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2023年 第44卷 第1期    刊出日期：2023-01-01

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论文

Reconfigurable metamaterial for asymmetric and symmetric elastic wave absorption based on exceptional point in resonant bandgap

Jianlin YI, Zheng WU, Rongyu XIA, Zheng LI

2023, 44(1):  1-20.  doi:10.1007/s10483-023-2949-7

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Elastic wave absorption at subwavelength scale is of significance in many engineering applications. Non-Hermitian metamaterials show the ability in high-efficiency wave absorption. However, the single functionality of metamaterials is an important limitation on their practical applications for lack of tunability and reconfigurability. Here, we propose a tunable and reconfigurable non-Hermitian piezoelectric metamaterial bar, in which piezoelectric bars connect with resonant circuits, to achieve asymmetric unidirectional perfect absorption (UPA) and symmetric bidirectional perfect absorption (PA) at low frequencies. The two functions can be arbitrarily switched by rearranging shunted circuits. Based on the reverberation-ray matrix (RRM) method, an approach is provided to achieve UPA by setting an exceptional point (EP) in the coupled resonant bandgap. By using the transfer matrix method (TMM) and the finite element method (FEM), it is observed that a non-Hermitian pseudo-band forms between two resonant bandgaps, and the EP appears at the bottom of the pseudo-band. In addition, the genetic algorithm is used to accurately and efficiently design the shunted circuits for desired low-frequency UPA and PA. The present work may provide new strategies for vibration suppression and guided waves manipulation in wide potential applications.



Size effects on the mixed modes and defect modes for a nano-scale phononic crystal slab

Jun JIN, Ningdong HU, Hongping HU

2023, 44(1):  21-34.  doi:10.1007/s10483-023-2945-6

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The size-dependent band structure of an Si phononic crystal (PnC) slab with an air hole is studied by utilizing the non-classic wave equations of the nonlocal strain gradient theory (NSGT). The three-dimensional (3D) non-classic wave equations for the anisotropic material are derived according to the differential form of the NSGT. Based on the the general form of partial differential equation modules in COMSOL, a method is proposed to solve the non-classic wave equations. The bands of the in-plane modes and mixed modes are identified. The in-plane size effect and thickness effect on the band structure of the PnC slab are compared. It is found that the thickness effect only acts on the mixed modes. The relative width of the band gap is widened by the thickness effect. The effects of the geometric parameters on the thickness effect of the mixed modes are further studied, and a defect is introduced to the PnC supercell to reveal the influence of the size effects with stiffness-softening and stiffness-hardening on the defect modes. This study paves the way for studying and designing PnC slabs at nano-scale.

Wave propagation analysis of porous functionally graded piezoelectric nanoplates with a visco-Pasternak foundation

Zhaonian LI, Juan LIU, Biao HU, Yuxing WANG, Huoming SHEN

2023, 44(1):  35-52.  doi:10.1007/s10483-023-2953-7

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This study investigates the size-dependent wave propagation behaviors under the thermoelectric loads of porous functionally graded piezoelectric (FGP) nanoplates deposited in a viscoelastic foundation. It is assumed that (i) the material parameters of the nanoplates obey a power-law variation in thickness and (ii) the uniform porosity exists in the nanoplates. The combined effects of viscoelasticity and shear deformation are considered by using the Kelvin-Voigt viscoelastic model and the refined higher-order shear deformation theory. The scale effects of the nanoplates are captured by employing nonlocal strain gradient theory (NSGT). The motion equations are calculated in accordance with Hamilton’s principle. Finally, the dispersion characteristics of the nanoplates are numerically determined by using a harmonic solution. The results indicate that the nonlocal parameters (NLPs) and length scale parameters (LSPs) have exactly the opposite effects on the wave frequency. In addition, it is found that the effect of porosity volume fractions (PVFs) on the wave frequency depends on the gradient indices and damping coefficients. When these two values are small, the wave frequency increases with the volume fraction. By contrast, at larger gradient index and damping coefficient values, the wave frequency decreases as the volume fraction increases.

Three-dimensional general magneto-electro-elastic finite element model for multiphysics nonlinear analysis of layered composites

Zheng GONG, Yinxiao ZHANG, Ernian PAN, Chao ZHANG

2023, 44(1):  53-72.  doi:10.1007/s10483-023-2943-8

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In this paper, by defining a general potential energy for the multiphase coupled multiferroics and applying the minimum energy principle, the coupled governing equations are derived. This system of equations is then discretized as a general three-dimensional (3D) finite element (FE) model based on the COMSOL software. After validating the formulation, it is then applied to the analysis and design of the common sandwich structure of multiferroics composites. Under the typical static loading, the effects of general lateral boundary conditions, material grading, nonlinearity, as well as polarization orientation on the composites are analyzed. For the magneto-electro-elastic (MEE) sandwich made of piezoelectric BaTiO₃ and magnetostrictive CoFe₂O₄ with different stacking sequences, various interesting features are observed which should be very helpful for the design of high-performance multiphase composites.

An investigation on multilayer shape memory polymers under finite bending through nonlinear thermo-visco-hyperelasticity

A. BAKHTIYARI, M. BAGHANI, S. SOHRABPOUR

2023, 44(1):  73-88.  doi:10.1007/s10483-023-2952-6

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This study presents a semi-analytical solution to describe the behavior of shape memory polymers (SMPs) based on the nonlinear thermo-visco-hyperelasticity which originates from the concepts of internal state variables and rational thermodynamics. This method is developed for the finite bending of multilayers in a dual-shape memory effect (SME) cycle. The layer number and layering order are investigated for two different SMPs and a hyperelastic material. In addition to the semi-analytical solution, the finite element simulation is performed to verify the predicted results, where the outcomes demonstrate the excellent accuracy of the proposed solution for predicting the behavior of the multilayer SMPs. Since this method has a much lower computational cost than the finite element method (FEM), it can be used as an effective tool to analyze the SMP behavior under different conditions, including different materials, different geometries, different layer numbers, and different layer arrangements.

