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2023年 第44卷 第2期    刊出日期：2023-02-01

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论文

Flexural wave bandgap properties of phononic crystal beams with interval parameters

Feiyang HE, Zhiyu SHI, Denghui QIAN, Y. K. LU, Yujia XIANG, Xuelei FENG

2023, 44(2):  173-188.  doi:10.1007/s10483-023-2947-8

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Uncertainties are unavoidable in practical engineering, and phononic crystals are no exception. In this paper, the uncertainties are treated as the interval parameters, and an interval phononic crystal beam model is established. A perturbation-based interval finite element method (P-IFEM) and an affine-based interval finite element method (A-IFEM) are proposed to study the dynamic response of this interval phononic crystal beam, based on which an interval vibration transmission analysis can be easily implemented and the safe bandgap can be defined. Finally, two numerical examples are investigated to demonstrate the effectiveness and accuracy of the P-IFEM and A-IFEM. Results show that the safe bandgap range may even decrease by 10% compared with the deterministic bandgap without considering the uncertainties.



Electro-chemo-mechanical analysis of the effect of bending deformation on the interface of flexible solid-state battery

Yutao SHI, Chengjun XU, Bingbing CHEN, Jianqiu ZHOU, Rui CAI

2023, 44(2):  189-206.  doi:10.1007/s10483-023-2920-7

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Flexible solid-state battery has several unique characteristics including high flexibility, easy portability, and high safety, which may have broad application prospects in new technology products such as rollup displays, power implantable medical devices, and wearable equipments. The interfacial mechanical and electrochemical problems caused by bending deformation, resulting in the battery damage and failure, are particularly interesting. Herein, a fully coupled electro-chemo-mechanical model is developed based on the actual solid-state battery structure. Concentration-dependent material parameters, stress-dependent diffusion, and potential shift are considered. According to four bending forms (k = 8/mm, 0/mm, -8/mm, and free), the results show that the negative curvature bending is beneficial to reducing the plastic strain during charging/discharging, while the positive curvature is detrimental. However, with respect to the electrochemical performance, the negative curvature bending creates a negative potential shift, which causes the battery to reach the cut-off voltage earlier and results in capacity loss. These results enlighten us that suitable electrode materials and charging strategy can be tailored to reduce plastic deformation and improve battery capacity for different forms of battery bending.

Random vibration of hysteretic systems under Poisson white noise excitations

Lincong CHEN, Zi YUAN, Jiamin QIAN, J. Q. SUN

2023, 44(2):  207-220.  doi:10.1007/s10483-023-2941-6

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Hysteresis widely exists in civil structures, and dissipates the mechanical energy of systems. Research on the random vibration of hysteretic systems, however, is still insufficient, particularly when the excitation is non-Gaussian. In this paper, the radial basis function (RBF) neural network (RBF-NN) method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise excitations. The solution to the reduced generalized Fokker-PlanckKolmogorov (GFPK) equation is expressed in terms of the RBF-NNs with the Gaussian activation functions, whose weights are determined by minimizing the loss function of the reduced GFPK equation residual and constraint associated with the normalization condition. A steel fiber reinforced ceramsite concrete (SFRCC) column loaded by the Poisson white noise is studied as an example to illustrate the solution process. The effects of several important parameters of both the system and the excitation on the stochastic response are evaluated, and the obtained results are compared with those obtained by the Monte Carlo simulations (MCSs). The numerical results show that the RBF-NN method can accurately predict the stationary response with a considerable high computational efficiency.

