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2022年 第43卷 第11期    刊出日期：2022-11-01

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论文

Bandgap characteristics of the two-dimensional missing rib lattice structure

Fan YANG, Zhaoyang MA, Xingming GUO

2022, 43(11):  1631-1640.  doi:10.1007/s10483-022-2923-6

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In this paper, the bandgap characteristics of a missing rib lattice structure composed of beam elements are investigated by using the Floquet-Bloch theorem. The tuning of the width and position of the bandgap is achieved by changing the local structural parameters, i.e., the rotation angle, the short beam length, and the beam thickness. In order to expand the regulation of the bandgap, the influence of the material parameters of the crossed long beams inside the structure on the bandgap is analyzed. The results show that the mass density and stiffness of the structure have significant effects on the bandgap, while Poisson's ratio has no effect on the bandgap. By analyzing the first ten bands of the reference unit cell, it can be found that the missing rib lattice structure generates multiple local resonance bandgaps for vibration reduction, and these bandgap widths are wider. The modal analysis reveals that the formation of the bandgap is due to the dipole resonance of the lattice structure, and this dipole resonance originates from the coupling of the bending deformation of the beam elements. In the band structure, the vibrational mode of the 9th band with a negative slope corresponds to a rotational resonance, which is different from that with the conventional negative slope formed by the coupling of two resonance modes. This study can provide a theoretical reference for the design of simple and lightweight elastic metamaterials, as well as for the regulation of bandgaps and the suppression of elastic waves.



A novel design scheme for acoustic cloaking of complex shape based on region partitioning and multi-origin coordinate transformation

Pengfei LI, Fan YANG, Peng WANG, Jinfeng ZHAO, Zheng ZHONG

2022, 43(11):  1641-1656.  doi:10.1007/s10483-022-2928-7

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Acoustic cloaking is an important application of acoustic metamaterials. This article proposes a novel design scheme for acoustic cloaking based on the region partitioning and multi-origin coordinate transformation. The cloaked region is partitioned into multiple narrow strips. For each strip, a local coordinate system is established with the local origin located at the strip center, and a coordinate transformation in the local coordinate system is conducted to squeeze the material along the strip length direction to form the cloaked region. To facilitate the implementation of the acoustic cloak, the multilayer effective medium is used to approximate the non-uniform anisotropic material parameters. The effectiveness of the proposed coordinate transformation method is verified by comparing the results from our method with those in the literature. Firstly, the results of a circular acoustic cloak in the literature are reproduced by using our finite element (FE) simulations for validation. Then, a comparison is made between the traditional coordinate transformation scheme and our new scheme for simulating an elliptical acoustic cloak. The results indicate that the proposed multi-origin coordinate transformation method has a better cloaking effect on the incident wave along the ellipse minor axis direction than the traditional method. This means that for the same object, an appropriate transformation scheme can be selected for different incident wave directions to achieve the optimal control effect. The validated scheme is further used to design an arch-shaped cloak composed of an upper semicircular area and a lower rectangular area, by combining the traditional single-centered coordinate transformation method for the semicircular area and the proposed multi-origin method for the rectangular area. The results show that the designed cloak can effectively control the wave propagation with significantly reduced acoustic pressure level. This work provides a flexible acoustic cloak design method applicable for arbitrary shapes and different wave incident directions, enriching the theory of acoustic cloaking based on coordinate transformation.

Investigation on two-phase flow-induced vibrations of a piping structure with an elbow

Heng SU, Yegao QU, Guoxu WANG, Zhike PENG

2022, 43(11):  1657-1674.  doi:10.1007/s10483-022-2916-6

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The dynamic behaviors of a horizontal piping structure with an elbow due to the two-phase flow excitation are experimentally investigated. The effects of flow patterns and superficial velocities on the pressure pulsations and vibration responses are evaluated in detail. A strong partition coupling algorithm is used to calculate the flow-induced vibration (FIV) responses of the pipe, and the theoretical values agree well with the experimental results. It is found that the lateral and axial vibration responses of the bend pipe are related to the momentum flux of the two-phase flow, and the vibration amplitudes of the pipe increase with an increase in the liquid mass flux. The vertical vibration responses are strongly affected by the flow pattern, and the maximum response occurs in the transition region from the slug flow to the bubbly flow. Moreover, the standard deviation (STD) amplitudes of the pipe vibration in three directions increase with an increase in the gas flux for both the slug and bubbly flows. The blockage of liquid slugs at the elbow section is found to strengthen the vibration amplitude of the bend pipe, and the water-blocking phenomenon disappears as the superficial gas velocity increases.

