and poor dynamic tunability of 2D nanochannels under temperature stimulation.Here,we present a biomimetic negatively thermo-responsive MXene membrane by covalently grafting poly(N-isopropylacrylamide)(PNIPAm)onto MXene nanosheets.The uniformly grafted PNIPAm polymer chains can enlarge the interlayer spacings for increasing water permeability while also allowing more tunability of 2D nanochannels for enhancing the capability of gradually separating multiple molecules of different sizes.As expected,the constructed membrane exhibits ultrahigh water permeance of 95.6 L m^(-2) h^(-1) bar^(-1) at 25℃,which is eight-fold higher than the state-of-the-art negatively thermoresponsive 2D membranes.Moreover,the highly temperature-tunable 2D nanochannels enable the constructed membrane to perform excellent graded molecular sieving for dye-and antibiotic-based ternary mixtures.This strategy provides new perspectives in engineering smart 2D membrane and expands the scope of temperature-responsive membranes,showing promising applications in micro/nanofluidics and molecular separation.

Exact solution for thermal vibration of multi-directional functionally graded porous plates submerged in fluid medium

An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study.Mechanical properties of MFG porous plates change according to the length,width,and thickness directions for various materials and the porosity distribution which can be widely applied in many fields of engineering and defence technology.Especially,new porous rules that depend on spatial coordinates and grading indexes are proposed in the present work.Applying Hamilton's principle and the refined higher-order shear deformation plate theory,the governing equation of motion of an MFG porous rectangular plate in a fluid medium(the fluid-plate system)is obtained.The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to compute the extra mass.The GalerkinVlasov solution is used to solve and give natural frequencies of MFG porous plates with various boundary conditions in a fluid medium.The validity and reliability of the suggested method are confirmed by comparing numerical results of the present work with those from available works in the literature.The effects of different parameters on the thermal vibration response of MFG porous rectangular plates are studied in detail.These findings demonstrate that the behavior of the structure within a liquid medium differs significantly from that within a vacuum medium.Thereby,they offer appropriate operational approaches for the structure when employed in various mediums.

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.

Free vibration and buckling analysis of polymeric composite beams reinforced by functionally graded bamboo fbers

Natural fibers have been extensively researched as reinforcement materials in polymers on account of their environmental and economic advantages in comparison with synthetic fibers in the recent years.Bamboo fibers are renowned for their good mechanical properties,abundance,and short cycle growth.As beams are one of the fundamental structural components and are susceptible to mechanical loads in engineering applications,this paper performs a study on the free vibration and buckling responses of bamboo fiber reinforced composite(BFRC)beams on the elastic foundation.Three different functionally graded(FG)layouts and a uniform one are the considered distributions for unidirectional long bamboo fibers across the thickness.The elastic properties of the composite are determined with the law of mixture.Employing Hamilton’s principle,the governing equations of motion are obtained.The generalized differential quadrature method(GDQM)is then applied to the equations to obtain the results.The achieved outcomes exhibit that the natural frequency and buckling load values vary as the fiber volume fractions and distributions,elastic foundation stiffness values,and boundary conditions(BCs)and slenderness ratio of the beam change.Furthermore,a comparative study is conducted between the derived analysis outcomes for BFRC and homogenous polymer beams to examine the effectiveness of bamboo fibers as reinforcement materials,demonstrating the significant enhancements in both vibration and buckling responses,with the exception of natural frequencies for cantilever beams on the Pasternak foundation with the FG-◇fiber distribution.Eventually,the obtained analysis results of BFRC beams are also compared with those for carbon nanotube reinforced composite(CNTRC)beams found in the literature,indicating that the buckling loads and natural frequencies of BFRC beams are lower than those of CNTRC beams.

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.

A Hybrid Level Set Optimization Design Method of Functionally Graded Cellular Structures Considering Connectivity

With the continuous advancement in topology optimization and additive manufacturing(AM)technology,the capability to fabricate functionally graded materials and intricate cellular structures with spatially varying microstructures has grown significantly.However,a critical challenge is encountered in the design of these structures–the absence of robust interface connections between adjacent microstructures,potentially resulting in diminished efficiency or macroscopic failure.A Hybrid Level Set Method(HLSM)is proposed,specifically designed to enhance connectivity among non-uniform microstructures,contributing to the design of functionally graded cellular structures.The HLSM introduces a pioneering algorithm for effectively blending heterogeneous microstructure interfaces.Initially,an interpolation algorithm is presented to construct transition microstructures seamlessly connected on both sides.Subsequently,the algorithm enables the morphing of non-uniform unit cells to seamlessly adapt to interconnected adjacent microstructures.The method,seamlessly integrated into a multi-scale topology optimization framework using the level set method,exhibits its efficacy through numerical examples,showcasing its prowess in optimizing 2D and 3D functionally graded materials(FGM)and multi-scale topology optimization.In essence,the pressing issue of interface connections in complex structure design is not only addressed but also a robust methodology is introduced,substantiated by numerical evidence,advancing optimization capabilities in the realm of functionally graded materials and cellular structures.

