当期目录

2022年 第43卷 第6期    刊出日期：2022-06-01

上一期    下一期

论文

Nonlinear modal coupling in a T-shaped piezoelectric resonator induced by stiffness hardening effect

Lei LI, Hanbiao LIU, Jianxin HAN, Wenming ZHANG

2022, 43(6):  777-792.  doi:10.1007/s10483-022-2861-6

摘要 ( 765 )   HTML ( 26)   PDF (2312KB) ( 240 )  

参考文献 | 相关文章 | 多维度评价

The nonlinear modal coupling in a T-shaped piezoelectric resonator, when the former two natural frequencies are away from 1:2, is studied. Experimentally sweeping up the exciting frequency shows that the horizontal beam exhibits a nonlinear hardening behavior. The first primary resonance of the vertical beam, owing to modal coupling, exhibits an abrupt amplitude increase, namely the Hopf bifurcation. The frequency comb phenomenon induced by modal coupling is measured experimentally. A Duffing-Mathieu coupled model is theoretically introduced to derive the conditions of the modal coupling and frequency comb phenomenon. The results demonstrate that the modal coupling results from nonlinear stiffness hardening and is strictly dependent on the loading range and sweeping form of the driving voltage and the frequency of the piezoelectric patches.

Nonlinear dynamic analysis of dielectric elastomer membrane with electrostriction

Yaode YIN, Demin ZHAO, Jianlin LIU, Zengyao XU

2022, 43(6):  793-812.  doi:10.1007/s10483-022-2853-9

摘要 ( 866 )   HTML ( 4)   PDF (5916KB) ( 188 )  

参考文献 | 相关文章 | 多维度评价

The dielectric elastomer (DE) is an important intelligent soft material widely used in soft actuators, and the dynamic response of the DE is highly nonlinear due to the material properties. In the DE, electrostriction denotes the deformation-dependent permittivity. In the present study, we formulate the nonlinear dynamic governing equations of the DE membrane considering the electrostriction effect. The free vibration and parametric excitation of the DE membrane with different geometric sizes are calculated. The free vibration bifurcations induced by the initial location and the voltage are both discussed according to an energy-based approach. The amplitude-frequency characteristics and bifurcation diagrams of parametric excitation are also given. The results show that electrostriction decreases the free vibration amplitude and increases the frequency, but it has less influence on the parametric excitation oscillation frequency and decreases the parametric excitation amplitude except when the membrane resonates. The initial location and the applied voltage can induce the snap-through instability of the free vibration. A large geometric size will lead to a much lower resonance frequency. The resonance amplitudes increase while the resonance frequencies decrease with the increase in the applied voltage. The critical voltage of snap-through instability for the parametric excitation is larger than that for the free vibration one.



Cascaded quasi-zero stiffness nonlinear low-frequency vibration isolator inspired by human spine

Guoxin JIN, Zhenghao WANG, Tianzhi YANG

2022, 43(6):  813-824.  doi:10.1007/s10483-022-2852-5

摘要 ( 933 )   HTML ( 6)   PDF (3394KB) ( 151 )  

参考文献 | 相关文章 | 多维度评价

Human motion induced vibration has very low frequency, ranging from 2 Hz to 5 Hz. Traditional vibration isolators are not effective in low-frequency regions due to the trade-off between the low natural frequency and the high load capacity. In this paper, inspired by the human spine, we propose a novel bionic human spine inspired quasi-zero stiffness (QZS) vibration isolator which consists of a cascaded multi-stage negative stiffness structure. The force and stiffness characteristics are investigated first, the dynamic model is established by Newton's second law, and the isolation performance is analyzed by the harmonic balance method (HBM). Numerical results show that the bionic isolator can obtain better low-frequency isolation performance by increasing the number of negative structure stages, and reducing the damping values and external force values can obtain better low-frequency isolation performance. In comparison with the linear structure and existing traditional QZS isolator, the bionic spine isolator has better vibration isolation performance in low-frequency regions. It paves the way for the design of bionic ultra-low-frequency isolators and shows potential in many engineering applications.

