Table of Content

01 November 2021, Volume 42 Issue 11

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Articles

A new tunable elastic metamaterial structure for manipulating band gaps/wave propagation

Zhenyu WANG, Zhaoyang MA, Xingming GUO, Dongsheng ZHANG

2021, 42(11):  1543-1554.  doi:10.1007/s10483-021-2787-8

Abstract ( 1314 )   HTML ( 30)   PDF (3181KB) ( 174 )  

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A one-dimensional mechanical lattice system with local resonators is proposed as an elastic metamaterial model, which shows negative mass and negative modulus under specific frequency ranges. The proposed representative units, consisting of accurately arranged rigid components, can generate controllable translational resonance and achieve negative mass and negative modulus by adjusting the local structural parameters. A shape memory polymer is adopted as a spring component, whose Young's modulus is obviously affected by temperature, and the proposed metamaterials' tunable ability is achieved by adjusting temperature. The effect of the shape memory polymer's stiffness variation on the band gaps is investigated detailedly, and the special phenomenon of intersecting dispersion curves is discussed, which can be designed and controlled by adjusting temperature. The dispersion relationship of the continuum metamaterial model affected by temperature is obtained, which shows great tunable ability to manipulate wave propagation.

Bandgaps and vibration isolation of local resonance sandwich-like plate with simply supported overhanging beam

Chenxu QIANG, Yuxin HAO, Wei ZHANG, Jinqiang LI, Shaowu YANG, Yuteng CAO

2021, 42(11):  1555-1570.  doi:10.1007/s10483-021-2790-7

Abstract ( 1105 )   HTML ( 4)   PDF (4709KB) ( 116 )  

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The concept of local resonance phononic crystals proposed in recent years provides a new chance for theoretical and technical breakthroughs in the structural vibration reduction. In this paper, a novel sandwich-like plate model with local resonator to acquire specific low-frequency bandgaps is proposed. The core layer of the present local resonator is composed by the simply supported overhanging beam, linear spring and mass block, and well connected with the upper and lower surface panels. The simply supported overhanging beam is free at right end, and an additional linear spring is added at the left end. The wave equation is established based on the Hamilton principle, and the bending wave bandgap is further obtained. The theoretical results are verified by the COMSOL finite element software. The bandgaps and vibration characteristics of the local resonance sandwich-like plate are studied in detail. The factors which could have effects on the bandgap characteristics, such as the structural damping, mass of vibrator, position of vibrator, bending stiffness of the beam, and the boundary conditions of the sandwich-like plates, are analyzed. The result shows that the stopband is determined by the natural frequency of the resonator, the mass ratio of the resonator, and the surface panel. It shows that the width of bandgap is greatly affected by the damping ratio of the resonator. Finally, it can also be found that the boundary conditions can affect the isolation efficiency.

Study on the static properties of spiral springs under static loading

Zhixiang LI, Zhen ZHAO, Caishan LIU, Qingyun WANG

2021, 42(11):  1571-1580.  doi:10.1007/s10483-021-2782-8

Abstract ( 1035 )   HTML ( 4)   PDF (669KB) ( 105 )  

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Spiral springs have a wide range of applications in various fields. As a result of the complexity of friction, few theoretical analyses of spring belts under static loading have been carried out. Considering the piecewise smooth property of the whole contact area, a simplified static model of spiral springs under loading is established in this paper. Besides, three main stress and friction distribution areas of the spring belt are proposed, namely, internal, transitional, and external regions. Since the outermost side of the spring is not subject to any pressure, a recursive method is adopted from the outside to the inside. The model provides the parameter conditions, i.e., the internal and external forces are independent or dependent. Therefore, the case that the whole contact region of the spring belt has one subregion, two subregions, and three subregions is obtained. The model gives a theoretical basis for the parameter optimization of spiral springs.

On the consistency of two-phase local/nonlocal piezoelectric integral model

Yanming REN, Hai QING

2021, 42(11):  1581-1598.  doi:10.1007/s10483-021-2785-7

Abstract ( 1012 )   HTML ( 6)   PDF (7908KB) ( 177 )  

