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2021年 第42卷 第5期    刊出日期：2021-05-01

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论文

Influence of vehicle-road coupled vibration on tire adhesion based on nonlinear foundation

Junning ZHANG, Shaopu YANG, Shaohua LI, Yongjie LU, Hu DING

2021, 42(5):  607-624.  doi:10.1007/s10483-021-2724-6

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The influence of pavement vibration on tire adhesion is of great significance to the structure design of vehicle and pavement. The adhesion between tire and road is the key to studying vehicle dynamics, and the precise description of tire adhesion affects the accuracy of dynamic vehicle responses. However, in most models, only road roughness is considered, and the pavement vibration caused by vehicle-road interaction is ignored. In this paper, a vehicle is simplified as a spring-mass-damper oscillator, and the vehicle-pavement system is modeled as a vehicle moving along an Euler-Bernoulli beam with finite length on a nonlinear foundation. The road roughness is considered as a sine wave, and the shear stress is ignored on the pavement. According to the contact form between tire and road, the LuGre tire model is established to calculate the tire adhesion force. The Galerkin method is used to simplify the partial differential equations of beam vibration into finite ordinary differential equations. A product-to-sum formula and a Dirac delt function are used to deal with the nonlinear term caused by the nonlinear foundation, which realizes the fast and accurate calculation of super-high dimensional nonlinear ordinary differential equations. In addition, the dynamic responses between the coupled system and the traditional uncoupled system are compared with each other. The obtained results provide an important theoretical basis for research on the influence of vehicle-road coupled vibration on tire adhesion.



Surface effects on a mode-III reinforced nano-elliptical hole embedded in one-dimensional hexagonal piezoelectric quasicrystals

Zhina ZHAO, Junhong GUO

2021, 42(5):  625-640.  doi:10.1007/s10483-021-2721-5

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To effectively reduce the field concentration around a hole or crack, an anti-plane shear problem of a nano-elliptical hole or a nano-crack pasting a reinforcement layer in a one-dimensional (1D) hexagonal piezoelectric quasicrystal (PQC) is investigated subject to remotely mechanical and electrical loadings. The surface effect and dielectric characteristics inside the hole are considered for actuality. By utilizing the technique of conformal mapping and the complex variable method, the phonon stresses, phason stresses, and electric displacements in the matrix and reinforcement layer are exactly derived under both electrically permeable and impermeable boundary conditions. Three size-dependent field intensity factors near the nano-crack tip are further obtained when the nano-elliptical hole is reduced to the nano-crack. Numerical examples are illustrated to show the effects of material properties of the surface layer and reinforced layer, the aspect ratio of the hole, and the thickness of the reinforcing layer on the field concentration of the nano-elliptical hole and the field intensity factors near the nano-crack tip. The results indicate that the properties of the surface layer and reinforcement layer and the electrical boundary conditions have great effects on the field concentration of the nano-hole and nano-crack, which are useful for optimizing and designing the microdevices by PQC nanocomposites in engineering practice.

Complex response analysis of a non-smooth oscillator under harmonic and random excitations

Shichao MA, Xin NING, Liang WANG, Wantao JIA, Wei XU

2021, 42(5):  641-648.  doi:10.1007/s10483-021-2731-5

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It is well-known that practical vibro-impact systems are often influenced by random perturbations and external excitation forces, making it challenging to carry out the research of this category of complex systems with non-smooth characteristics. To address this problem, by adequately utilizing the stochastic response analysis approach and performing the stochastic response for the considered non-smooth system with the external excitation force and white noise excitation, a modified conducting process has proposed. Taking the multiple nonlinear parameters, the non-smooth parameters, and the external excitation frequency into consideration, the steady-state stochastic P-bifurcation phenomena of an elastic impact oscillator are discussed. It can be found that the system parameters can make the system stability topology change. The effectiveness of the proposed method is verified and demonstrated by the Monte Carlo (MC) simulation. Consequently, the conclusions show that the process can be applied to stochastic non-autonomous and non-smooth systems.

Surface contact behavior of functionally graded thermoelectric materials indented by a conducting punch

Xiaojuan TIAN, Yueting ZHOU, Lihua WANG, Shenghu DING

2021, 42(5):  649-664.  doi:10.1007/s10483-021-2732-8

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The contact problem for thermoelectric materials with functionally graded properties is considered. The material properties, such as the electric conductivity, the thermal conductivity, the shear modulus, and the thermal expansion coefficient, vary in an exponential function. Using the Fourier transform technique, the electro-thermoelastic problems are transformed into three sets of singular integral equations which are solved numerically in terms of the unknown normal electric current density, the normal energy flux, and the contact pressure. Meanwhile, the complex homogeneous solutions of the displacement fields caused by the gradient parameters are simplified with the help of Euler’s formula. After addressing the non-linearity excited by thermoelectric effects, the particular solutions of the displacement fields can be assessed. The effects of various combinations of material gradient parameters and thermoelectric loads on the contact behaviors of thermoelectric materials are presented. The results give a deep insight into the contact damage mechanism of functionally graded thermoelectric materials (FGTEMs).

