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    Deep bed filtration model for cake filtration and erosion
    L.I. KUZMINA, Y.V. OSIPOV, A.R. PESTEREV
    Applied Mathematics and Mechanics (English Edition)    2024, 45 (2): 355-372.   DOI: 10.1007/s10483-024-3077-9
    Abstract249)   HTML2)    PDF(pc) (249KB)(745)       Save

    Many phenomena in nature and technology are associated with the filtration of suspensions and colloids in porous media. Two main types of particle deposition, namely, cake filtration at the inlet and deep bed filtration throughout the entire porous medium, are studied by different models. A unified approach for the transport and deposition of particles based on the deep bed filtration model is proposed. A variable suspension flow rate, proportional to the number of free pores at the inlet of the porous medium, is considered. To model cake filtration, this flow rate is introduced into the mass balance equation of deep bed filtration. For the cake filtration without deposit erosion, the suspension flow rate decreases to zero, and the suspension does not penetrate deep into the porous medium. In the case of the cake filtration with erosion, the suspension flow rate is nonzero, and the deposit is distributed throughout the entire porous medium. An exact solution is obtained for a constant filtration function. The method of characteristics is used to construct the asymptotics of the concentration front of suspended and retained particles for a filtration function in a general form. Explicit formulae are obtained for a linear filtration function. The properties of these solutions are studied in detail.

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    Preface: machine-learning approaches for computational mechanics
    Z. LI, Guohui HU, Zhiliang WANG, G. E. KARNIADAKIS
    Applied Mathematics and Mechanics (English Edition)    2023, 44 (7): 1035-1038.   DOI: 10.1007/s10483-023-2999-7
    Abstract287)   HTML4)    PDF(pc) (90KB)(531)       Save
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    Supposition of graphene stacks to estimate the contact resistance and conductivity of nanocomposites
    Y. ZARE, M. T. MUNIR, G. J. WENG, K. Y. RHEE
    Applied Mathematics and Mechanics (English Edition)    2024, 45 (4): 663-676.   DOI: 10.1007/s10483-024-3102-7
    Abstract102)   HTML1)    PDF(pc) (1022KB)(413)       Save

    In this study, the effects of stacked nanosheets and the surrounding interphase zone on the resistance of the contact region between nanosheets and the tunneling conductivity of samples are evaluated with developed equations superior to those previously reported. The contact resistance and nanocomposite conductivity are modeled by several influencing factors, including stack properties, interphase depth, tunneling size, and contact diameter. The developed model's accuracy is verified through numerous experimental measurements. To further validate the models and establish correlations between parameters, the effects of all the variables on contact resistance and nanocomposite conductivity are analyzed. Notably, the contact resistance is primarily dependent on the polymer tunnel resistivity, contact area, and tunneling size. The dimensions of the graphene nanosheets significantly influence the conductivity, which ranges from 0 S/m to 90 S/m. An increased number of nanosheets in stacks and a larger gap between them enhance the nanocomposite's conductivity. Furthermore, the thicker interphase and smaller tunneling size can lead to higher sample conductivity due to their optimistic effects on the percolation threshold and network efficacy.

