Authors:Fei Fang; Guanghui Xia; Jianguo Wang Abstract: The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Euler–Bernoulli model with inextensible deformation. A nonlinear distributed parameter model of cantilevered piezoelectric energy harvesters is proposed using the generalized Hamilton’s principle. The proposed model includes geometric and inertia nonlinearity, but neglects the material nonlinearity. Using the Galerkin decomposition method and harmonic balance method, analytical expressions of the frequency–response curves are presented when the first bending mode of the beam plays a dominant role. Using these expressions, we investigate the effects of the damping, load resistance, electromechanical coupling, and excitation amplitude on the frequency–response curves. We also study the difference between the nonlinear lumped-parameter and distributed-parameter model for predicting the performance of the energy harvesting system. Only in the case of parametric excitation, we demonstrate that the energy harvesting system has an initiation excitation threshold below which no energy can be harvested. We also illustrate that the damping and load resistance affect the initiation excitation threshold. PubDate: 2018-02-05 DOI: 10.1007/s10409-017-0743-y

Authors:Wencai Sun; Zichun Yang; Guobing Chen Abstract: In small-sample problems, determining and controlling the errors of ordinary rigid convex set models are difficult. Therefore, a new uncertainty model called the fuzzy convex set (FCS) model is built and investigated in detail. An approach was developed to analyze the fuzzy properties of the structural eigenvalues with FCS constraints. Through this method, the approximate possibility distribution of the structural eigenvalue can be obtained. Furthermore, based on the symmetric F-programming theory, the conditional maximum and minimum values for the structural eigenvalue are presented, which can serve as non-fuzzy quantitative indicators for fuzzy problems. A practical application is provided to demonstrate the practicability and effectiveness of the proposed methods. PubDate: 2018-02-05 DOI: 10.1007/s10409-017-0744-x

Authors:Z. J. Meng; H. Cheng; L. D. Ma; Y. M. Cheng Abstract: This paper presents the dimension split element-free Galerkin (DSEFG) method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares (IMLS) approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method. PubDate: 2018-02-02 DOI: 10.1007/s10409-017-0747-7

Authors:Xu-Dong Zheng; Qi Wang Abstract: The main purpose of this paper is to present a linear complementarity problem (LCP) method for a planar passive dynamic walker with round feet based on an event-driven scheme. The passive dynamic walker is treated as a planar multi-rigid-body system. The dynamic equations of the passive dynamic walker are obtained by using Lagrange’s equations of the second kind. The normal forces and frictional forces acting on the feet of the passive walker are described based on a modified Hertz contact model and Coulomb’s law of dry friction. The state transition problem of stick-slip between feet and floor is formulated as an LCP, which is solved with an event-driven scheme. Finally, to validate the methodology, four gaits of the walker are simulated: the stance leg neither slips nor bounces; the stance leg slips without bouncing; the stance leg bounces without slipping; the walker stands after walking several steps. PubDate: 2018-02-02 DOI: 10.1007/s10409-018-0749-0

Authors:W. T. Liu; P. N. Sun; F. R. Ming; A. M. Zhang Abstract: Smoothed particle hydrodynamics (SPH) method with numerical diffusive terms shows satisfactory stability and accuracy in some violent fluid–solid interaction problems. However, in most simulations, uniform particle distributions are used and the multi-resolution, which can obviously improve the local accuracy and the overall computational efficiency, has seldom been applied. In this paper, a dynamic particle splitting method is applied and it allows for the simulation of both hydrostatic and hydrodynamic problems. The splitting algorithm is that, when a coarse (mother) particle enters the splitting region, it will be split into four daughter particles, which inherit the physical parameters of the mother particle. In the particle splitting process, conservations of mass, momentum and energy are ensured. Based on the error analysis, the splitting technique is designed to allow the optimal accuracy at the interface between the coarse and refined particles and this is particularly important in the simulation of hydrostatic cases. Finally, the scheme is validated by five basic cases, which demonstrate that the present SPH model with a particle splitting technique is of high accuracy and efficiency and is capable for the simulation of a wide range of hydrodynamic problems. PubDate: 2018-01-24 DOI: 10.1007/s10409-017-0739-7

