Table of Content

01 August 2022, Volume 43 Issue 8

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Articles

Tunable low frequency band gaps and sound transmission loss of a lever-type metamaterial plate

Wenzheng QUE, Xiaodong YANG, Wei ZHANG

2022, 43(8):  1145-1158.  doi:10.1007/s10483-022-2890-9

Abstract ( 1265 )   HTML ( 49)   PDF (4633KB) ( 207 )  

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A novel metamaterial plate with subwavelength lever-type resonators is proposed to obtain low frequency broadband band gaps and good sound insulation performance. The band structure is theoretically derived, and the validity of the theoretical method is verified by the finite element method. The formation mechanisms of the band gaps are illustrated by the analysis of the effective dynamic mass density and group velocity. The effect of the lever ratio on the band gaps is analyzed. The results indicate that as the lever ratio increases, the first band gap shifts to lower frequencies, while the bandwidth is widened. Moreover, the sound insulation performance of the proposed metamaterial plate is evaluated via examining the sound transmission loss (STL). Compared with the metamaterial plates without lever accessories, the proposed metamaterial plates with a suitable lever ratio have better sound insulation performance at low frequencies.

Snap-through path in a bistable dielectric elastomer actuator

Wenjie SUN, Wentao MA, Fei ZHANG, Wei HONG, Bo LI

2022, 43(8):  1159-1170.  doi:10.1007/s10483-022-2888-6

Abstract ( 1176 )   HTML ( 8)   PDF (3586KB) ( 118 )  

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The dielectric elastomer (DE) has attracted significant attention due to its desired features, including large deformation, fast response, and high energy density. However, for a DE actuator (DEA) utilizing a snap-through deformation mode, most existing theoretical models fail to predict its deformation path. This paper develops a new finite element method (FEM) based on the three-parameter Gent-Gent model suitable for capturing strain-stiffening behaviors. The simulation results are verified by experiments, indicating that the FEM can accurately characterize the snap-through path of a DE. The method proposed in this paper provides theoretical guidance and inspiration for designing and applying DEs and bistable electroactive actuators.

Interaction between bending and mobile charges in a piezoelectric semiconductor bimorph

Lei YANG, Jianke DU, J. S. YANG

2022, 43(8):  1171-1186.  doi:10.1007/s10483-022-2889-7

Abstract ( 1120 )   HTML ( 6)   PDF (846KB) ( 141 )  

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We study the bending of a two-layer piezoelectric semiconductor plate (bimorph). The macroscopic theory of piezoelectric semiconductors is employed. A set of two-dimensional plate equations is derived from the three-dimensional equations. The plate equations exhibit direct couplings among bending, electric polarization along the plate thickness, and mobile charges. In the case of pure bending, a combination of physical and geometric parameters is identified which characterizes the strength of the interaction between the mechanical load and the distribution of mobile charges. In the bending of a rectangular plate under a distributed transverse mechanical load, it is shown that mobile charge distributions and potential barriers/wells develop in the plate. When the mechanical load is local and self-balanced, the induced carrier distributions and potential barriers/wells are also localized near the loading area. The results are fundamentally useful for mechanically manipulating mobile charges in piezoelectric semiconductor devices.

Contact vibration analysis of the functionally graded material coated half-space under a rigid spherical punch

Xin LYU, Liaoliang KE, Jiayong TIAN, Jie SU

2022, 43(8):  1187-1202.  doi:10.1007/s10483-022-2885-7

Abstract ( 1116 )   HTML ( 6)   PDF (459KB) ( 333 )  

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This paper studies the contact vibration problem of an elastic half-space coated with functionally graded materials (FGMs) subject to a rigid spherical punch. A static force superimposing a dynamic time-harmonic force acts on the rigid spherical punch. Firstly, we give the static contact problem of FGMs by a least-square fitting approach. Next, the dynamic contact pressure is solved by employing the perturbation method. Lastly, the dynamic contact stiffness with different dynamic contact displacement conditions is derived for the FGM coated half-space. The effects of the gradient index, coating thickness, internal friction, and punch radius on the dynamic contact stiffness factor are discussed in detail.

Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions

Qingdong CHAI, Yanqing WANG, Meiwen TENG

2022, 43(8):  1203-1218.  doi:10.1007/s10483-022-2892-7

Abstract ( 1208 )   HTML ( 5)   PDF (2650KB) ( 136 )  

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The aim of the present study is to investigate the nonlinear free vibration of spinning cylindrical shells under spinning and arbitrary boundary conditions. Artificial springs are used to simulate arbitrary boundary conditions. Sanders' shell theory is employed, and von Kármán nonlinear terms are considered in the theoretical modeling. By using Chebyshev polynomials as admissible functions, motion equations are derived with the Ritz method. Then, a direct iteration method is used to obtain the nonlinear vibration frequencies. The effects of the circumferential wave number, the boundary spring stiffness, and the spinning speed on the nonlinear vibration characteristics of the shells are highlighted. It is found that there exist sensitive intervals for the boundary spring stiffness, which makes the variation of the nonlinear frequency ratio more evident. The decline of the frequency ratio caused by the spinning speed is more significant for the higher vibration amplitude and the smaller boundary spring stiffness.

A variational differential quadrature solution to finite deformation problems of hyperelastic shell-type structures: a two-point formulation in Cartesian coordinates

M. FARAJI-OSKOUIE, R. ANSARI, M. DARVIZEH

2022, 43(8):  1219-1232.  doi:10.1007/s10483-022-2887-9

Abstract ( 1158 )   HTML ( 3)   PDF (2932KB) ( 149 )  

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A new numerical approach is presented to compute the large deformations of shell-type structures made of the Saint Venant-Kirchhoff and Neo-Hookean materials based on the seven-parameter shell theory. A work conjugate pair of the first Piola Kirchhoff stress tensor and deformation gradient tensor is considered for the stress and strain measures in the paper. Through introducing the displacement vector, the deformation gradient, and the stress tensor in the Cartesian coordinate system and by means of the chain rule for taking derivative of tensors, the difficulties in using the curvilinear coordinate system are bypassed. The variational differential quadrature (VDQ) method as a pointwise numerical method is also used to discretize the weak form of the governing equations. Being locking-free, the simple implementation, computational efficiency, and fast convergence rate are the main features of the proposed numerical approach. Some well-known benchmark problems are solved to assess the approach. The results indicate that it is capable of addressing the large deformation problems of elastic and hyperelastic shell-type structures efficiently.

New analytic solutions to 2D transient heat conduction problems with/without heat sources in the symplectic space

Dian XU, Xinran ZHENG, Dongqi AN, Chao ZHOU, Xiuwen HUANG, Rui LI

2022, 43(8):  1233-1248.  doi:10.1007/s10483-022-2891-6

Abstract ( 1181 )   HTML ( 6)   PDF (4765KB) ( 144 )  

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The two-dimensional (2D) transient heat conduction problems with/without heat sources in a rectangular domain under different combinations of temperature and heat flux boundary conditions are studied by a novel symplectic superposition method (SSM). The solution process is within the Hamiltonian system framework such that the mathematical procedures in the symplectic space can be implemented, which provides an exceptional direct rigorous derivation without any assumptions or predetermination of the solution forms compared with the conventional inverse/semi-inverse methods. The distinctive advantage of the SSM offers an access to new analytic heat conduction solutions. The results obtained by the SSM agree well with those obtained from the finite element method (FEM), which confirms the accuracy of the SSM.