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    Variational inference in neural functional prior using normalizing flows: application to differential equation and operator learning problems
    Xuhui MENG
    Applied Mathematics and Mechanics (English Edition)    2023, 44 (7): 1111-1124.   DOI: 10.1007/s10483-023-2997-7
    Abstract327)   HTML2)    PDF(pc) (3658KB)(376)       Save
    Physics-informed deep learning has recently emerged as an effective tool for leveraging both observational data and available physical laws. Physics-informed neural networks (PINNs) and deep operator networks (DeepONets) are two such models. The former encodes the physical laws via the automatic differentiation, while the latter learns the hidden physics from data. Generally, the noisy and limited observational data as well as the over-parameterization in neural networks (NNs) result in uncertainty in predictions from deep learning models. In paper "MENG, X., YANG, L., MAO, Z., FERRANDIS, J. D., and KARNIADAKIS, G. E. Learning functional priors and posteriors from data and physics. Journal of Computational Physics, 457, 111073 (2022)" has two stages: (i) prior learning, and (ii) posterior estimation. At the first stage, the GANs are utilized to learn a functional prior either from a prescribed function distribution, e.g., the Gaussian process, or from historical data and available physics. At the second stage, the Hamiltonian Monte Carlo (HMC) method is utilized to estimate the posterior in the latent space of GANs. However, the vanilla HMC does not support the mini-batch training, which limits its applications in problems with big data. In the present work, we propose to use the normalizing flow (NF) models in the context of variational inference (VI), which naturally enables the mini-batch training, as the alternative to HMC for posterior estimation in the latent space of GANs. A series of numerical experiments, including a nonlinear differential equation problem and a 100-dimensional (100D) Darcy problem, are conducted to demonstrate that the NFs with full-/mini-batch training are able to achieve similar accuracy as the "gold rule" HMC. Moreover, the mini-batch training of NF makes it a promising tool for quantifying uncertainty in solving the high-dimensional partial differential equation (PDE) problems with big data.
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    Kinematic analysis of flexible bipedal robotic systems
    R. FAZEL, A. M. SHAFEI, S. R. NEKOO
    Applied Mathematics and Mechanics (English Edition)    2024, 45 (5): 795-818.   DOI: 10.1007/s10483-024-3081-8
    Abstract151)   HTML1)    PDF(pc) (5564KB)(338)       Save

    In spite of its intrinsic complexities, the passive gait of bipedal robots on a sloping ramp is a subject of interest for numerous researchers. What distinguishes the present research from similar works is the consideration of flexibility in the constituent links of this type of robotic systems. This is not a far-fetched assumption because in the transient (impact) phase, due to the impulsive forces which are applied to the system, the likelihood of exciting the vibration modes increases considerably. Moreover, the human leg bones that are involved in walking are supported by viscoelastic muscles and ligaments. Therefore, for achieving more exact results, it is essential to model the robot links with viscoelastic properties. To this end, the Gibbs-Appell formulation and Newton's kinematic impact law are used to derive the most general form of the system's dynamic equations in the swing and transient phases of motion. The most important issue in the passive walking motion of bipedal robots is the determination of the initial robot configuration with which the system could accomplish a periodic and stable gait solely under the effect of gravitational force. The extremely unstable nature of the system studied in this paper and the vibrations caused by the impulsive forces induced by the impact of robot feet with the inclined surface are some of the very serious challenges encountered for achieving the above-mentioned goal. To overcome such challenges, an innovative method that uses a combination of the linearized equations of motion in the swing phase and the algebraic motion equations in the transition phase is presented in this paper to obtain an eigenvalue problem. By solving this problem, the suitable initial conditions that are necessary for the passive gait of this bipedal robot on a sloping surface are determined. The effects of the characteristic parameters of elastic links including the modulus of elasticity and the Kelvin-Voigt coefficient on the walking stability of this type of robotic systems are also studied. The findings of this parametric study reveal that the increase in the Kelvin-Voigt coefficient enhances the stability of the robotic system, while the increase in the modulus of elasticity has an opposite effect.

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    Semi-analytical investigation of heat transfer in a porous convective radiative moving longitudinal fln exposed to magnetic fleld in the presence of a shape-dependent trihybrid nanofluid
    C. G. PAVITHRA, B. J. GIREESHA, M. L. KEERTHI
    Applied Mathematics and Mechanics (English Edition)    2024, 45 (1): 197-216.   DOI: 10.1007/s10483-024-3069-6
    Abstract225)   HTML212)    PDF(pc) (4356KB)(333)       Save