Authors:Yuping Ying; Yanping Lian; Shaoqiang Tang; Wing Kam Liu Abstract: The reproducing kernel particle method (RKPM) has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modeled by a fractional advection–diffusion equation (FADE), which exhibits a boundary layer with low regularity. We formulate this method on a moving least-square approach. Via the enrichment of fractional-order power functions to the traditional integer-order basis for RKPM, leading terms of the solution to the FADE can be exactly reproduced, which guarantees a good approximation to the boundary layer. Numerical tests are performed to verify the proposed approach. PubDate: 2018-01-19 DOI: 10.1007/s10409-017-0742-z

Authors:Yuhui Li; Yuan Hong; Guang-Kui Xu; Shaobao Liu; Qiang Shi; Deding Tang; Hui Yang; Guy M. Genin; Tian Jian Lu; Feng Xu Abstract: Many structures and materials in nature and physiology have important “meso-scale” structures at the micron length-scale whose tensile responses have proven difficult to characterize mechanically. Although techniques such as atomic force microscopy and micro- and nano-identation are mature for compression and indentation testing at the nano-scale, and standard uniaxial and shear rheometry techniques exist for the macroscale, few techniques are applicable for tensile-testing at the micrometre-scale, leaving a gap in our understanding of hierarchical biomaterials. Here, we present a novel magnetic mechanical testing (MMT) system that enables viscoelastic tensile testing at this critical length scale. The MMT system applies non-contact loading, avoiding gripping and surface interaction effects. We demonstrate application of the MMT system to the first analyses of the pure tensile responses of several native and engineered tissue systems at the mesoscale, showing the broad potential of the system for exploring micro- and meso-scale analysis of structured and hierarchical biological systems. PubDate: 2018-01-12 DOI: 10.1007/s10409-017-0740-1

Authors:Z. M. Zheng; B. Wang Abstract: Conventional heat transfer fluids usually have low thermal conductivity, limiting their efficiency in many applications. Many experiments have shown that adding nanosize solid particles to conventional fluids can greatly enhance their thermal conductivity. To explain this anomalous phenomenon, many theoretical investigations have been conducted in recent years. Some of this research has indicated that the particle agglomeration effect that commonly occurs in nanofluids should play an important role in such enhancement of the thermal conductivity, while some have shown that the enhancement of the effective thermal conductivity might be accounted for by the structure of nanofluids, which can be described using the radial distribution function of particles. However, theoretical predictions from these studies are not in very good agreement with experimental results. This paper proposes a prediction model for the effective thermal conductivity of nanofluids, considering both the agglomeration effect and the radial distribution function of nanoparticles. The resulting theoretical predictions for several sets of nanofluids are highly consistent with experimental data. PubDate: 2018-01-02 DOI: 10.1007/s10409-017-0738-8

Authors:Bo-Xi Lin; Chao Yan; Shu-Sheng Chen Abstract: Many all-speed Roe schemes have been proposed to improve performance in terms of low speeds. Among them, the F-Roe and T-D-Roe schemes have been found to get incorrect density fluctuation in low Mach flows, which is expected to be with the square of Mach number. Asymptotic analysis presents the mechanism of how the density fluctuation problem relates to the incorrect order of terms in the energy equation \({{\tilde{\rho }} {\tilde{a}} {\tilde{U}}\varDelta U}\) . It is known that changing the upwind scheme coefficients of the pressure-difference dissipation term \(D^P\) and the velocity-difference dissipation term in the momentum equation \(D^{\rho U}\) to the order of \(O(c^{-1})\) and \(O(c^{0})\) can improve the level of pressure and velocity accuracy at low speeds. This paper shows that corresponding changes in energy equation can also improve the density accuracy in low speeds. We apply this modification to a recently proposed scheme, TV-MAS, to get a new scheme, TV-MAS2. Unsteady Gresho vortex flow, double shear-layer flow, low Mach number flows over the inviscid cylinder, and NACA0012 airfoil show that energy equation modification in these schemes can obtain the expected square Ma scaling of density fluctuations, which is in good agreement with corresponding asymptotic analysis. Therefore, this density correction is expected to be widely implemented into all-speed compressible flow solvers. PubDate: 2018-01-02 DOI: 10.1007/s10409-017-0737-9