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In this paper, we propose general strain- and stress-driven two-phase local/nonlocal piezoelectric integral models, which can distinguish the difference of nonlocal effects on the elastic and piezoelectric behaviors of nanostructures. The nonlocal piezoelectric model is transformed from integral to an equivalent differential form with four constitutive boundary conditions due to the difficulty in solving intergro-differential equations directly. The nonlocal piezoelectric integral models are used to model the static bending of the Euler-Bernoulli piezoelectric beam on the assumption that the nonlocal elastic and piezoelectric parameters are coincident with each other. The governing differential equations as well as constitutive and standard boundary conditions are deduced. It is found that purely strain- and stress-driven nonlocal piezoelectric integral models are ill-posed, because the total number of differential orders for governing equations is less than that of boundary conditions. Meanwhile, the traditional nonlocal piezoelectric differential model would lead to inconsistent bending response for Euler-Bernoulli piezoelectric beam under different boundary and loading conditions. Several nominal variables are introduced to normalize the governing equations and boundary conditions, and the general differential quadrature method (GDQM) is used to obtain the numerical solutions. The results from current models are validated against results in the literature. It is clearly established that a consistent softening and toughening effects can be obtained for static bending of the Euler-Bernoulli beam based on the general strain- and stress-driven local/nonlocal piezoelectric integral models, respectively.

Static response of functionally graded multilayered two-dimensional quasicrystal plates with mixed boundary conditions

Xin FENG, Liangliang ZHANG, Yuxuan WANG, Jinming ZHANG, Han ZHANG, Yang GAO

2021, 42(11):  1599-1618.  doi:10.1007/s10483-021-2783-9

Abstract ( 1051 )   HTML ( 1)   PDF (493KB) ( 132 )  

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The unusual properties of quasicrystals (QCs) have attracted tremendous attention from researchers. In this paper, a semi-analytical solution is presented for the static response of a functionally graded (FG) multilayered two-dimensional (2D) decagonal QC rectangular plate with mixed boundary conditions. Based on the elastic theory of FG 2D QCs, the state-space method is used to derive the state equations composed of partial differential along the thickness direction. Besides, the Fourier series expansion and the differential quadrature technique are utilized to simulate the simply supported boundary conditions and the mixed boundary conditions, respectively. Then, the propagator matrix which connects the field variables at the upper interface to those at the lower interface of any homogeneous layer can be derived based on the state equations. Combined with the interface continuity condition, the static response can be obtained by imposing the sinusoidal load on the top surfaces of laminates. Finally, the numerical examples are presented to verify the effectiveness of this method, and the results are very useful for the design and understanding of the characterization of FG QC materials in their applications to multilayered systems.

Complicated deformation simulating on temperature-driven 4D printed bilayer structures based on reduced bilayer plate model

Junjie SONG, Yixiong FENG, Yong WANG, Siyuan ZENG, Zhaoxi HONG, Hao QIU, Jianrong TAN

2021, 42(11):  1619-1632.  doi:10.1007/s10483-021-2788-9

Abstract ( 1117 )   HTML ( 2)   PDF (5982KB) ( 198 )  

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The four-dimensional (4D) printing technology, as a combination of additive manufacturing and smart materials, has attracted increasing research interest in recent years. The bilayer structures printed with smart materials using this technology can realize complicated deformation under some special stimuli due to the material properties. The deformation prediction of bilayer structures can make the design process more rapid and thus is of great importance. However, the previous works on deformation prediction of bilayer structures rarely study the complicated deformations or the influence of the printing process on deformation. Thus, this paper proposes a new method to predict the complicated deformations of temperature-sensitive 4D printed bilayer structures, in particular to the bilayer structures based on temperature-driven shape-memory polymers (SMPs) and fabricated using the fused deposition modeling (FDM) technology. The programming process to the material during printing is revealed and considered in the simulation model. Simulation results are compared with experiments to verify the validity of the method. The advantages of this method are stable convergence and high efficiency, as the three-dimensional (3D) problem is converted to a two-dimensional (2D) problem. The simulation parameters in the model can be further associated with the printing parameters, which shows good application prospect in 4D printed bilayer structure design.

Interfacial fracture analysis for a two-dimensional decagonal quasi-crystal coating layer structure

Minghao ZHAO, Cuiying FAN, C. S. LU, Huayang DANG

2021, 42(11):  1633-1648.  doi:10.1007/s10483-021-2786-5

Abstract ( 1102 )   HTML ( 1)   PDF (1284KB) ( 152 )  

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The interface crack problems in the two-dimensional (2D) decagonal quasicrystal (QC) coating are theoretically and numerically investigated with a displacement discontinuity method. The 2D general solution is obtained based on the potential theory. An analogy method is proposed based on the relationship between the general solutions for 2D decagonal and one-dimensional (1D) hexagonal QCs. According to the analogy method, the fundamental solutions of concentrated point phonon displacement discontinuities are obtained on the interface. By using the superposition principle, the hypersingular boundary integral-differential equations in terms of displacement discontinuities are determined for a line interface crack. Further, Green's functions are found for uniform displacement discontinuities on a line element. The oscillatory singularity near a crack tip is eliminated by adopting the Gaussian distribution to approximate the delta function. The stress intensity factors (SIFs) with ordinary singularity and the energy release rate (ERR) are derived. Finally, a boundary element method is put forward to investigate the effects of different factors on the fracture.