    The thermal examination of a non-integer-ordered mobile fin with a magnetism in the presence of a trihybrid nanofluid (Fe3O4-Au-Zn-blood) is carried out. Three types of nanoparticles, each having a different shape, are considered. These shapes include spherical (Fe3O4), cylindrical (Au), and platelet (Zn) configurations. The combination approach is utilized to evaluate the physical and thermal characteristics of the trihybrid and hybrid nanofluids, excluding the thermal conductivity and dynamic viscosity. These two properties are inferred by means of the interpolation method based on the volume fraction of nanoparticles. The governing equation is transformed into a dimensionless form, and the Adomian decomposition Sumudu transform method (ADSTM) is adopted to solve the conundrum of a moving fin immersed in a trihybrid nanofluid. The obtained results agree well with those numerical simulation results, indicating that this research is reliable. The influence of diverse factors on the thermal overview for varying noninteger values of γ is analyzed and presented in graphical representations. Furthermore, the fluctuations in the heat transfer concerning the pertinent parameters are studied. The results show that the heat flux in the presence of the combination of spherical, cylindrical, and platelet nanoparticles is higher than that in the presence of the combination of only spherical and cylindrical nanoparticles. The temperature at the fin tip increases by 0.705 759% when the value of the Peclet number increases by 400%, while decreases by 11.825 13% when the value of the Hartman number increases by 400%.

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    Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model
    Runqing CAO, Zilong GUO, Wei CHEN, Huliang DAI, Lin WANG
    Applied Mathematics and Mechanics (English Edition)    2024, 45 (2): 261-276.   DOI: 10.1007/s10483-024-3084-7
    Abstract258)   HTML3)    PDF(pc) (2371KB)(318)       Save

    Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine, the investigations on the mechanical responses of the pipes have attracted considerable attention. The fluid-structure interaction (FSI) between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes, especially when the pipe is highly flexible and usually undergoes large deformations. In this work, the geometrically exact model (GEM) for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle. The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow. Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid, which is often encountered in practical engineering. By constructing bifurcation diagrams, oscillating shapes, phase portraits, time traces, and Poincaré maps, the dynamic responses of the curved pipe under various system parameters are revealed. The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical. The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors, including periodic and quasi-periodic motions. It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode. For a moderate value of the mass ratio, however, a third-mode flutter may occur, which is quite different from that of a straight pipe system.

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    Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics
    W. WU, M. DANEKER, M. A. JOLLEY, K. T. TURNER, L. LU
    Applied Mathematics and Mechanics (English Edition)    2023, 44 (7): 1039-1068.   DOI: 10.1007/s10483-023-2995-8
    Abstract328)   HTML14)    PDF(pc) (7194KB)(282)       Save
    Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions. However, material identification is a challenging task, especially when the characteristic of the material is highly nonlinear in nature, as is common in biological tissue. In this work, we identify unknown material properties in continuum solid mechanics via physics-informed neural networks (PINNs). To improve the accuracy and efficiency of PINNs, we develop efficient strategies to nonuniformly sample observational data. We also investigate different approaches to enforce Dirichlet-type boundary conditions (BCs) as soft or hard constraints. Finally, we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space. The estimated material parameters achieve relative errors of less than 1%. As such, this work is relevant to diverse applications, including optimizing structural integrity and developing novel materials.
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    Dynamic and electrical responses of a curved sandwich beam with glass reinforced laminate layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact
    N. SHAHVEISI, S. FELI
    Applied Mathematics and Mechanics (English Edition)    2024, 45 (1): 155-178.   DOI: 10.1007/s10483-024-3074-6
    Abstract195)   HTML1)    PDF(pc) (1482KB)(276)       Save

    The dynamic responses and generated voltage in a curved sandwich beam with glass reinforced laminate (GRL) layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact (LVI) are investigated. The current study aims to carry out a dynamic analysis on the sandwich beam when the impactor hits the top face sheet with an initial velocity. For the layer analysis, the high-order shear deformation theory (HSDT) and Frostig's second model for the displacement fields of the core layer are used. The classical non-adhesive elastic contact theory and Hunter's principle are used to calculate the dynamic responses in terms of time. In order to validate the analytical method, the outcomes of the current investigation are compared with those gained by the experimental tests carried out by other researchers for a rectangular composite plate subject to the LVI. Finite element (FE) simulations are conducted by means of the ABAQUS software. The effects of the parameters such as foam modulus, layer material, fiber angle, impactor mass, and its velocity on the generated voltage are reviewed.

