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2023年 第44卷 第10期    刊出日期：2023-10-01

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论文

Effects of time-delayed vibration absorber on bandwidth of beam for low broadband vibration suppression

Xiuting SUN, Yipeng QU, Feng WANG, Jian XU

2023, 44(10):  1629-1650.  doi:10.1007/s10483-023-3038-6

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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.



On complete and micropolar-based incomplete strain gradient theories for periodic lattice structures

Zeyang CHI, Jinxing LIU, A. K. SOH

2023, 44(10):  1651-1674.  doi:10.1007/s10483-023-3033-9

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The micropolar (MP) and strain gradient (SG) continua have been generally adopted to investigate the relations between the macroscopic elastic constants and the microstructural geometric parameters. Owing to the fact that the microrotation in the MP theory can be expressed in terms of the displacement gradient components, we may regard the MP theory as a particular incomplete SG theory called the MPSG theory, compared with the existing SG theories which are deemed complete since all the SGs are included. Taking the triangular lattice comprising zigzag beams as an example, it is found that as the angle of the zigzag beams increases, the bending of the beams plays a more important role in the total strain energy, and the difference between the results by the two theories gradually decreases. Finally, the models are verified with the pure bending and simple shear of lattices by comparing with the results obtained by the finite element method (FEM)-based structure analyses.

The semi-analytical modeling and vibration reduction analysis of the cylindrical shell with piezoelectric shunt damping patches

Dongxu DU, Jun YANG, Wei SUN, Hongwei MA, Kunpeng XU

2023, 44(10):  1675-1700.  doi:10.1007/s10483-023-3034-7

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By considering electromechanical coupling, a unified dynamic model of the cylindrical shell with the piezoelectric shunt damping patch (PSDP) is created. The model is universal and can simulate the vibration characteristic of the shell under different states including the states in which PSDP cannot be connected, partially connected, and completely connected to the shunt circuit. The equivalent loss factor and elastic modulus with frequency dependence are proposed to consider the electrical damping effect of resistance shunt circuits. Moreover, the semi-analytical dynamic equation of the cylindrical shell with PSDP is derived by the Lagrange equation. An experimental test is carried out on the cylindrical shell with PSDP to verify the vibration suppression ability of PSDP on the cylindrical shell and the correctness of the proposed model. Furthermore, the parameter analysis shows that determining the appropriate resistance value in the shunt circuit can achieve a good vibration suppression effect.

Closed-form steady-state solutions for forced vibration of second-order axially moving systems

Jingming FAN, Bo CHEN, Yinghui LI

2023, 44(10):  1701-1720.  doi:10.1007/s10483-023-3035-5

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Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered. In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.

Vertical vibration control using nonlinear energy sink with inertial amplifier

Weixing ZHANG, Wei ZHANG, Xiangying GUO

2023, 44(10):  1721-1738.  doi:10.1007/s10483-023-3036-8

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To reduce additional mass, this work proposes a nonlinear energy sink (NES) with an inertial amplifier (NES-IA) to control the vertical vibration of the objects under harmonic and shock excitations. Moreover, this paper constructs pure nonlinear stiffness without neglecting the gravity effect of the oscillator. Both analytical and numerical methods are used to evaluate the performance of the NES-IA. The research findings indicate that even if the actual mass is 1% of the main oscillator, the NES-IA with proper inertia angles and mass distribution ratios can still effectively attenuate the steady-state and transient responses of the main oscillator. Nonlinear stiffness and damping also have important effects. Due to strongly nonlinear factors, the coupled system may exhibit higher branch responses under harmonic excitation. In shock excitation environment, the NES-IA with a large dynamic mass can trigger energy capture of both main resonance and high-frequency resonance. Furthermore, the comparison with the traditional NES also confirms the advantages of the NES-IA in overcoming mass dependence.

Nonlinear dynamic response and stability analysis of the stapes reconstruction in human middle ear

Lele WANG, Liang WANG, Yueting ZHU, Zhanli LIU, Yongtao SUN, Jie WANG, Hongge HAN, Shuyi XIANG, Huibin SHI, Qian DING

2023, 44(10):  1739-1760.  doi:10.1007/s10483-023-3037-9

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Stapes fracture causes hearing loss and instability in the middle ear hearing system (MEHS). The material used in the stapes reconstruction restores stapes, but the effects of the nonlinear material parameters on the stability of the MEHS are still unknown. To address this challenge, the nonlinear dynamic response and stability of the stapes reconstruction are investigated using a multi-degree-of-freedom mechanical model. The material parameters of the implant are tentatively determined by analyzing the natural frequencies of the undamped system. The dynamical properties of the MEHS are characterized under different external excitations. The approximate solution of the MEHS near the resonant frequency is derived through the multiple-time-scale method (MTSM). The results show that the nonlinear stiffness of the material has little influence on the MEHS in the healthy state, but it causes resonant phenomena between the ossicle and the implant in the pathological state.