Dynamic stiffness characteristics of aero-engine elastic support structure and its effects on rotor systems: mechanism and numerical and experimental studies

Lei LI, Zhong LUO, Kaining LIU, Jilai ZHOU

2023, 44(2):  221-236.  doi:10.1007/s10483-023-2950-8

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The support structure of a rotor system is subject to vibration excitation, which results in the stiffness of the support structure varying with the excitation frequency (i.e., the dynamic stiffness). However, the dynamic stiffness and its effect mechanism have been rarely incorporated in open studies of the rotor system. Therefore, this study theoretically reveals the effect mechanism of dynamic stiffness on the rotor system. Then, the numerical study and experimental verification are conducted on the dynamic stiffness characteristics of a squirrel cage, which is a common support structure for aero-engine. Moreover, the static stiffness experiment is also performed for comparison. Finally, a rotor system model considering the dynamic stiffness of the support structure is presented. The presented rotor model is used to validate the results of the theoretical analysis. The results illustrate that the dynamic stiffness reduces the critical speed of the rotor system and may lead to a new resonance.

Green’s functions of two-dimensional piezoelectric quasicrystal in half-space and bimaterials

Xiaoyu FU, Xiang MU, Jinming ZHANG, Liangliang ZHANG, Yang GAO

2023, 44(2):  237-254.  doi:10.1007/s10483-023-2955-9

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In this paper, we obtain Green’s functions of two-dimensional (2D) piezoelectric quasicrystal (PQC) in half-space and bimaterials. Based on the elastic theory of QCs, the Stroh formalism is used to derive the general solutions of displacements and stresses. Then, we obtain the analytical solutions of half-space and bimaterial Green’s functions. Besides, the interfacial Green’s function for bimaterials is also obtained in the analytical form. Before numerical studies, a comparative study is carried out to validate the present solutions. Typical numerical examples are performed to investigate the effects of multi-physics loadings such as the line force, the line dislocation, the line charge, and the phason line force. As a result, the coupling effect among the phonon field, the phason field, and the electric field is prominent, and the butterfly-shaped contours are characteristic in 2D PQCs. In addition, the changes of material parameters cause variations in physical quantities to a certain degree.

Transient multi-physics behavior of an insert high temperature superconducting no-insulation coil in hybrid superconducting magnets with inductive coupling

Xiang KANG, Yujin TONG, Wei WU, Xingzhe WANG

2023, 44(2):  255-272.  doi:10.1007/s10483-023-2960-6

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A transient multi-physics model incorporated with an electromagneto-thermomechanical coupling is developed to capture the multi-field behavior of a single-pancake (SP) insert no-insulation (NI) coil in a hybrid magnet during the charging and discharging processes. The coupled problem is resolved by means of the finite element method (FEM) for the magneto-thermo-elastic behaviors and the Runge-Kutta method for the transient responses of the electrical circuits of the hybrid superconducting magnet system. The results reveal that the transient multi-physics responses of the insert NI coil primarily depend on the charging/discharging procedure of the hybrid magnet. Moreover, a reverse azimuthal current and a compressive hoop stress are induced in the insert NI coil during the charging process, while a forward azimuthal current and a tensile hoop stress are observed during the discharging process. The induced voltages in the insert NI coil can drive the currents flowing across the radial turns where the contact resistance exists. Therefore, it brings forth significant Joule heat, causing a temperature rise and a uniform distribution of this heat in the coil turns. Accordingly, a thermally/mechanically unstable or quenching event may be encountered when a high operating current is flowing in the insert NI coil. It is numerically predicted that a quick charging will induce a compressive hoop stress which may bring a risk of buckling instability in the coil, while a discharging will not. The simulations provide an insight of hybrid superconducting magnets under transient start-up or shutdown phases which are inevitably encountered in practical applications.

Transient swelling-induced finite bending of hydrogel-based bilayers: analytical and FEM approaches

A. AMIRI, M. BANIASSADI, M. BAGHANI

2023, 44(2):  273-288.  doi:10.1007/s10483-023-2964-7

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Hydrogels with their time-dependent intrinsic behaviors have recently been used widely in soft structures as sensors/actuators. One of the most interesting structures is the bilayer made up of hydrogels which may undergo swelling-induced bending. In this work, by proposing a semi-analytical method, the transient bending of hydrogel-based bilayers is investigated. Utilizing nonlinear solid mechanics, a robust semi-analytical solution is developed which captures the transient finite bending of hydrogel-based bilayers. Moreover, the multiphysics model of the hydrogels is implemented in the finite element method (FEM) framework to verify the developed semi-analytical procedure results. The effects of different material properties are investigated to illustrate the nonlinear behavior of these structures. The von-Mises stress contour extracted from FEM shows that the critical area of these soft structures is at the interface of the layers which experiences the maximum stress, and this area is most likely to rupture in large deformations.