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    Dynamics and vibration reduction performance of asymmetric tristable nonlinear energy sink
    Hongyan CHEN, Youcheng ZENG, Hu DING, Siukai LAI, Liqun CHEN
    Applied Mathematics and Mechanics (English Edition)    2024, 45 (3): 389-406.   DOI: 10.1007/s10483-024-3095-9
    Abstract229)   HTML11)    PDF(pc) (3713KB)(252)       Save

    With its complex nonlinear dynamic behavior, the tristable system has shown excellent performance in areas such as energy harvesting and vibration suppression, and has attracted a lot of attention. In this paper, an asymmetric tristable design is proposed to improve the vibration suppression efficiency of nonlinear energy sinks (NESs) for the first time. The proposed asymmetric tristable NES (ATNES) is composed of a pair of oblique springs and a vertical spring. Then, the three stable states, symmetric and asymmetric, can be achieved by the adjustment of the distance and stiffness asymmetry of the oblique springs. The governing equations of a linear oscillator (LO) coupled with the ATNES are derived. The approximate analytical solution to the coupled system is obtained by the harmonic balance method (HBM) and verified numerically. The vibration suppression efficiency of three types of ATNES is compared. The results show that the asymmetric design can improve the efficiency of vibration reduction through comparing the chaotic motion of the NES oscillator between asymmetric steady states. In addition, compared with the symmetrical tristable NES (TNES), the ATNES can effectively control smaller structural vibrations. In other words, the ATNES can effectively solve the threshold problem of TNES failure to weak excitation. Therefore, this paper reveals the vibration reduction mechanism of the ATNES, and provides a pathway to expand the effective excitation amplitude range of the NES.