Unified two-phase nonlocal formulation for vibration of functionally graded beams resting on nonlocal viscoelastic Winkler-Pasternak foundation

Pei ZHANG, P. SCHIAVONE, Hai QING

2023, 44(1):  89-108.  doi:10.1007/s10483-023-2948-9

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A nonlocal study of the vibration responses of functionally graded (FG) beams supported by a viscoelastic Winkler-Pasternak foundation is presented. The damping responses of both the Winkler and Pasternak layers of the foundation are considered in the formulation, which were not considered in most literature on this subject, and the bending deformation of the beams and the elastic and damping responses of the foundation as nonlocal by uniting the equivalently differential formulation of well-posed strain-driven (ε-D) and stress-driven (σ-D) two-phase local/nonlocal integral models with constitutive constraints are comprehensively considered, which can address both the stiffness softening and toughing effects due to scale reduction. The generalized differential quadrature method (GDQM) is used to solve the complex eigenvalue problem. After verifying the solution procedure, a series of benchmark results for the vibration frequency of different bounded FG beams supported by the foundation are obtained. Subsequently, the effects of the nonlocality of the foundation on the undamped/damping vibration frequency of the beams are examined.

Free vibration of thermo-elastic microplate based on spatiotemporal fractional-order derivatives with nonlocal characteristic length and time

Lingkang ZHAO, Peijun WEI, Yueqiu LI

2023, 44(1):  109-124.  doi:10.1007/s10483-023-2933-8

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A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the free vibration of a higher-order shear microplate. The nonlocal strain gradient theory is modified with the introduction of the fractional-order derivatives and the nonlocal characteristic length. The Fourier heat conduction is replaced by the non-Fourier heat conduction with the introduction of the fractional order and the memory characteristic time. Numerical calculations are performed to analyze the effects of the nonlocal strain gradient parameters, the spatiotemporal fractional order, the nonlocal characteristic length, and the memory characteristic time on the natural frequencies, the vibration attenuation, and the phase shift between the temperature field and the displacement field. The numerical results show that the new thermo-elastic model with the spatiotemporal fractional order can provide more exquisite descriptions of the thermo-elastic behavior at a small scale.

Nonlinear coupling modeling and dynamics analysis of rotating flexible beams with stretching deformation effect

Xiaokang DU, Yuanzhao CHEN, Jing ZHANG, Xian GUO, Liang LI, Dingguo ZHANG

2023, 44(1):  125-140.  doi:10.1007/s10483-023-2951-9

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Dynamic coupling modeling and analysis of rotating beams based on the nonlinear Green-Lagrangian strain are introduced in this work. With the reservation of the axial nonlinear strain, there are more coupling terms for axial and transverse deformations. The discretized dynamic governing equations are obtained by using the finite element method and Lagrange’s equations of the second kind. Time responses are conducted to compare the proposed model with other previous models. The stretching deformation due to rotating motion is observed and calculated by special formulations under dynamic equilibrium. The stretching deformation and the change of the associated equilibrium position are taken into account to analyze the free vibration and frequency response of the rotating beams. Analytical and numerical comparisons show that the proposed model can provide reliable results, while the previous models may lead to imprecise results, especially in high-speed conditions.

Effects of viscoelasticity on the stability and bifurcations of nonlinear energy sinks

A. MOSLEMI, M. R. HOMAEINEZHAD

2023, 44(1):  141-158.  doi:10.1007/s10483-023-2944-9

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Due to the increasing use of passive absorbers to control unwanted vibrations, many studies have been done on energy absorbers ideally, but the lack of studies of real environmental conditions on these absorbers is felt. The present work investigates the effect of viscoelasticity on the stability and bifurcations of a system attached to a nonlinear energy sink (NES). In this paper, the Burgers model is assumed for the viscoelasticity in an NES, and a linear oscillator system is considered for investigating the instabilities and bifurcations. The equations of motion of the coupled system are solved by using the harmonic balance and pseudo-arc-length continuation methods. The results show that the viscoelasticity affects the frequency intervals of the Hopf and saddle-node branches, and by increasing the stiffness parameters of the viscoelasticity, the conditions of these branches occur in larger ranges of the external force amplitudes, and also reduce the frequency range of the branches. In addition, increasing the viscoelastic damping parameter has the potential to completely eliminate the instability of the system and gradually reduce the amplitude of the jump phenomenon.

Data-driven optimization study of the multi-relaxation-time lattice Boltzmann method for solid-liquid phase change

Yanlin REN, Zhaomiao LIU, Zixiao KANG, Yan PANG

2023, 44(1):  159-172.  doi:10.1007/s10483-023-2946-7

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Sharp phase interfaces and accurate temperature distributions are important criteria in the simulation of solid-liquid phase changes. The multi-relaxation-time lattice Boltzmann method (MRT-LBM) shows great numerical performance during simulation; however, the value method of the relaxation parameters needs to be specified. Therefore, in this study, a random forest (RF) model is used to discriminate the importance of different relaxation parameters to the convergence, and a support vector machine (SVM) is used to explore the decision boundary of the convergent samples in each dimensional model. The results show that the convergence of the samples is consistent with the sign of the decision number, and two types of the numerical deviations appear, i.e., the phase mushy zone and the non-physical heat transfer. The relaxation parameters chosen on the decision boundary can further suppress the numerical bias and improve numerical accuracy.