Coupling effects between elastic and electromagnetic fields from the perspective of conservation of energy

Peng ZHOU

2021, 42(11):  1649-1662.  doi:10.1007/s10483-021-2792-9

Abstract ( 1105 )   HTML ( 3)   PDF (361KB) ( 110 )  

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Coupling effects among different physical fields reflect the conversion of energies from one field into another substantially. For simple physical processes, their governing or constitutive equations all satisfy the law of conservation of energy (LCE). Then, an analysis is extended to the coupling effects. First, for the linear direct and converse piezoelectric and piezomagnetic effects, their constitutive equations guarantee that the total energy is conserved during the process of energy conversion between the elastic and electromagnetic fields. However, the energies are converted via the work terms, $(\beta_{ijk} E_i)_{,k} v_j$ and $(\gamma_{ijk} H_i)_{,k} v_j$, rather than via the energy terms, $\beta_{ijk} E_i e_{jk}$ and $\gamma_{ijk} H_i e_{jk}$. Second, for the generalized Villari effects, the electromagnetic energy can be treated as an extra contribution to the generalized elastic energy. Third, for electrostriction and magnetostriction, both effects are induced by the Maxwell stress. Moreover, their energies are purely electromagnetic and thus both have no converse effects. During these processes, the energies can be converted in three different ways, i.e., via the non-potential forces, via the cross-dependence of the energy terms, and directly via the electromagnetic interactions of ions and electrons. In the end, the general coupling processes which involve elastic, electromagnetic fields and diffusion are also analyzed. The advantages of using this energy formulation are that it facilitates discussion of the conversion of energies and provides better physical insights into the mechanisms of these coupling effects.

Optimization of heat transfer in the thermal Marangoni convective flow of a hybrid nanomaterial with sensitivity analysis

J. MACKOLIL, B. MAHANTHESH

2021, 42(11):  1663-1674.  doi:10.1007/s10483-021-2784-6

Abstract ( 1156 )   HTML ( 2)   PDF (641KB) ( 116 )  

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The heat transfer rate of the thermal Marangoni convective flow of a hybrid nanomaterial is optimized by using the response surface methodology (RSM). The thermal phenomenon is modeled in the presence of a variable inclined magnetic field, thermal radiation, and an exponential heat source. Experimentally estimated values of the thermal conductivity and viscosity of the hybrid nanomaterial are utilized in the calculation. The governing intricate nonlinear problem is treated numerically, and a parametric analysis is carried out by using graphical visualizations. A finite difference-based numerical scheme is utilized in conjunction with the 4-stage Lobatto IIIa formula to solve the nonlinear governing problem. The interactive effects of the pertinent parameters on the heat transfer rate are presented by plotting the response surfaces and the contours obtained from the RSM. The mono and hybrid nanomaterial flow fields are compared. The hybrid nanomaterial possesses enhanced thermal fields for nanoparticle volume fractions less than 2%. The irregular heat source and the thermal radiation enhance the temperature profiles. The high level of the thermal radiation and the low levels of the exponential heat source and the angle of inclination (of the magnetic field) lead to the optimized heat transfer rate (Nu_x=7.462 75).

Mathematical modeling and parametric investigation of blood flow through a stenosis artery

A. ALI, M. HUSSAIN, M. S. ANWAR, M. INC

2021, 42(11):  1675-1684.  doi:10.1007/s10483-021-2791-8

Abstract ( 1123 )   HTML ( 4)   PDF (877KB) ( 245 )  

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In this study, a mathematical model is formulated to examine the blood flow through a cylindrical stenosed blood vessel. The stenosis disease is caused because of the abnormal narrowing of flow in the body. This narrowing causes serious health issues like heart attack and may decrease blood flow in the blood vessel. Mathematical modeling helps us analyze such issues. A mathematical model is considered in this study to explore the blood flow in a stenosis artery and is solved numerically with the finite difference method. The artery is an elastic cylindrical tube containing blood defined as a viscoelastic fluid. A complete parametric analysis has been done for the flow velocity to clarify the applicability of the defined problem. Moreover, the flow characteristics such as the impedance, the wall shear stress in the stenotic region, the shear stresses in the throat of the stenosis and at the critical stenosis height are discussed. The obtained results show that the intensity of the stenosis occurs mostly at the highest narrowing areas compared with all other areas of the vessel, which has a direct impact on the wall shear stress. It is also observed that the resistive impedance and wall shear pressure get the maximum values at the critical height of the stenosis.