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2023年 第44卷 第8期    刊出日期：2023-08-01

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论文

Dynamic modeling of fluid-conveying pipes restrained by a retaining clip

Bo DOU, Hu DING, Xiaoye MAO, Sha WEI, Liqun CHEN

2023, 44(8):  1225-1240.  doi:10.1007/s10483-023-3016-9

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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.



Flexural-wave-generation using a phononic crystal with a piezoelectric defect

S. H. JO, D. LEE

2023, 44(8):  1241-1262.  doi:10.1007/s10483-023-3015-7

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This paper proposes a method to amplify the performance of a flexuralwave-generation system by utilizing the energy-localization characteristics of a phononic crystal (PnC) with a piezoelectric defect and an analytical approach that accelerates the predictions of such wave-generation performance. The proposed analytical model is based on the Euler-Bernoulli beam theory. The proposed analytical approach, inspired by the transfer matrix and S-parameter methods, is used to perform band-structure and timeharmonic analyses. A comparison of the results of the proposed approach with those of the finite element method validates the high predictive capability and time efficiency of the proposed model. A case study is explored; the results demonstrate an almost ten-fold amplification of the velocity amplitudes of flexural waves leaving at a defectband frequency, compared with a system without the PnC. Moreover, design guidelines for piezoelectric-defect-introduced PnCs are provided by analyzing the changes in wavegeneration performance that arise depending on the defect location.

A bio-inspired spider-like structure isolator for low-frequency vibration

Guangdong SUI, Shuai HOU, Xiaofan ZHANG, Xiaobiao SHAN, Chengwei HOU, Henan SONG, Weijie HOU, Jianming LI

2023, 44(8):  1263-1286.  doi:10.1007/s10483-023-3020-9

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This paper proposes a quasi-zero stiffness (QZS) isolator composed of a curved beam (as spider foot) and a linear spring (as spider muscle) inspired by the precise capturing ability of spiders in vibrating environments. The curved beam is simplified as an inclined horizontal spring, and a static analysis is carried out to explore the effects of different structural parameters on the stiffness performance of the QZS isolator. The finite element simulation analysis verifies that the QZS isolator can significantly reduce the first-order natural frequency under the load in the QZS region. The harmonic balance method (HBM) is used to explore the effects of the excitation amplitude, damping ratio, and stiffness coefficient on the system’s amplitude-frequency response and transmissibility performance, and the accuracy of the analytical results is verified by the fourth-order Runge-Kutta integral method (RK-4). The experimental data of the QZS isolator prototype are fitted to a ninth-degree polynomial, and the RK-4 can theoretically predict the experimental results. The experimental results show that the QZS isolator has a lower initial isolation frequency and a wider isolation frequency bandwidth than the equivalent linear isolator. The frequency sweep test of prototypes with different harmonic excitation amplitudes shows that the initial isolation frequency of the QZS isolator is 3 Hz, and it can isolate 90% of the excitation signal at 7 Hz. The proposed biomimetic spider-like QZS isolator has high application prospects and can provide a reference for optimizing low-frequency or ultra-low-frequency isolators.

Theoretical analysis of surface waves in piezoelectric medium with periodic shunting circuits

Youqi ZHANG, Rongyu XIA, Jie XU, Kefu HUANG, Zheng LI

2023, 44(8):  1287-1304.  doi:10.1007/s10483-023-3011-7

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The investigations of surface waves in the piezoelectric medium bring out great possibility in designing smart surface acoustic wave (SAW) devices. It is important to study the dispersion properties and manipulation mechanism of surface waves in the semi-infinite piezoelectric medium connected with periodic arrangement of shunting circuits. In this study, the extended Stroh formalism is developed to theoretically analyze the dispersion relations of surface waves under different external circuits. The band structures of both the Rayleigh wave and the Bleustein-Gulyaev (BG) wave can be determined and manipulated with proper electrical boundary conditions. Furthermore, the electromechanical coupling effects on the band structures of surface waves are discussed to figure out the manipulation mechanism of adjusting electric circuit. The results indicate that the proposed method can explain the propagation behaviors of surface waves under the periodic electrical boundary conditions, and can provide an important theoretical guidance for designing novel SAW devices and exploring extensive applications in practice.