Application of the homotopy analysis method to nonlinear characteristics of a piezoelectric semiconductor fiber

Minghao ZHAO, Zelong MA, Chunsheng LU, Qiaoyun ZHANG

2021, 42(5):  665-676.  doi:10.1007/s10483-021-2726-5

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Based on the nonlinear constitutive equation, a piezoelectric semiconductor (PSC) fiber under axial loads and Ohmic contact boundary conditions is investigated. The analytical solutions of electromechanical fields are derived by the homotopy analysis method (HAM), indicating that the HAM is efficient for the nonlinear analysis of PSC fibers, along with a rapid rate of convergence. Furthermore, the nonlinear characteristics of electromechanical fields are discussed through numerical results. It is shown that the asymmetrical distribution of electromechanical fields is obvious under a symmetrical load, and the piezoelectric effect is weakened by an applied electric field. With the increase in the initial carrier concentration, the electric potential decreases, and owing to the screening effect of electrons, the distribution of electromechanical fields tends to be symmetrical.

Effects of surface impedance on current density in a piezoelectric resonator for impedance distribution sensing

Jing LIU, Jianke DU, Ji WANG, Jiashi YANG

2021, 42(5):  677-688.  doi:10.1007/s10483-021-2723-9

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We study the relationship between the surface mechanical load represented by distributed acoustic impedance and the current density distribution in a shear mode piezoelectric plate acoustic wave resonator. A theoretical analysis based on the theory of piezoelectricity and trigonometric series is performed. In the specific and basic case when the surface load is due to a local mass layer, numerical results show that the current density concentrates under the mass layer and is sensitive to the physical as well as geometric parameters of the mass layer such as its location and size. This provides the theoretical foundation for predicting the surface impedance pattern from the current density distribution, which is fundamental to the relevant acoustic wave sensors.

Mechanics of nonbuckling interconnects with prestrain for stretchable electronics

Zixuan LU, Liang GUO, Hongyu ZHAO

2021, 42(5):  689-702.  doi:10.1007/s10483-021-2715-7

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The performance of the flexibility and stretchability of flexible electronics depends on the mechanical structure design, for which a great progress has been made in past years. The use of prestrain in the substrate, causing the compression of the transferred interconnects, can provide high elastic stretchability. Recently, the nonbuckling interconnects have been designed, where thick bar replaces thin ribbon layout to yield scissor-like in-plane deformation instead of in- or out-of-plane buckling modes. The nonbuckling interconnect design achieves significantly enhanced stretchability. However, combined use of prestrain and nonbuckling interconnects has not been explored. This paper aims to study the mechanical behavior of nonbuckling interconnects bonded to the prestrained substrate analytically and numerically. It is found that larger prestrain, longer straight segment, and smaller arc radius yield smaller strain in the interconnects. On the other hand, larger prestrain can also cause larger strain in the interconnects after releasing the prestrain. Therefore, the optimization of the prestrain needs to be found to achieve favorable stretchability.

New insight into the stability and dynamics of fluid-conveying supported pipes with small geometric imperfections

Kun ZHOU, Qiao NI, Wei CHEN, Huliang DAI, Zerui PENG, Lin WANG

2021, 42(5):  703-720.  doi:10.1007/s10483-021-2729-6

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In several previous studies, it was reported that a supported pipe with small geometric imperfections would lose stability when the internal flow velocity became sufficiently high. Recently, however, it has become clear that this conclusion may be at best incomplete. A reevaluation of the problem is undertaken here by essentially considering the flow-induced static deformation of a pipe. With the aid of the absolute nodal coordinate formulation (ANCF) and the extended Lagrange equations for dynamical systems containing non-material volumes, the nonlinear governing equations of a pipe with three different geometric imperfections are introduced and formulated. Based on extensive numerical calculations, the static equilibrium configuration, the stability, and the nonlinear dynamics of the considered pipe system are determined and analyzed. The results show that for a supported pipe with the geometric imperfection of a half sinusoidal wave, the dynamical system could not lose stability even if the flow velocity reaches an extremely high value of 40. However, for a supported pipe with the geometric imperfection of one or one and a half sinusoidal waves, the first-mode buckling instability would take place at high flow velocity. Moreover, based on a further parametric analysis, the effects of the amplitude of the geometric imperfection and the aspect ratio of the pipe on the static deformation, the critical flow velocity for buckling instability, and the nonlinear responses of the supported pipes with geometric imperfections are analyzed.

Mathematical modeling and numerical computation of the effective interfacial conditions for Stokes flow on an arbitrarily rough solid surface

A. T. TRAN, H. LE QUANG, Q. C. HE, D. H. NGUYEN

2021, 42(5):  721-746.  doi:10.1007/s10483-021-2733-9

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The present work is concerned with a two-dimensional (2D) Stokes flow through a channel bounded by two parallel solid walls. The distance between the walls may be arbitrary, and the surface of one of the walls can be arbitrarily rough. The main objective of this work consists in homogenizing the heterogeneous interface between the rough wall and fluid so as to obtain an equivalent smooth slippery fluid/solid interface characterized by an effective slip length. To solve the corresponding problem, two efficient numerical approaches are elaborated on the basis of the method of fundamental solution (MFS) and the boundary element methods (BEMs). They are applied to different cases where the fluid/solid interface is periodically or randomly rough. The results obtained by the proposed two methods are compared with those given by the finite element method and some relevant ones reported in the literature. This comparison shows that the two proposed methods are particularly efficient and accurate.

An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor

Tianbo WANG, Dinglin YANG, Chen LI, Diwei SHI

2021, 42(5):  747-754.  doi:10.1007/s10483-021-2718-9

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Based on the Cayley-Hamilton theorem and fixed-point method, we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional (3D) inner-product space, which avoids introducing the generating function and Taylor series expansion. The proof is also extended to any finite-dimensional inner-product space.