Rational design of thermoelastic damping in microresonators with phase-lagging heat conduction law

Yu FU, Li LI, Hongfang CHEN, Xuelin WANG, Ling LING, Yujin HU

2022, 43(11):  1675-1690.  doi:10.1007/s10483-022-2914-5

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The design of thermoelastic damping (TED) affected by the phase-lagging non-Fourier heat conduction effects becomes significant but challenging for enlarging the quality factor of widely-used microresonators operating in extreme situations, including ultra-high excitation frequency and ultra-low working temperature. However, there does not exist a rational method for designing the TED in the framework of non-Fourier heat conduction law. This work, therefore, proposes a design framework to achieve low thermoelastic dissipation of microresonators governed by the phase-lagging heat conduction law. The equation of motion and the heat conduction equation for phase-lagging TED microresonators are derived first, and then the non-Fourier TED design problem is proposed. A topology optimization-based rational design method is used to resolve the design problem. What is more, a two-dimensional (2D) plain-strain-based finite element method (FEM) is developed as a solver for the topology optimization process. Based on the suggested rational design technique, numerical instances with various phase lags are investigated. The results show that the proposed design method can remarkably reduce the dissipation of microresonators by tailoring their substructures.

Thermoelectric field for a coated hole of arbitrary shape in a nonlinearly coupled thermoelectric material

Xu WANG, P. SCHIAVONE

2022, 43(11):  1691-1700.  doi:10.1007/s10483-022-2924-7

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We study the thermoelectric field for an electrically and thermally insulated coated hole of arbitrary shape embedded in an infinite nonlinearly coupled thermoelectric material subject to uniform remote electric current density and uniform remote energy flux. A conformal mapping function for the coating and matrix is introduced, which simultaneously maps the hole boundary and the coating-matrix interface onto two concentric circles in the image plane. Using analytic continuation, we derive a general solution in terms of two auxiliary functions. The general solution satisfies the insulating conditions along the hole boundary and all of the continuity conditions across the perfect coating-matrix interface. Once the two auxiliary functions have been obtained in the elementary-form, the four original analytic functions in the coating and matrix characterizing the thermoelectric fields are completely and explicitly determined. The design of a neutral coated circular hole that does not disturb the prescribed thermoelectric field in the thermoelectric matrix is achieved when the relative thickness parameter and the two mismatch parameters satisfy a simple condition. Finally, the neutrality of a coated circular thermoelectric inhomogeneity is also accomplished.

Effective property of piezoelectric composites containing coated nano-elliptical fibers with interfacial debonding

Yu CHEN, Junhong GUO

2022, 43(11):  1701-1716.  doi:10.1007/s10483-022-2918-9

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Based on both the spring layer interface model and the Gurtin-Murdoch surface/interface model, the anti-plane shear problem is studied for piezoelectric composites containing coated nano-elliptical fibers with imperfect interfaces. By using the complex function method and the technique of conformal mapping, the exact solutions of the electroelastic fields in fiber, coating, and matrix of piezoelectric nanocomposites are derived under far-field anti-plane mechanical and in-plane electrical loads. Furthermore, the generalized self-consistent method is used to accurately predict the effective electroelastic moduli of the piezoelectric nanocomposites containing coated nano-elliptical fibers with imperfect interfaces. Numerical examples are illustrated to show the effects of the material constants of the imperfect interface layers, the aspect ratio of the fiber section, and the fiber volume fraction on the effective electroelastic moduli of the piezoelectric nanocomposites. The results indicate that the effective electroelastic moduli of the piezoelectric nanocomposites can be significantly reduced by the interfacial debonding, but it can be improved by the surface/interface stresses at the small scale, which provides important theoretical reference for the design and optimization of piezoelectric nanodevices and nanostructures.