A symplectic finite element method based on Galerkin discretization for solving linear systems

Zhiping QIU, Zhao WANG, Bo ZHU

2023, 44(8):  1305-1316.  doi:10.1007/s10483-023-3012-5

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We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems. For the dynamic responses of continuous medium structures, the traditional numerical algorithm is the dissipative algorithm and cannot maintain long-term energy conservation. Thus, a symplectic finite element method with energy conservation is constructed in this paper. A linear elastic system can be discretized into multiple elements, and a Hamiltonian system of each element can be constructed. The single element is discretized by the Galerkin method, and then the Hamiltonian system is constructed into the Birkhoffian system. Finally, all the elements are combined to obtain the vibration equation of the continuous system and solved by the symplectic difference scheme. Through the numerical experiments of the vibration response of the Bernoulli-Euler beam and composite plate, it is found that the vibration response solution and energy obtained with the algorithm are superior to those of the Runge-Kutta algorithm. The results show that the symplectic finite element method can keep energy conservation for a long time and has higher stability in solving the dynamic responses of linear elastic systems.

Adaptive enhancement design of triply periodic minimal surface lattice structure based on non-uniform stress distribution

Yijin ZHANG, Bin LIU, Fei PENG, Heran JIA, Zeang ZHAO, Shengyu DUAN, Panding WANG, Hongshuai LEI

2023, 44(8):  1317-1330.  doi:10.1007/s10483-023-3013-9

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The Schwarz primitive triply periodic minimal surface (P-type TPMS) lattice structures are widely used. However, these lattice structures have weak load-bearing capacity compared with other cellular structures. In this paper, an adaptive enhancement design method based on the non-uniform stress distribution in structures with uniform thickness is proposed to design the P-type TPMS lattice structures with higher mechanical properties. Two types of structures are designed by adjusting the adaptive thickness distribution in the TPMS. One keeps the same relative density, and the other keeps the same of non-enhanced region thickness. Compared with the uniform lattice structure, the elastic modulus for the structure with the same relative density increases by more than 17%, and the yield strength increases by more than 10.2%. Three kinds of TPMS lattice structures are fabricated by laser powder bed fusion (L-PBF) with 316L stainless steel to verify the proposed enhanced design. The manufacture-induced geometric deviation between the as-design and as-printed models is measured by micro X-ray computed tomography (μ-CT) scans. The quasi-static compression experimental results of P-type TPMS lattice structures show that the reinforced structures have stronger elastic moduli, ultimate strengths, and energy absorption capabilities than the homogeneous P-TPMS lattice structure.

Analytic solution of quasicrystal microsphere considering the thermoelectric effect and surface effect in the elastic matrix

Yunzhi HUANG, Wenqing ZHENG, Xiuhua CHEN, Miaolin FENG

2023, 44(8):  1331-1350.  doi:10.1007/s10483-023-3018-5

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The incorporation of the quasicrystalline phase into the metal matrix offers a wide range of potential applications in particle-reinforced metal-matrix composites. The analytic solution of the piezoelectric quasicrystal (QC) microsphere considering the thermoelectric effect and surface effect contained in the elastic matrix is presented in this study. The governing equations for the QC microsphere in the matrix subject to the external electric loading are derived based on the nonlocal elastic theory, electro-elastic interface theory, and eigenvalue method. A comparison between the existing results and the finite-element simulation validates the present approach. Numerical examples reveal the effects of temperature variation, nonlocal parameters, surface properties, elastic coefficients, and phason coefficients on the phonon, phason, and electric fields. The results indicate that the QC microsphere enhances the mechanical properties of the matrix. The results are useful for the design and understanding of the characterization of QCs in micro-structures.

Multi-field coupling and free vibration of a sandwiched functionally-graded piezoelectric semiconductor plate

Xueqian FANG, Qilin HE, Hongwei MA, Changsong ZHU

2023, 44(8):  1351-1366.  doi:10.1007/s10483-023-3017-6

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Sandwiched functionally-graded piezoelectric semiconductor (FGPS) plates possess high strength and excellent piezoelectric and semiconductor properties, and have significant potential applications in micro-electro-mechanical systems. The multi-field coupling and free vibration of a sandwiched FGPS plate are studied, and the governing equation and natural frequency are derived with the consideration of electron movement. The material properties in the functionally-graded layers are assumed to vary smoothly, and the first-order shear deformation theory is introduced to derive the multi-field coupling in the plate. The total strain energy of the plate is obtained, and the governing equations are presented by using Hamilton’s principle. By introducing the boundary conditions, the coupling physical fields are solved. In numerical examples, the natural frequencies of sandwiched FGPS plates under different geometrical and physical parameters are discussed. It is found that the initial electron density can be used to modulate the natural frequencies and vibrational displacement of sandwiched FGPS plates in the case of nano-size. The effects of the material properties of FGPS layers on the natural frequencies are also examined in detail.