Authors:Songsong Ji; Shaoqiang Tang Pages: 992 - 998 Abstract: In this paper, artificial boundary conditions are designed for out-of-plane waves in penta-graphene, a newly proposed allotrope of carbon. By matching the dispersion relation for acoustic branch phonons in the long wave limit, we determine parameters in proposed linear constraints among displacements and velocities at the boundary and nearby atoms. Reflection analysis for normal incidences and a numerical test demonstrate the effectiveness of the artificial boundary conditions. These conditions may be used for studying mechanical behaviours of the novel complex lattice of penta-graphene. PubDate: 2017-12-01 DOI: 10.1007/s10409-017-0668-5 Issue No:Vol. 33, No. 6 (2017)

Authors:Mingle Deng; Baozeng Yue Pages: 1095 - 1102 Abstract: This paper is focused on attitude tracking control of a spacecraft that is equipped with flexible appendage and partially filled liquid propellant tank. The large amplitude liquid slosh is included by using a moving pulsating ball model that is further improved to estimate the settling location of liquid in microgravity or a zero-g environment. The flexible appendage is modelled as a three-dimensional Bernoulli–Euler beam, and the assumed modal method is employed. A hybrid controller that combines sliding mode control with an adaptive algorithm is designed for spacecraft to perform attitude tracking. The proposed controller has proved to be asymptotically stable. A nonlinear model for the overall coupled system including spacecraft attitude dynamics, liquid slosh, structural vibration and control action is established. Numerical simulation results are presented to show the dynamic behaviors of the coupled system and to verify the effectiveness of the control approach when the spacecraft undergoes the disturbance produced by large amplitude slosh and appendage vibration. Lastly, the designed adaptive algorithm is found to be effective to improve the precision of attitude tracking. PubDate: 2017-12-01 DOI: 10.1007/s10409-017-0700-9 Issue No:Vol. 33, No. 6 (2017)

Authors:Yantao Yang; Junzhi Cui; Yifan Yu; Meizhen Xiang Abstract: In this paper the macroscopic damping model for dynamical behavior of the structures with random polycrystalline configurations at micro–nano scales is established. First, the global motion equation of a crystal is decomposed into a set of motion equations with independent single degree of freedom (SDOF) along normal discrete modes, and then damping behavior is introduced into each SDOF motion. Through the interpolation of discrete modes, the continuous representation of damping effects for the crystal is obtained. Second, from energy conservation law the expression of the damping coefficient is derived, and the approximate formula of damping coefficient is given. Next, the continuous damping coefficient for polycrystalline cluster is expressed, the continuous dynamical equation with damping term is obtained, and then the concrete damping coefficients for a polycrystalline Cu sample are shown. Finally, by using statistical two-scale homogenization method, the macroscopic homogenized dynamical equation containing damping term for the structures with random polycrystalline configurations at micro–nano scales is set up. PubDate: 2017-12-28 DOI: 10.1007/s10409-017-0733-0

Authors:T. Y. Ma; Y. N. Wang; L. Yuan; J. S. Wang; Q. H. Qin Abstract: Natural and artificial chiral materials such as deoxyribonucleic acid (DNA), chromatin fibers, flagellar filaments, chiral nanotubes, and chiral lattice materials widely exist. Due to the chirality of intricately helical or twisted microstructures, such materials hold great promise for use in diverse applications in smart sensors and actuators, force probes in biomedical engineering, structural elements for absorption of microwaves and elastic waves, etc. In this paper, a Timoshenko beam model for chiral materials is developed based on noncentrosymmetric micropolar elasticity theory. The governing equations and boundary conditions for a chiral beam problem are derived using the variational method and Hamilton’s principle. The static bending and free vibration problem of a chiral beam are investigated using the proposed model. It is found that chirality can significantly affect the mechanical behavior of beams, making materials more flexible compared with nonchiral counterparts, inducing coupled twisting deformation, relatively larger deflection, and lower natural frequency. This study is helpful not only for understanding the mechanical behavior of chiral materials such as DNA and chromatin fibers and characterizing their mechanical properties, but also for the design of hierarchically structured chiral materials. PubDate: 2017-12-22 DOI: 10.1007/s10409-017-0735-y