Nonlinear free vibration of piezoelectric semiconductor doubly-curved shells based on nonlinear drift-diffusion model

Changsong ZHU, Xueqian FANG, Jinxi LIU

2023, 44(10):  1761-1776.  doi:10.1007/s10483-023-3039-7

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In this paper, the nonlinear free vibration behaviors of the piezoelectric semiconductor (PS) doubly-curved shell resting on the Pasternak foundation are studied within the framework of the nonlinear drift-diffusion (NLDD) model and the first-order shear deformation theory. The nonlinear constitutive relations are presented, and the strain energy, kinetic energy, and virtual work of the PS doubly-curved shell are derived. Based on Hamilton's principle as well as the condition of charge continuity, the nonlinear governing equations are achieved, and then these equations are solved by means of an efficient iteration method. Several numerical examples are given to show the effect of the nonlinear drift current, elastic foundation parameters as well as geometric parameters on the nonlinear vibration frequency, and the damping characteristic of the PS doubly-curved shell. The main innovations of the manuscript are that the difference between the linearized drift-diffusion (LDD) model and the NLDD model is revealed, and an effective method is proposed to select a proper initial electron concentration for the LDD model.

Differential flatness-based distributed control of underactuated robot swarms

Ningbo AN, Qishao WANG, Xiaochuan ZHAO, Qingyun WANG

2023, 44(10):  1777-1790.  doi:10.1007/s10483-023-3040-8

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This paper proposes a distributed control method based on the differential flatness (DF) property of robot swarms. The swarm DF mapping is established for underactuated differentially flat dynamics, according to the control objective. The DF mapping refers to the fact that the system state and input of each robot can be derived algebraically from the flat outputs of the leaders and the cooperative errors and their finite order derivatives. Based on the proposed swarm DF mapping, a distributed controller is designed. The distributed implementation of swarm DF mapping is achieved through observer design. The effectiveness of the proposed method is validated through a numerical simulation of quadrotor swarm synchronization.

Approximate solutions to fractional differential equations

Yue LIU, Zhen ZHAO, Yanni ZHANG, Jing PANG

2023, 44(10):  1791-1802.  doi:10.1007/s10483-023-3041-9

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In this paper, the time-fractional coupled viscous Burgers' equation (CVBE) and Drinfeld-Sokolov-Wilson equation (DSWE) are solved by the Sawi transform coupled homotopy perturbation method (HPM). The approximate series solutions to these two equations are obtained. Meanwhile, the absolute error between the approximate solution given in this paper and the exact solution given in the literature is analyzed. By comparison of the graphs of the function when the fractional order $\alpha$ takes different values, the properties of the equations are given as a conclusion.

Bending and wave propagation analysis of axially functionally graded beams based on a reformulated strain gradient elasticity theory

Shaopeng WANG, Jun HONG, Dao WEI, Gongye ZHANG

2023, 44(10):  1803-1820.  doi:10.1007/s10483-023-3042-6

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A new size-dependent axially functionally graded (AFG) micro-beam model is established with the application of a reformulated strain gradient elasticity theory (RSGET). The new micro-beam model incorporates the strain gradient, velocity gradient, and couple stress effects, and accounts for the material variation along the axial direction of the two-component functionally graded beam. The governing equations and complete boundary conditions of the AFG beam are derived based on Hamilton's principle. The correctness of the current model is verified by comparing the static behavior results of the current model and the finite element model (FEM) at the micro-scale. The influence of material inhomogeneity and size effect on the static and dynamic responses of the AFG beam is studied. The numerical results show that the static and vibration responses predicted by the newly developed model are different from those based on the classical model at the micro-scale. The new model can be applied not only in the optimization of micro acoustic wave devices but also in the design of AFG micro-sensors and micro-actuators.

Wave propagation responses of porous bi-directional functionally graded magneto-electro-elastic nanoshells via nonlocal strain gradient theory

Xinte WANG, Juan LIU, Biao HU, Bo ZHANG, Huoming SHEN

2023, 44(10):  1821-1840.  doi:10.1007/s10483-023-3043-7

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This study examines the wave propagation characteristics for a bi-directional functional grading of barium titanate (BaTiO$_{3}$) and cobalt ferrite (CoFe$_{2}$O$_{4}$) porous nanoshells, the porosity distribution of which is simulated by the honeycomb-shaped symmetrical and asymmetrical distribution functions. The nonlocal strain gradient theory (NSGT) and first-order shear deformation theory are used to determine the size effect and shear deformation, respectively. Nonlocal governing equations are derived for the nanoshells by Hamilton's principle. The resulting dimensionless differential equations are solved by means of an analytical solution of the combined exponential function after dimensionless treatment. Finally, extensive parametric surveys are conducted to investigate the influence of diverse parameters, such as dimensionless scale parameters, radius-to-thickness ratios, bi-directional functionally graded (FG) indices, porosity coefficients, and dimensionless electromagnetic potentials on the wave propagation characteristics. Based on the analysis results, the effect of the dimensionless scale parameters on the dispersion relationship is found to be related to the ratio of the scale parameters. The wave propagation characteristics of nanoshells in the presence of a magnetoelectric field depend on the bi-directional FG indices.