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    Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving partial differential equations with sharp solutions
    Zhiping MAO, Xuhui MENG
    Applied Mathematics and Mechanics (English Edition)    2023, 44 (7): 1069-1084.   DOI: 10.1007/s10483-023-2994-7
    Abstract362)   HTML5)    PDF(pc) (3076KB)(248)       Save
    We consider solving the forward and inverse partial differential equations (PDEs) which have sharp solutions with physics-informed neural networks (PINNs) in this work. In particular, to better capture the sharpness of the solution, we propose the adaptive sampling methods (ASMs) based on the residual and the gradient of the solution. We first present a residual only-based ASM denoted by ASM I. In this approach, we first train the neural network using a small number of residual points and divide the computational domain into a certain number of sub-domains, then we add new residual points in the sub-domain which has the largest mean absolute value of the residual, and those points which have the largest absolute values of the residual in this sub-domain as new residual points. We further develop a second type of ASM (denoted by ASM II) based on both the residual and the gradient of the solution due to the fact that only the residual may not be able to efficiently capture the sharpness of the solution. The procedure of ASM II is almost the same as that of ASM I, and we add new residual points which have not only large residuals but also large gradients. To demonstrate the effectiveness of the present methods, we use both ASM I and ASM II to solve a number of PDEs, including the Burger equation, the compressible Euler equation, the Poisson equation over an L-shape domain as well as the high-dimensional Poisson equation. It has been shown from the numerical results that the sharp solutions can be well approximated by using either ASM I or ASM II, and both methods deliver much more accurate solutions than the original PINNs with the same number of residual points. Moreover, the ASM II algorithm has better performance in terms of accuracy, efficiency, and stability compared with the ASM I algorithm. This means that the gradient of the solution improves the stability and efficiency of the adaptive sampling procedure as well as the accuracy of the solution. Furthermore, we also employ the similar adaptive sampling technique for the data points of boundary conditions (BCs) if the sharpness of the solution is near the boundary. The result of the L-shape Poisson problem indicates that the present method can significantly improve the efficiency, stability, and accuracy.
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    Effects of time-delayed vibration absorber on bandwidth of beam for low broadband vibration suppression
    Xiuting SUN, Yipeng QU, Feng WANG, Jian XU
    Applied Mathematics and Mechanics (English Edition)    2023, 44 (10): 1629-1650.   DOI: 10.1007/s10483-023-3038-6
    Abstract190)   HTML4)    PDF(pc) (4650KB)(222)       Save
    The effects of time-delayed vibration absorber (TDVA) on the dynamic characteristics of a flexible beam are investigated. First, the vibration suppression effect of a single TDVA on a continuous beam is studied. The first optimization criterion is given, and the results show that the introduction of time-delayed feedback control (TDFC) is beneficial to improving the vibration suppression at the anti-resonance band. When a single TDVA is used, the anti-resonance is located at a specific frequency by the optimum design of TDFC parameters. Then, in order to obtain low-frequency and broad bands for vibration suppression, multiple TDVAs are uniformly distributed on a continuous beam, and the relationship between the dynamic responses and the TDFC parameters is investigated. The obtained relationship shows that the TDVA has a significant regulatory effect on the vibration behavior of the continuous beam. The effects of the number of TDVAs and the nonlinearity on the bandgap variation are discussed. As the multiple TDVAs are applied, according to the different requirements on the location and bandwidth of the effective vibration suppression band, the optimization criteria for the TDFC parameters are given, which provides guidance for the applications of TDVAs in practical projects such as bridge and aerospace.
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    Integrated multi-scale approach combining global homogenization and local refinement for multi-field analysis of high-temperature superconducting composite magnets
    Hanxiao GUO, Peifeng GAO, Xingzhe WANG
    Applied Mathematics and Mechanics (English Edition)    2024, 45 (5): 747-762.   DOI: 10.1007/s10483-024-3112-8
    Abstract169)   HTML14)    PDF(pc) (5789KB)(221)       Save

    Second-generation high-temperature superconducting (HTS) conductors, specifically rare earth-barium-copper-oxide (REBCO) coated conductor (CC) tapes, are promising candidates for high-energy and high-field superconducting applications. With respect to epoxy-impregnated REBCO composite magnets that comprise multilayer components, the thermomechanical characteristics of each component differ considerably under extremely low temperatures and strong electromagnetic fields. Traditional numerical models include homogenized orthotropic models, which simplify overall field calculation but miss detailed multi-physics aspects, and full refinement (FR) ones that are thorough but computationally demanding. Herein, we propose an extended multi-scale approach for analyzing the multi-field characteristics of an epoxy-impregnated composite magnet assembled by HTS pancake coils. This approach combines a global homogenization (GH) scheme based on the homogenized electromagnetic T-A model, a method for solving Maxwell's equations for superconducting materials based on the current vector potential T and the magnetic field vector potential A, and a homogenized orthotropic thermoelastic model to assess the electromagnetic and thermoelastic properties at the macroscopic scale. We then identify "dangerous regions" at the macroscopic scale and obtain finer details using a local refinement (LR) scheme to capture the responses of each component material in the HTS composite tapes at the mesoscopic scale. The results of the present GH-LR multi-scale approach agree well with those of the FR scheme and the experimental data in the literature, indicating that the present approach is accurate and efficient. The proposed GH-LR multi-scale approach can serve as a valuable tool for evaluating the risk of failure in large-scale HTS composite magnets.