Multi-layer analytic solution for k-ω model equations via a symmetry approach

Fan TANG, Weitao BI, Zhensu SHE

2023, 44(2):  289-306.  doi:10.1007/s10483-023-2957-7

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Despite being one of the oldest and most widely-used turbulence models in engineering computational fluid dynamics (CFD), the k-ω model has not been fully understood theoretically because of its high nonlinearity and complex model parameter setting. Here, a multi-layer analytic expression is postulated for two lengths (stress and kinetic energy lengths), yielding an analytic solution for the k-ω model equations in pipe flow. Approximate local balance equations are analyzed to determine the key parameters in the solution, which are shown to be rather close to the empirically-measured values from the numerical solution of the Wilcox k-ω model, and hence the analytic construction is fully validated. The results provide clear evidence that the k-ω model sets in it a multilayer structure, which is similar to but different, in some insignificant details, from the Navier-Stokes (N-S) turbulence. This finding explains why the k-ω model is so popular, especially in computing the near-wall flow. Finally, the analysis is extended to a newly-refined k-ω model called the structural ensemble dynamics (SED) k-ω model, showing that the SED k-ω model has improved the multi-layer structure in the outer flow but preserved the setting of the k-ω model in the inner region.

Thermo-diffusion impact on immiscible flow characteristics of convectively heated vertical two-layered Baffle saturated porous channels in a suspension of nanoparticles: an analytical study

S. P. V. ANANTH, B. N. HANUMAGOWDA, S. V. K. VARMA, C. S. K. RAJU, I. KHAN, P. RANA

2023, 44(2):  307-324.  doi:10.1007/s10483-023-2956-6

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The heat and mass transfer of two immiscible fluids in an inclined channel with thermal diffusion, vicious, and Darcy dissipation is studied. The first region consists of a clear fluid, and the second one is filled with a nanofluid saturated with a porous medium. The behaviors of Cu-H₂O, In-H₂O, and Au-H₂O nanofluids are analyzed. The transport properties are assumed to be constant. The coupled non-linear equations of the flow model are transformed into the dimensionless form, and the solutions for the velocity, temperature, and concentration are obtained by the regular perturbation technique. Investigations are carried out on the flow characteristics for various values of the material parameters. The results show that the velocity and temperature of the fluids enhance with the thermal Grashof number, solutal Grashof number, and Brinkman number while decrease with the porosity parameter and solid volume fraction.

Thermogram-based estimation of foot arterial blood flow using neural networks

Yueping WANG, Lizhong MU, Ying HE

2023, 44(2):  325-344.  doi:10.1007/s10483-023-2959-9

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The altered blood flow in the foot is an important indicator of early diabetic foot complications. However, it is challenging to measure the blood flow at the whole foot scale. This study presents an approach for estimating the foot arterial blood flow using the temperature distribution and an artificial neural network. To quantify the relationship between the blood flow and the temperature distribution, a bioheat transfer model of a voxel-meshed foot tissue with discrete blood vessels is established based on the computed tomography (CT) sequential images and the anatomical information of the vascular structure. In our model, the heat transfer from blood vessels and tissue and the inter-domain heat exchange between them are considered thoroughly, and the computed temperatures are consistent with the experimental results. Analytical data are then used to train a neural network to determine the foot arterial blood flow. The trained network is able to estimate the objective blood flow for various degrees of stenosis in multiple blood vessels with an accuracy rate of more than 90%. Compared with the Pennes bioheat transfer equation, this model fully describes intra- and inter-domain heat transfer in blood vessels and tissue, closely approximating physiological conditions. By introducing a vascular component to an inverse model, the blood flow itself, rather than blood perfusion, can be estimated, directly informing vascular health.