Finite deformation analysis of the rotating cylindrical hollow disk composed of functionally-graded incompressible hyper-elastic material

Libiao XIN, Yang WANG, Zhiqiang LI, Y. B. LI

2023, 44(8):  1367-1384.  doi:10.1007/s10483-023-3014-6

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The deformations and stresses of a rotating cylindrical hollow disk made of incompressible functionally-graded hyper-elastic material are theoretically analyzed based on the finite elasticity theory. The hyper-elastic material is described by a new micro-macro transition model. Specially, the material shear modulus and density are assumed to be a function with a power law form through the radial direction, while the material inhomogeneity is thus reflected on the power index m. The integral forms of the stretches and stress components are obtained. With the obtained complicated integral forms, the composite trapezoidal rule is utilized to derive the analytical solutions, and the explicit solutions for both the stretches and the stress components are numerically obtained. By comparing the results with two classic models, the superiority of the model in our work is demonstrated. Then, the distributions of the stretches and normalized stress components are discussed in detail under the effects of m. The results indicate that the material inhomogeneity and the rotating angular velocity have significant effects on the distributions of the normalized radial and hoop stress components and the stretches. We believe that by appropriately choosing the material inhomogeneity and configuration parameters, the functionally-graded material (FGM) hyper-elastic hollow cylindrical disk can be designed to meet some unique requirements in the application fields, e.g., soft robotics, medical devices, and conventional aerospace and mechanical industries.

Analysis of fracture propagation and shale gas production by intensive volume fracturing

Qingdong ZENG, Long BO, Lijun LIU, Xuelong LI, Jianmeng SUN, Zhaoqin HUANG, Jun YAO

2023, 44(8):  1385-1408.  doi:10.1007/s10483-023-3021-6

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This paper presents an integrated study from fracture propagation modeling to gas flow modeling and a correlation analysis to explore the key controlling factors of intensive volume fracturing. The fracture propagation model takes into account the interaction between hydraulic fracture and natural fracture by means of the displacement discontinuity method (DDM) and the Picard iterative method. The shale gas flow considers multiple transport mechanisms, and the flow in the fracture network is handled by the embedded discrete fracture model (EDFM). A series of numerical simulations are conducted to analyze the effects of the cluster number, stage spacing, stress difference coefficient, and natural fracture distribution on the stimulated fracture area, fractal dimension, and cumulative gas production, and their correlation coefficients are obtained. The results show that the most influential factors to the stimulated fracture area are the stress difference ratio, stage spacing, and natural fracture density, while those to the cumulative gas production are the stress difference ratio, natural fracture density, and cluster number. This indicates that the stress condition dominates the gas production, and employing intensive volume fracturing (by properly increasing the cluster number) is beneficial for improving the final cumulative gas production.

Partial wetting of the soft elastic graded substrate due to elastocapillary deformation

Xu WANG, Hailiang MA, Yonglin YANG, Xing LI, Yueting ZHOU

2023, 44(8):  1409-1422.  doi:10.1007/s10483-023-3019-8

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Surface tension plays a central role in the mechanical behavior of soft materials such as gels. Elastocapillary deformation of elastic graded substrates is ubiquitous in soft materials. In this work, the effect of a partially wetting sessile liquid droplet on the elastocapillary deformation of a soft elastic graded substrate is studied. The modulus is assumed to have an exponential form along the thickness direction. By applying the Fourier transformation, a mixed boundary-value problem is reduced into a dual integral equation. The numerical results show that the surface displacement is strongly affected by the inhomogeneity of the material. The study of the wetting properties of gel substrates is essential for both understanding the wetting phenomena of gels and developing gels for applications as soft actuators and sensors that can be used in wearable electronics and soft robotics.