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    Dynamic modeling of fluid-conveying pipes restrained by a retaining clip
    Bo DOU, Hu DING, Xiaoye MAO, Sha WEI, Liqun CHEN
    Applied Mathematics and Mechanics (English Edition)    2023, 44 (8): 1225-1240.   DOI: 10.1007/s10483-023-3016-9
    Abstract250)   HTML12)    PDF(pc) (2386KB)(220)       Save
    Although most pipes are restrained by retaining clips in aircraft, the influence of the clip parameters on the vibration of the fluid-conveying pipe has not been revealed. By considering the clip width, a new dynamic model of a fluid-conveying pipe restrained by an intermediate clip is established in this paper. To demonstrate the necessity of the proposed model, a half pipe model is established by modeling the clip as one end. By comparing the two models, it is found that the half pipe model overestimates the critical velocity and may estimate the dynamical behavior of the pipe incorrectly. In addition, with the increase in the clip stiffness, the conversion processes of the first two modes of the pipe are shown. Furthermore, by ignoring the width of the clip, the effect of the flow velocity on the accuracy of a concentrated restraint clip model is presented. When the flow velocity is close to the critical velocity, the accuracy of the concentrated restraint clip model significantly reduces, especially when the width of the clip is large. In general, the contribution of this paper is to establish a dynamic model of the fluid-conveying pipe which can describe the influence of the clip parameters, and to demonstrate the necessity of this model.
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    Free vibration and buckling analysis of polymeric composite beams reinforced by functionally graded bamboo fibers
    H.M. FEIZABAD, M.H. YAS
    Applied Mathematics and Mechanics (English Edition)    2024, 45 (3): 543-562.   DOI: 10.1007/s10483-024-3090-8
    Abstract172)   HTML3)    PDF(pc) (642KB)(211)       Save

    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.

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    Effects of multiple shapes for steady flow with transformer oil+Fe3O4+TiO2 between two stretchable rotating disks
    M. RAHMAN, M. TURKYILMAZOGLU, Z. MUSHTAQ
    Applied Mathematics and Mechanics (English Edition)    2024, 45 (2): 373-388.   DOI: 10.1007/s10483-024-3088-7
    Abstract241)   HTML4)    PDF(pc) (1207KB)(209)       Save

    In this study, we examine the effects of various shapes of nanoparticles in a steady flow of hybrid nanofluids between two stretchable rotating disks. The steady flow of hybrid nanofluids with transformer oil as the base fluid and Fe3O4+TiO2 as the hybrid nanofluid is considered. Several shapes of Fe3O4+TiO2 hybrid nanofluids, including sphere, brick, blade, cylinder, and platelet, are studied. Every shape exists in the same volume of a nanoparticle. The leading equations (partial differential equations (PDEs)) are transformed to the nonlinear ordinary differential equations (ODEs) with the help of similarity transformations. The system of equations takes the form of ODEs depending on the boundary conditions, whose solutions are computed numerically by the bvp4c MATLAB solver. The outputs are compared with the previous findings, and an intriguing pattern is discovered, such that the tangential velocity is increased for the rotation parameter, while it is decreased by the stretching values because of the lower disk. For the reaction rate parameter, the concentration boundary layer becomes shorter, and the activation energy component increases the rate at which mass transfers come to the higher disk but have the opposite effect on the bottom disk. The ranges of various parameters taken into account are Pr = 6.2, Re = 2, M = 1.0, ϕ1 = ϕ2 = 0.03, K = 0.5, S = -0.1, Br = 0.3, Sc = 2.0, α1 = 0.2, γ = 0.1, En = 2.0, and q = 1.0, and the rotation factor K is within the range of 0 to 1.

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    Multi-blade rubbing characteristics of the shaft-disk-blade-casing system with large rotation
    Zhiyuan WU, Linchuan ZHAO, Han YAN, Ge YAN, Ao CHEN, Wenming ZHANG
    Applied Mathematics and Mechanics (English Edition)    2024, 45 (1): 111-136.   DOI: 10.1007/s10483-024-3071-5
    Abstract177)   HTML6)    PDF(pc) (20536KB)(209)       Save