Authors:Hong-Ping Wang; Shi-Zhao Wang; Guo-Wei He Abstract: The pre-multiplied spanwise energy spectra of streamwise velocity fluctuations are investigated in this paper. Two distinct spectral peaks in the spanwise spectra are observed in low-Reynolds-number wall-bounded turbulence. The spectra are calculated from direct numerical simulation (DNS) of turbulent channel flows and zero-pressure-gradient boundary layer flows. These two peaks locate in the near-wall and outer regions and are referred to as the inner peak and the outer peak, respectively. This result implies that the streamwise velocity fluctuations can be separated into large and small scales in the spanwise direction even though the friction Reynolds number \(Re_\tau \) can be as low as 1000. The properties of the inner and outer peaks in the spanwise spectra are analyzed. The locations of the inner peak are invariant over a range of Reynolds numbers. However, the locations of the outer peak are associated with the Reynolds number, which are much higher than those of the outer peak of the pre-multiplied streamwise energy spectra of the streamwise velocity. PubDate: 2017-12-20 DOI: 10.1007/s10409-017-0731-2

Authors:Yang Zhao; Shuhong Dong; Peishi Yu; Junhua Zhao Abstract: The loading direction-dependent shear behavior of single-layer chiral graphene sheets at different temperatures is studied by molecular dynamics (MD) simulations. Our results show that the shear properties (such as shear stress–strain curves, buckling strains, and failure strains) of chiral graphene sheets strongly depend on the loading direction due to the structural asymmetry. The maximum values of both the critical buckling shear strain and the failure strain under positive shear deformation can be around 1.4 times higher than those under negative shear deformation. For a given chiral graphene sheet, both its failure strain and failure stress decrease with increasing temperature. In particular, the amplitude to wavelength ratio of wrinkles for different chiral graphene sheets under shear deformation using present MD simulations agrees well with that from the existing theory. These findings provide physical insights into the origins of the loading direction-dependent shear behavior of chiral graphene sheets and their potential applications in nanodevices. PubDate: 2017-12-15 DOI: 10.1007/s10409-017-0736-x

Authors:Takasar Hussain; Faiz Ahmad; Muhammad Ozair Abstract: Zero group velocity (ZGV) modes are studied in an isotropic cylinder. The L(0, 2) mode behaves anomalously for the materials with a value of the bulk velocity ratio, \(\kappa \) , in the range \(\sqrt{2}<\kappa <2.64\) and normally otherwise. All higher modes, except the first few, have no ZGV point for all isotropic materials. This is explained analytically by finding the slope of phase velocity dispersion curves of modes first when the phase velocity equals \(\kappa \) and then at their initial state. PubDate: 2017-12-15 DOI: 10.1007/s10409-017-0730-3

Authors:Pengbo Su; Bin Han; Zhongnan Zhao; Qiancheng Zhang; Tian Jian Lu Abstract: A novel square honeycomb-cored sandwich beam with perforated bottom facesheet is investigated under three-point bending, both analytically and numerically. Perforated square holes in the bottom facesheet are characterized by the area ratio of the hole to intact facesheet (perforation ratio). While for large-scale engineering applications like the decks of cargo vehicles and transportation ships, the perforations are needed to facilitate the fabrication process (e.g., laser welding) as well as service maintenance, it is demonstrated that these perforations, when properly designed, can also enhance the resistance of the sandwich to bending. For illustration, fair comparisons among competing sandwich designs having different perforation ratios but equal mass is achieved by systematically thickening the core webs. Further, the perforated sandwich beam is designed with a relatively thick facesheet to avoid local indention failure so that it mainly fails in two competing modes: (1) bending failure, i.e., yielding of beam cross-section and buckling of top facesheet caused by bending moment; (2) shear failure, i.e., yielding and buckling of core webs due to shear forcing. The sensitivity of the failure loads to the ratio of core height to beam span is also discussed for varying perforation ratios. As the perforation ratio is increased, the load of shear failure increases due to thickening core webs, while that of bending failure decreases due to the weakening bottom facesheet. Design of a sandwich beam with optimal perforation ratio is realized when the two failure loads are equal, leading to significantly enhanced failure load (up to 60% increase) relative to that of a non-perforated sandwich beam with equal mass. Graphical PubDate: 2017-12-15 DOI: 10.1007/s10409-017-0734-z