Electric-magnetic-force characteristics of rare earth barium copper oxide superconductor high-field coils based on screening effect and strain sensitivity

Wenhai ZHOU, Youhe ZHOU

2022, 43(8):  1249-1268.  doi:10.1007/s10483-022-2884-6

Abstract ( 1253 )   HTML ( 5)   PDF (6215KB) ( 85 )  

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Rare earth barium copper oxide (REBCO) is the most researched and commercialized second-generation high-temperature superconducting material. Due to the anisotropic structure, strong deformation sensitivity, and central field errors caused by screening current effects, it is still a challenge for commercialization applications. In this study, the transversely isotropic constitutive relationship is selected as the mechanical model based on the structural characteristics of REBCO tapes, and suitable microelements are selected to equate the elastic constants using their average stress-strain relationships. Then, a two-dimensional axisymmetric model for coils wound by single-layer tapes is constructed to analyze the dependence of the electric-magnetic-force distribution in the tape on the strain. Finally, the anisotropic approximation of the homogenized bulk method is used to equate large-turn high-field coils, and the electric-magnetic-force distribution characteristics of the coils with/without screening effects and mechanical strain conditions are investigated, respectively. The results reveal that the mechanical strain has a weakening effect on the electromagnetic field distribution of superconducting tapes, but causes a significant enhancement in the force field distribution. In the presence of 0.5% mechanical strain, the maximum weakening of the peak value of the current density and the critical current density inside the high-field coil can reach about 8% and 13%, respectively, with a nearly 5 times increase in the peak stress. The screening current makes the current field distribution inside the coil improve by about 10 times. The screening current induced magnetic field can reach up to 0.8 T, making the relative error of the high-field coil center up to 7.8%.

Improved frequency modeling and solution for parallel liquid-filled pipes considering both fluid-structure interaction and structural coupling

Xumin GUO, Chunliang XIAO, Hui MA, Hui LI, Xufang ZHANG, Bangchun WEN

2022, 43(8):  1269-1288.  doi:10.1007/s10483-022-2883-9

Abstract ( 1200 )   HTML ( 4)   PDF (13346KB) ( 166 )  

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The dynamic characteristics of a single liquid-filled pipe have been broadly studied in the previous literature. The parallel liquid-filled pipe (PLFP) system is also widely used in engineering, and its structure is more complex than that of a single pipe. However, there are few reports about the dynamic characteristics of the PLFPs. Therefore, this paper proposes improved frequency modeling and solution for the PLFPs, involving the logical alignment principle and coupled matrix processing. The established model incorporates both the fluid-structure interaction (FSI) and the structural coupling of the PLFPs. The validity of the established model is verified by modal experiments. The effects of some unique parameters on the dynamic characteristics of the PLFPs are discussed. This work provides a feasible method for solving the FSI of multiple pipes in parallel and potential theoretical guidance for the dynamic analysis of the PLFPs in engineering.

Electrokinetic flow and energy conversion in a curved microtube

Zhaodong DING, Kai TIAN, Yongjun JIAN

2022, 43(8):  1289-1306.  doi:10.1007/s10483-022-2886-5

Abstract ( 1152 )   HTML ( 5)   PDF (2713KB) ( 120 )  

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Curved channels are ubiquitous in microfluidic systems. The pressuredriven electrokinetic flow and energy conversion in a curved microtube are investigated analytically by using a perturbation analysis method under the assumptions of the small curvature ratio and the Reynolds number. The results indicate that the curvature of the microtube leads to a skewed pattern in the distribution of the electrical double layer (EDL) potential. The EDL potential at the outer side of the bend is larger than that at the inner side of the bend. The curvature shows an inhibitory effect on the magnitude of the streaming potential field induced by the pressure-driven flow. Since the spanwise pressure gradient is dominant over the inertial force, the resulting axial velocity profile is skewed into the inner region of the curved channel. Furthermore, the flow rate in a curved microtube could be larger than that in a straight one with the same pressure gradient and shape of cross section. The asymptotic solutions of the axial velocity and flow rate in the absence of the electrokinetic effect are in agreement with the classical results for low Reynolds number flows. Remarkably, the curved geometry could be beneficial to improving the electrokinetic energy conversion (EKEC) efficiency.