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.

Functionally graded structure of a nitride-strengthened Mg_(2)Si-based hybrid composite

The ex-situ incorporation of the secondary SiC reinforcement,along with the in-situ incorporation of the tertiary and quaternary Mg_(3)N_(2) and Si_(3)N_(4) phases,in the primary matrix of Mg_(2)Si is employed in order to provide ultimate wear resistance based on the laser-irradiation-induced inclusion of N_(2) gas during laser powder bed fusion.This is substantialized based on both the thermal diffusion-and chemical reactionbased metallurgy of the Mg_(2)Si–SiC/nitride hybrid composite.This study also proposes a functional platform for systematically modulating a functionally graded structure and modeling build-direction-dependent architectonics during additive manufacturing.This strategy enables the development of a compositional gradient from the center to the edge of each melt pool of the Mg_(2)Si–SiC/nitride hybrid composite.Consequently,the coefficient of friction of the hybrid composite exhibits a 309.3%decrease to–1.67 compared to–0.54 for the conventional nonreinforced Mg_(2)Si structure,while the tensile strength exhibits a 171.3%increase to 831.5 MPa compared to 485.3 MPa for the conventional structure.This outstanding mechanical behavior is due to the(1)the complementary and synergistic reinforcement effects of the SiC and nitride compounds,each of which possesses an intrinsically high hardness,and(2)the strong adhesion of these compounds to the Mg_(2)Si matrix despite their small sizes and low concentrations.

Size-dependent thermomechanical vibration characteristics of rotating pre-twisted functionally graded shear deformable microbeams

A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress theory(MCST).The material properties are assumed to follow a power-law distribution along the chordwise direction.The model introduces one axial stretching variable and four transverse deflection variables including two pure bending components and two pure shear ones.The complex modal analysis and assumed mode methods are used to solve the governing equations of motion under different boundary conditions(BCs).Several examples are presented to verify the effectiveness of the developed model.By coupling the slenderness ratio,gradient index,rotation speed,and size effect with the pre-twisted angle,the effects of these factors on the thermomechanical vibration of the microbeam with different BCs are investigated.It is found that with the increase in the pre-twisted angle,the critical slenderness ratio and gradient index corresponding to the thermal instability of the microbeam increase,while the critical material length scale parameter(MLSP)and rotation speed decrease.The sensitivity of the fundamental frequency to temperature increases with the increasing slenderness ratio and gradient index,and decreases with the other increasing parameters.Moreover,the size effect can suppress the dynamic stiffening effect and enhance the Coriolis effect.Finally,the mode transition is quantitatively demonstrated by a modal assurance criterion(MAC).

THERMAL STRESSES RELAXATION DESIGN OF Ni/NiFe_(2)O_(4) SYSTEM FUNCTIONALLY GRADED CERMET INERT ANODE

The thermal stresses relaxation of Ni/NiFe2O4 system functionally graded cermet inert anode for aluminum electrolysis was optimally designed. The transient thermal stresses of the inert anode under complex boundary condition during high-temp （955℃） electrolysis were calculated using the finite-element software ANSYS, the influence of different parameters on the distribution of the thermal stresses were analyzed. The results showed that, during the process of thermal shock, the thermal hoop tensile stress on the surface of the anode is very large, which is possibly the major cause of anode crack; when the radius of the anode is between 0.05-0.15m, a range that can be realized by recent manufacturing technology, the optimum composition distribution exponent p is 0.25; The hoop tensile stresses reduce with the decrease of anode scale and also decrease with the decrease of the convection coefficient between the electrolyte and the anode.

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.