    Blade rubbing faults cause detrimental impact on the operation of aeroengines. Most of the existing studies on blade rubbing in the shaft-disk-blade-casing (SDBC) system have overlooked the elastic deformation of the blade, while some only consider the whirl of the rotor, neglecting its spin. To address these limitations, this paper proposes a dynamic model with large rotation for the SDBC system. The model incorporates the spin and whirl of the rotor, enabling the realistic reproduction of multi-blade rubbing faults. To verify the accuracy of the SDBC model with large rotation and demonstrate its capability to effectively consider the rotational effects such as the centrifugal stiffening and gyroscopic effects, the natural characteristics and dynamic responses of the proposed model are compared with those obtained from reported research and experimental results. Furthermore, the effects of the rotating speed, contact stiffness, and blade number on the dynamic characteristics of the SDBC system with multi-blade rubbing are investigated. The results indicate that the phase angle between the rotor deflection and the unbalance excitation force increases with the increasing rotating speed, which significantly influences the rubbing penetration of each blade. The natural frequency of the SDBC system with rubbing constrain can be observed in the acceleration response of the casing and the torsional response of the shaft, and the frequency is related to the contact stiffness. Moreover, the vibration amplitude increases significantly with the product of the blade number under rubbing, and the rotating frequency approaches the natural frequency of the SDBC system. The proposed model can provide valuable insight for the fault diagnosis of rubbing in bladed rotating machinery.

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    Vibration and sound transmission loss characteristics of porous foam functionally graded sandwich panels in thermal environment
    Wenhao YUAN, Haitao LIAO, Ruxin GAO, Fenglian LI
    Applied Mathematics and Mechanics (English Edition)    2023, 44 (6): 897-916.   DOI: 10.1007/s10483-023-3004-7
    Abstract1110)   HTML236)    PDF(pc) (1290KB)(209)       Save
    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.
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    Adaptive state-constrained/model-free iterative sliding mode control for aerial robot trajectory tracking
    Chen AN, Jiaxi ZHOU, Kai WANG
    Applied Mathematics and Mechanics (English Edition)    2024, 45 (4): 603-618.   DOI: 10.1007/s10483-024-3103-8
    Abstract116)   HTML3)    PDF(pc) (1245KB)(208)       Save

    This paper develops a novel hierarchical control strategy for improving the trajectory tracking capability of aerial robots under parameter uncertainties. The hierarchical control strategy is composed of an adaptive sliding mode controller and a model-free iterative sliding mode controller (MFISMC). A position controller is designed based on adaptive sliding mode control (SMC) to safely drive the aerial robot and ensure fast state convergence under external disturbances. Additionally, the MFISMC acts as an attitude controller to estimate the unmodeled dynamics without detailed knowledge of aerial robots. Then, the adaption laws are derived with the Lyapunov theory to guarantee the asymptotic tracking of the system state. Finally, to demonstrate the performance and robustness of the proposed control strategy, numerical simulations are carried out, which are also compared with other conventional strategies, such as proportional-integral-derivative (PID), backstepping (BS), and SMC. The simulation results indicate that the proposed hierarchical control strategy can fulfill zero steady-state error and achieve faster convergence compared with conventional strategies.

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    Influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel
    N. HUMNEKAR, D. SRINIVASACHARYA
    Applied Mathematics and Mechanics (English Edition)    2024, 45 (3): 563-580.   DOI: 10.1007/s10483-024-3096-6
    Abstract196)   HTML3)    PDF(pc) (752KB)(199)       Save

    The influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel is investigated. The Darcy-Brinkman model is used to characterize the fluid flow dynamics in porous materials. The analytical solutions are obtained for the unidirectional and completely developed flow. Based on a normal mode analysis, the generalized eigenvalue problem under a perturbed state is solved. The eigenvalue problem is then solved by the spectral method. Finally, the critical Rayleigh number with the corresponding wavenumber is evaluated at the assigned values of the other flow-governing parameters. The results show that increasing the Darcy number, the Lewis number, the Dufour parameter, or the Soret parameter increases the stability of the system, whereas increasing the inclination angle of the channel destabilizes the flow. Besides, the flow is the most unstable when the channel is vertically oriented.

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