Nonlinear free vibrations of porous composite microplates incorporating various microstructural-dependent strain gradient tensors

Duquan ZUO, B. SAFAEI, S. SAHMANI, Guoling MA

2022, 43(6):  825-844.  doi:10.1007/s10483-022-2851-7

摘要 ( 759 )   HTML ( 5)   PDF (2507KB) ( 168 )  

参考文献 | 相关文章 | 多维度评价

The main objective of the present numerical analysis is to predict the nonlinear frequency ratios associated with the nonlinear free vibration response of porous composite plates at microscale in the presence of different microstructural gradient tensors. To achieve this end, by taking cubic-type elements into account, isogeometric models of porous composite microplates are obtained with and without a central cutout and relevant to various porosity patterns of distribution along the plate thickness. The established unconventional models have the capability to capture the effects of various unconventional gradient tensors continuity on the basis of a refined shear deformable plate formulation. For the simply supported microsized uniform porous functionally graded material (UPFGM) plate having the oscillation amplitude equal to the plate thickness, it is revealed that the rotation gradient tensor causes to reduce the frequency ratio about 0.73%, the dilatation gradient tensor causes to reduce it about 1.93%, and the deviatoric stretch gradient tensor leads to a decrease of it about 5.19%. On the other hand, for the clamped microsized U-PFGM plate having the oscillation amplitude equal to the plate thickness, these percentages are equal to 0.62%, 1.64%, and 4.40%, respectively. Accordingly, it is found that by changing the boundary conditions from clamped to simply supported, the effect of microsize on the reduction of frequency ratio decreases a bit.

Vibration of fluid-conveying pipe with nonlinear supports at both ends

Sha WEI, Xiong YAN, Xin FAN, Xiaoye MAO, Hu DING, Liqun CHEN

2022, 43(6):  845-862.  doi:10.1007/s10483-022-2857-6

摘要 ( 744 )   HTML ( 1)   PDF (639KB) ( 269 )  

参考文献 | 相关文章 | 多维度评价

The axial fluid-induced vibration of pipes is very widespread in engineering applications. The nonlinear forced vibration of a viscoelastic fluid-conveying pipe with nonlinear supports at both ends is investigated. The multi-scale method combined with the modal revision method is formulated for the fluid-conveying pipe system with nonlinear boundary conditions. The governing equations and the nonlinear boundary conditions are rescaled simultaneously as linear inhomogeneous equations and linear inhomogeneous boundary conditions on different time-scales. The modal revision method is used to transform the linear inhomogeneous boundary problem into a linear homogeneous boundary problem. The differential quadrature element method (DQEM) is used to verify the approximate analytical results. The results show good agreement between these two methods. A detailed analysis of the boundary nonlinearity is also presented. The obtained results demonstrate that the boundary nonlinearities have a significant effect on the dynamic characteristics of the fluid-conveying pipe, and can lead to significant differences in the dynamic responses of the pipe system.

Wavelet multiresolution interpolation Galerkin method for nonlinear boundary value problems with localized steep gradients

Xiaojing LIU, Youhe ZHOU, Jizeng WANG

2022, 43(6):  863-882.  doi:10.1007/s10483-022-2859-5

摘要 ( 808 )   HTML ( 2)   PDF (948KB) ( 144 )  

参考文献 | 相关文章 | 多维度评价

The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix. The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities, including transcendental ones, in which the discretization process is as simple as that in solving linear problems, and only common two-term connection coefficients are needed. All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton's method, which does not require numerical integration in the resulting nonlinear discrete system. The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers. The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids, and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids. In addition, Newton's method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method, including the initial guess far from real solutions.

Exact analysis of the orientation-adjusted adhesive full stick contact of layered structures with the asymmetric bipolar coordinates

Pengxu GUO, Yueting ZHOU

2022, 43(6):  883-898.  doi:10.1007/s10483-022-2860-9

摘要 ( 772 )   HTML ( 1)   PDF (300KB) ( 87 )  

参考文献 | 相关文章 | 多维度评价

The adhesion failure has become one dominant factor in determining the reliability and service life of miniaturized devices subject to loadings with arbitrary orientations. This article establishes an adhesive full stick contact model between an elastic half-space and a rigid cylinder loaded in any direction. Using the Papkovich-Neuber functions, the Fourier integral transform, and the asymmetric bipolar coordinates, the exact solution is obtained. Unlike the Johnson-Kendall-Roberts (JKR) model, the present adhesive contact model takes into account the effects of the load direction as well as the coupling of the normal and tangential contact stresses. Besides, it considers the full stick contact which has large values of the friction coefficient between contacting surfaces, contrary to the frictionless contact supposed in the JKR model. The result shows that suitable angles can be found, which makes the contact surfaces difficult to be peeled off or easy to be pressed into.