Wave propagation analysis of porous functionally graded piezoelectric nanoplates with a visco-Pasternak foundation

This study investigates the size-dependent wave propagation behaviors under the thermoelectric loads of porous functionally graded piezoelectric(FGP) nanoplates deposited in a viscoelastic foundation.It is assumed that(i) the material parameters of the nanoplates obey a power-law variation in thickness and(ii) the uniform porosity exists in the nanoplates.The combined effects of viscoelasticity and shear deformation are considered by using the Kelvin-Voigt viscoelastic model and the refined higher-order shear deformation theory.The scale effects of the nanoplates are captured by employing nonlocal strain gradient theory(NSGT).The motion equations are calculated in accordance with Hamilton’s principle.Finally,the dispersion characteristics of the nanoplates are numerically determined by using a harmonic solution.The results indicate that the nonlocal parameters(NLPs) and length scale parameters(LSPs) have exactly the opposite effects on the wave frequency.In addition,it is found that the effect of porosity volume fractions(PVFs) on the wave frequency depends on the gradient indices and damping coefficients.When these two values are small,the wave frequency increases with the volume fraction.By contrast,at larger gradient index and damping coefficient values,the wave frequency decreases as the volume fraction increases.

Symplectic analysis for regulating wave propagation in a one-dimensional nonlinear graded metamaterial

An analytical method,called the symplectic mathematical method,is proposed to study the wave propagation in a spring-mass chain with gradient arranged local resonators and nonlinear ground springs.Combined with the linearized perturbation approach,the symplectic transform matrix for a unit cell of the weakly nonlinear graded metamaterial is derived,which only relies on the state vector.The results of the dispersion relation obtained with the symplectic mathematical method agree well with those achieved by the Bloch theory.It is shown that wider and lower frequency bandgaps are formed when the hardening nonlinearity and incident wave intensity increase.Subsequently,the displacement response and transmission performance of nonlinear graded metamaterials with finite length are studied.The dual tunable effects of nonlinearity and gradation on the wave propagation are explored under different excitation frequencies.For small excitation frequencies,the gradient parameter plays a dominant role compared with the nonlinearity.The reason is that the gradient tuning aims at the gradient arrangement of local resonators,which is limited by the critical value of the local resonator mass.In contrast,for larger excitation frequencies,the hardening nonlinearity is dominant and will contribute to the formation of a new bandgap.

Vibration and sound transmission loss characteristics of porous foam functionally graded sandwich panels in thermal environment

This study investigates the vibration and acoustic properties of porous foam functionally graded(FG)plates under the influence of the temperature field.The dynamics equations of the system are established based on Hamilton's principle by using the higher-order shear deformation theory under the linear displacement-strain assumption.The displacement shape function is assumed according to the four-sided simply-supported(SSSS)boundary condition,and the characteristic equations of the system are derived by combining the motion control equations.The theoretical model of vibro-acoustic coupling is established by using the acoustic theory and fluid-structure coupling solution method under the simple harmonic acoustic wave.The system's natural frequency and sound transmission loss(STL)are obtained through programming calculations and compared with the literature and COMSOL simulation to verify the validity and reliability of the theoretical model.The effects of various factors,such as temperature,porosity coefficients,gradient index,core thickness,width-to-thickness ratio on the vibration,and STL characteristics of the system,are discussed.The results provide a theoretical basis for the application of porous foam FG plates in engineering to optimize vibration and sound transmission properties.

Explicit Isogeometric Topology Optimization Method with Suitably Graded Truncated Hierarchical B-Spline

This work puts forward an explicit isogeometric topology optimization(ITO)method using moving morphable components(MMC),which takes the suitably graded truncated hierarchical B-Spline based isogeometric analysis as the solver of physical unknown(SGTHB-ITO-MMC).By applying properly basis graded constraints to the hierarchical mesh of truncated hierarchical B-splines(THB),the convergence and robustness of the SGTHB-ITOMMC are simultaneously improved and the tiny holes occurred in optimized structure are eliminated,due to the improved accuracy around the explicit structural boundaries.Moreover,an efficient computational method is developed for the topological description functions(TDF)ofMMC under the admissible hierarchicalmesh,which consists of reducing the dimensionality strategy for design space and the locally computing strategy for hierarchical mesh.We apply the above SGTHB-ITO-MMC with improved efficiency to a series of 2D and 3Dcompliance design problems.The numerical results show that the proposed SGTHB-ITO-MMC method outperforms the traditional THB-ITO-MMCmethod in terms of convergence rate and efficiency.Therefore,the proposed SGTHB-ITO-MMC is an effective way of solving topology optimization(TO)problems.

Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.