Authors:Xingjian Lin; Guoyi He; Xinyi He; Qi Wang; Longsheng Chen Abstract: The propulsive performance of an oblique school of fish is numerically studied using an immersed boundary technique. The effect of the spacing and wiggling phase on the hydrodynamics of the system is investigated. The hydrodynamics of the system is deeply affected by the spacing between each fish in the school. When the horizontal separation is smaller than the length of the fish body, the downstream fish exhibits a larger thrust coefficient and greater propulsive efficiency than the isolated fish. However, the corresponding values for the upstream fish are smaller. The opposite behavior occurs when the horizontal separation increases beyond the length of fish body. The propulsive performance of the entire oblique school of fish can be substantially enhanced when the separations are optimized. PubDate: 2017-12-12 DOI: 10.1007/s10409-017-0732-1

Authors:Jian-Long Cheng; Sheng-Qi Yang; Kui Chen; Dan Ma; Feng-Yuan Li; Li-Ming Wang Abstract: In this paper, uniaxial compression tests were carried out on a series of composite rock specimens with different dip angles, which were made from two types of rock-like material with different strength. The acoustic emission technique was used to monitor the acoustic signal characteristics of composite rock specimens during the entire loading process. At the same time, an optical non-contact 3D digital image correlation technique was used to study the evolution of axial strain field and the maximal strain field before and after the peak strength at different stress levels during the loading process. The effect of bedding plane inclination on the deformation and strength during uniaxial loading was analyzed. The methods of solving the elastic constants of hard and weak rock were described. The damage evolution process, deformation and failure mechanism, and failure mode during uniaxial loading were fully determined. The experimental results show that the \(\theta = 0{^{\circ }}\) – \(45{^{\circ }}\) specimens had obvious plastic deformation during loading, and the brittleness of the \(\theta = 60{^{\circ }}\) – \(90{^{\circ }}\) specimens gradually increased during the loading process. When the anisotropic angle \(\theta \) increased from \(0{^{\circ }}\) to \(90{^{\circ }}\) , the peak strength, peak strain, and apparent elastic modulus all decreased initially and then increased. The failure mode of the composite rock specimen during uniaxial loading can be divided into three categories: tensile fracture across the discontinuities ( \(\theta = 0{^{\circ }}\) – \(30{^{\circ }})\) , sliding failure along the discontinuities ( \(\theta = 45{^{\circ }}\) – \(75{^{\circ }})\) , and tensile-split along the discontinuities ( \(\theta = 90{^{\circ }})\) . The axial strain of the weak and hard rock layers in the composite rock specimen during the loading process was significantly different from that of the \(\theta = 0{^{\circ }}\) – \(45{^{\circ }}\) specimens and was almost the same as that of the \(\theta = 60{^{\circ }}\) – \(90{^{\circ }}\) specimens. As for the strain localization highlighted in the maximum principal strain field, the \(\theta = 0{^{\circ }}\) – \(30{^{\circ }}\) specimens appeared in the rock matrix approximately parallel to the loading direction, while in the \(\theta = 45{^{\circ }}\) – \(90{^{\circ }}\) specimens it appeared at the hard and weak rock layer interface. PubDate: 2017-10-17 DOI: 10.1007/s10409-017-0706-3

Authors:Changda Wang; Xuejun Chen; Peijun Wei; Yueqiu Li Abstract: The reflection and transmission of elastic waves through a couple-stress elastic slab that is sandwiched between two couple-stress elastic half-spaces are studied in this paper. Because of the couple-stress effects, there are three types of elastic waves in the couple-stress elastic solid, two of which are dispersive. The interface conditions between two couple-stress solids involve the surface couple and rotation apart from the surface traction and displacement. The nontraditional interface conditions between the slab and two solid half-spaces are used to obtain the linear algebraic equation sets from which the amplitude ratios of reflection and transmission waves to the incident wave can be determined. Then, the energy fluxes carried by the various reflection and transmission waves are calculated numerically and the normal energy flux conservation is used to validate the numerical results. The special case, couple-stress elastic slab sandwiched by the classical elastic half-spaces, is also studied and compared with the situation that the classical elastic slab sandwiched by the classical elastic half-spaces. Incident longitudinal wave (P wave) and incident transverse wave (SV wave) are both considered. The influences of the couple-stress are mainly discussed based on the numerical results. It is found that the couple-stress mainly influences the transverse modes of elastic waves. PubDate: 2017-10-16 DOI: 10.1007/s10409-017-0712-5