A fluid flow model in the lacunar-canalicular system under the pressure gradient and electrical field driven loads

Xiaogang WU, Xiyu WANG, Chaoxin LI, Zhaowei WANG, Yuqin SUN, Yang YAN, Yixian QIN, Pengcui LI, Yanqin WANG, Xiaochun WEI, Weiyi CHEN

2022, 43(6):  899-916.  doi:10.1007/s10483-022-2856-9

摘要 ( 919 )   HTML ( 0)   PDF (4421KB) ( 132 )  

参考文献 | 相关文章 | 多维度评价

The lacunar-canalicular system (LCS) is acknowledged to directly participate in bone tissue remodeling. The fluid flow in the LCS is synergic driven by the pressure gradient and electric field loads due to the electro-mechanical properties of bone. In this paper, an idealized annulus Maxwell fluid flow model in bone canaliculus is established, and the analytical solutions of the fluid velocity, the fluid shear stress, and the fluid flow rate are obtained. The results of the fluid flow under pressure gradient driven (PGD), electric field driven (EFD), and pressure-electricity synergic driven (P-ESD) patterns are compared and discussed. The effects of the diameter of canaliculi and osteocyte processes are evaluated. The results show that the P-ESD pattern can combine the regulatory advantages of single PGD and EFD patterns, and the osteocyte process surface can feel a relatively uniform shear stress distribution. As the bone canalicular inner radius increases, the produced shear stress under the PGD or P-ESD pattern increases slightly but changes little under the EFD pattern. The increase in the viscosity makes the flow slow down but does not affect the fluid shear stress (FSS) on the canalicular inner wall and osteocyte process surface. The increase in the high-valent ions does not affect the flow velocity and the flow rate, but the FSS on the canalicular inner wall and osteocyte process surface increases linearly. In this study, the results show that the shear stress sensed by the osteocyte process under the P-ESD pattern can be regulated by changing the pressure gradient and the intensity of electric field, as well as the parameters of the annulus fluid and the canaliculus size, which is helpful for the osteocyte mechanical responses. The established model provides a basis for the study of the mechanisms of electro-mechanical signals stimulating bone tissue (cells) growth.

Electromagnetohydrodynamic (EMHD) flow of fractional viscoelastic fluids in a microchannel

Shujuan AN, Kai TIAN, Zhaodong DING, Yongjun JIAN

2022, 43(6):  917-930.  doi:10.1007/s10483-022-2882-7

摘要 ( 824 )   HTML ( 1)   PDF (1960KB) ( 193 )  

参考文献 | 相关文章 | 多维度评价

This study investigates the electromagnetohydrodynamic (EMHD) flow of fractional viscoelastic fluids through a microchannel under the Navier slip boundary condition. The flow is driven by the pressure gradient and electromagnetic force where the electric field is applied horizontally, and the magnetic field is vertically (upward or downward). When the electric field direction is consistent with the pressure gradient direction, the changes of the steady flow rate and velocity with the Hartmann number Ha are irrelevant to the direction of the magnetic field (upward or downward). The steady flow rate decreases monotonically to zero with the increase in Ha. In contrast, when the direction of the electric field differs from the pressure gradient direction, the flow behavior depends on the direction of the magnetic field, i.e., symmetry breaking occurs. Specifically, when the magnetic field is vertically upward, the steady flow rate increases first and then decreases with Ha. When the magnetic field is reversed, the steady flow rate first reduces to zero as Ha increases from zero. As Ha continues to increase, the steady flow rate (velocity) increases in the opposite direction and then decreases, and finally drops to zero for larger Ha. The increase in the fractional calculus parameter α or Deborah number De makes it take longer for the flow rate (velocity) to reach the steady state. In addition, the increase in the strength of the magnetic field or electric field, or in the pressure gradient tends to accelerate the slip velocity at the walls. On the other hand, the increase in the thickness of the electric double-layer tends to reduce it.

Performance enhancement of a DC-operated micropump with electroosmosis in a hybrid nanofluid: fractional Cattaneo heat flux problem

A. M. ALSHARIF, A. I. ABDELLATEEF, Y. A. ELMABOUD, S. I. ABDELSALAM

2022, 43(6):  931-944.  doi:10.1007/s10483-022-2854-6

摘要 ( 787 )   HTML ( 4)   PDF (1595KB) ( 127 )  

参考文献 | 相关文章 | 多维度评价

The purpose of this investigation is to theoretically shed some light on the effect of the unsteady electroosmotic flow (EOF) of an incompressible fractional secondgrade fluid with low-dense mixtures of two spherical nanoparticles, copper, and titanium. The flow of the hybrid nanofluid takes place through a vertical micro-channel. A fractional Cattaneo model with heat conduction is considered. For the DC-operated micropump, the Lorentz force is responsible for the pressure difference through the microchannel. The Debye-Hükel approximation is utilized to linearize the charge density. The semianalytical solutions for the velocity and heat equations are obtained with the Laplace and finite Fourier sine transforms and their numerical inverses. In addition to the analytical procedures, a numerical algorithm based on the finite difference method is introduced for the given domain. A comparison between the two solutions is presented. The variations of the velocity heat transfer against the enhancements in the pertinent parameters are thoroughly investigated graphically. It is noticed that the fractional-order parameter provides a crucial memory effect on the fluid and temperature fields. The present work has theoretical implications for biofluid-based microfluidic transport systems.