A novel physics-informed framework for reconstruction of structural defects

Qi LI, Fushun LIU, Bin WANG, D. Z. LIU, Zhenghua QIAN

2022, 43(11):  1717-1730.  doi:10.1007/s10483-022-2912-6

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The ultrasonic guided wave technology plays a significant role in the field of non-destructive testing as it employs acoustic waves with the advantages of high propagation efficiency and low energy consumption during the inspect process. However, the theoretical solutions to guided wave scattering problems with assumptions such as the Born approximation have led to the poor quality of the reconstructed results. Besides, the scattering signals collected from industry sectors are often noised and nonstationary. To address these issues, a novel physics-informed framework (PIF) for the quantitative reconstruction of defects by means of the integration of the data-driven method with the guided wave scattering analysis is proposed in this paper. Based on the geometrical information of defects and initial results obtained by the PIF-based analysis of defect reconstructions, a deep-learning neural network model is built to reveal the physical relationship between the defects and the noisy detection signals. This learning model is then adopted to assess and characterize the defect profiles in structures, improve the accuracy of the analytical model, and eliminate the impact of the noise pollution in the process of inspection. To demonstrate the advantages of the developed PIF for the complex defect reconstructions with the capability of denoising, several numerical examples are carried out. The results show that the PIF has greater accuracy for the reconstruction of defects in the structures than the analytical method, and provides a valuable insight into the development of artificial intelligence (AI)-assisted inspection systems with high accuracy and efficiency in the fields of structural integrity and condition monitoring.

Nonsmooth dynamic analysis of rigid-flexible interaction collision

Ling TAO, Zhongpan LI, Yan LI, Huijian CHEN, Zhiqiang FENG

2022, 43(11):  1731-1746.  doi:10.1007/s10483-022-2922-9

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This paper aims to explore the deformation of the collided bodies in multibody systems and to effectively simulate the motion path of colliding bodies. First, we describe the geometrically nonlinear problems of materials by the total Lagrangian formulation. Second, a first-order integration scheme is used to solve the dynamics equations. An algorithm combining the bi-potential method with the node-to-point contact identification is proposed to solve the interface problems of rigid-flexible interaction collision. To observe the collision process more intuitively, the internal software FER/VIEW is introduced to visualize the results. The accuracy is proved by comparing the proposed method with the analytical solution or another numerical solution. Moreover, the proposed method has more numerical robustness, such as occupying less computer storage, saving the computational cost, and broadening the application range of the bi-potential method.

Multiplicity-induced optimal gains of an inverted pendulum system under a delayed proportional-derivative-acceleration feedback

Zisong MEI, Zaihua WANG

2022, 43(11):  1747-1762.  doi:10.1007/s10483-022-2921-8

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This paper studies the stabilization to an inverted pendulum under a delayed proportional-derivative-acceleration (PDA) feedback, which can be used to understand human balance in quiet standing. The closed-loop system is described by a neutral delay differential equation (NDDE). The optimal feedback gains (OFGs) that make the exponential decaying rate maximized are determined when the characteristic equation of the closed-loop has a repeated real root with multiplicity 4. Such a property is called multiplicity-induced dominancy of time-delay systems, and has been discussed intensively by many authors for retarded delay differential equations (RDDEs). This paper shows that multiplicity-induced dominancy can be achieved in NDDEs. In addition, the OFGs are delay-dependent, and decrease sharply to small numbers correspondingly as the delay increases from zero and varies slowly with respect to moderate delays. Thus, the inverted pendulum can be well-stabilized with moderate delays and relatively small feedback gains. The result might be understandable that the elderly with obvious response delays can be well-stabilized with a delayed PDA feedback controller.

Numerical study of opposed zero-net-mass-flow jet-induced erythrocyte mechanoporation

Xinyue LIU, Jinfang AI, Jun XIE, Guohui HU

2022, 43(11):  1763-1776.  doi:10.1007/s10483-022-2931-6

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With the advantages of biosafety and efficiency, increasing attention has been paid to the devices for gene and macromolecular drug delivery based on mechanoporation. The transient pore formation on the cell membrane allows cargo transportation when the membrane areal strain is beyond the critical pore value and below the lysis tension threshold. Based on this principle, we propose a method to apply the proper fluid stress on cells moving in a microchannel under the action of zero-net-mass-flux (ZNMF) jets. In this study, an immersed finite element method (IFEM) is adopted to simulate the interaction between the cells and the fluid fields so as to investigate the cell movement and deformation in this mechanoporation system. To evaluate the efficiency of the cargo delivery, a pore integral is defined as the mean pore rate when the cell passes through the jet region. By analyzing the effects of the parameters, including the pressure gradient along the microchannel, the jet amplitude, and the jet frequency, on the pore integrals, a group of optimized parameters for cargo delivery efficiency are obtained. Additionally, the stability and safety of this system are analyzed in detail. These results are helpful in designing the mechanoporation devices and improving their efficiency of drug delivery.

Global weak solutions to a phase-field model for motion of grain boundaries

Zixian ZHU, Boling GUO, Shaomei FANG

2022, 43(11):  1777-1792.  doi:10.1007/s10483-022-2915-9

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We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational forces. The higher-order derivative of unknown S exists in the sense of local weak derivatives since it may be not summable over the original open domain. The existence proof is valid in the one-dimensional case.