1.

FREE VIBRATION ANALYSIS OF LATTICE SANDWICH BEAMS UNDER SEVERAL TYPICAL BOUNDARY CONDITIONS





Jia Lou Bing Wang Li Ma Linzhi Wu《Acta Mechanica Solida Sinica》,2013年第5期


Free vibration problems of lattice sandwich beams under several typical boundary conditions are investigated in the present paper. The lattice sandwich beam is transformed to an equivalent homogeneous threelayered sandwich beam. Unlike the traditional analytical model in which the rotation angles of the face sheets and the core are assumed the same, different rotation angles are considered in this paper to characterize the real response of sandwich beams. The analytical solutions of the natural frequencies for several typical boundary conditions are obtained. The effects of material properties and geometric parameters on the natural frequencies are also investigated.

2.

PARAMETRIC VARIATIONAL PRINCIPLE BASED ELASTICPLASTIC ANALYSIS OF HETEROGENEOUS MATERIALS WITH VORONOI FINITE ELEMENT METHOD





张洪武 王辉《应用数学和力学(英文版)》,2006年第27卷第8期


The Voronoi cell finite element method (VCFEM) is adopted to overcome the limitations of the classic displacement based finite element method in the numerical simulation of heterogeneous materials. The parametric variational principle and quadratic programming method are developed for elasticplastic Voronoi finite element analysis of twodimensional problems. Finite element formulations are derived and a standard quadratic programming model is deduced from the elasticplastic equations. Influence of microscopic heterogeneities on the overall mechanical response of heterogeneous materials is studied in detail. The overall properties of heterogeneous materials depend mostly on the size, shape and distribution of the material phases of the microstructure. Numerical examples are presented to demonstrate the validity and effectiveness of the method developed.

3.

Nanoscale finite element models for vibrations of singlewalled carbon nanotubes: atomistic versus continuum





R ANSARI S ROUHI M ARYAYI《应用数学和力学(英文版)》,2013年第34卷第10期


By the atomistic and continuum finite element models, the free vibration behavior of singlewalled carbon nanotubes （SWCNTs） is studied. In the atomistic finite element model, the bonds and atoms are modeled by the beam and point mass elements, respectively. The molecular mechanics is linked to structural mechanics to determine the elastic properties of the mentioned beam elements. In the continuum finite element approach, by neglecting the discrete nature of the atomic structure of the nanotubes, they are modeled with shell elements. By both models, the natural frequencies of SWCNTs are computed, and the effects of the geometrical parameters, the atomic structure, and the boundary conditions are investigated. The accuracy of the utilized methods is verified in comparison with molecular dynamic simulations. The molecular structural model leads to more reliable results, especially for lower aspect ratios. The present analysis provides valuable information about application of continuum models in the investigation of the mechanical behaviors of nanotubes.

4.

GENERAL ANALYTIC SOLUTION OF DYNAMIC RESPONSE OF BEAMS WITH NONHOMOGENEITY AND VARIABLE CROSSSECTION





叶开沅 童晓华 纪振义《应用数学和力学(英文版)》,1992年第13卷第9期


In this paper, a new method, the stepreduction method, is proposed to investigate the dynamic response of the BernoulliEuler beams with arbitrary nonhomogeneity and arbitrary variable crosssection under arbitrary loads. Both free vibration and forced vibration of such beams are studied. The new method requires to discretize the space domain into a number of elements. Each element can be treated as a homogeneous one with uniform thickness. Therefore, the general analytical solution of homogeneous beams with uniform crosssection can be used in each element. Then, the general analytic solution of the whole beam in terms of initial parameters can be obtained by satisfying the physical and geometric continuity conditions at the adjacent elements. In the case of free vibration, the frequency equation in analytic form can be obtained, and in the case of forced vibration, a final solution in analytical form can also be obtained which is involved in solving a set of simultaneous algebraic equations with only

5.

Coupled flexuraltorsional vibration band gap in periodic beam including warping effect





方剑宇 郁殿龙 韩小云 蔡力《中国物理 B》,2009年第18卷第4期


The propagation of coupled flexuraltorsional vibration in the periodic beam including warping effect is investigated with the transfer matrix theory. The band structures of the periodic beam, both including warping effect and ignoring warping effect, are obtained. The frequency response function of the finite periodic beams is simulated with finite element method, which shows large vibration attenuation in the frequency range of the gap as expected. The effect of warping stiffness on the band structure is studied and it is concluded that substantial error can be produced in high frequency range if the effect is ignored. The result including warping effect agrees quite well with the simulated result.

6.

NEURO FUZZY MODEL FOR PREDICTING THE DYNAMIC CHARACTERISTICS OF BEAMS





Imad O. Bachi Nabeel Abdulrazzaq Zeng He《Acta Mechanica Solida Sinica》,2014年第1期


An adaptive neurofuzzy inference system （ANFIS） is introduced to predict the dynamic behavior of beams. The effects of axial forces and large displacements are considered in the analysis. A database of tests for the dynamic characteristics of beams is developed from the experimental tests. The responses of nonlinear vibration force for the single and multiplestepped beams are calculated from the finite element method （FEM）, experimental tests and neurofuzzy model for comparison. The neurofuzzy model provides a general framework for the combination of neural networks and fuzzy logic. It is more flexible with more options of incorporating the fuzzy nature of the realworld system and is an useful estimation tool for the dynamic characteristics of beams. Therefore, ANFIS can be a useful tool for dynamic behaviour analysis of multiplestepped beams subjected to axial loads and large displacement.

7.

Coupled bendingtorsion vibration of a homogeneous beam with a single delamination subjected to axial loads and static end moments





Yang Liu DongWei Shu《Acta Mechanica Sinica》,2014年第30卷第4期


Delaminations in structures may significantly reduce the stiffness and strength of the structures and may affect their vibration characteristics. As structural components, beams have been used for various purposes, in many of which beams are often subjected to axial loads and static end moments. In the present study, an analytical solution is developed to study the coupled bendingtorsion vibration of a homogeneous beam with a single delamination subjected to axial loads and static end moments. Euler–Bernoulli beam theory and the "free mode" assumption in delamination vibration are adopted. This is the first study of the influences of static end moments upon the effects of delaminations on natural frequencies, critical buckling loads and critical moments for lateral instability. The results show that the effects of delamination on reducing natural frequencies, critical buckling load and critical moment for lateral instability are aggravated by the presence of static end moment. In turn, the effects of static end moments on vibration and instability characteristics are affected by the presence of delamination. The analytical results of this study can serve as a benchmark for finite element method and other numerical solutions.

8.

Novel implementation of homogenization method to predict effective properties of periodic materials





GengDong Cheng YuanWu Cai Liang Xu《Acta Mechanica Sinica》,2013年第29卷第4期


Representative volume element (RVE) method and asymptotic homogenization (AH) method are two widely used methods in predicting effective properties of periodic materials. This paper develops a novel implementation of the AH method, which has rigorous mathematical foundation of the AH method, and also simplicity as the RVE method. This implementation can be easily realized using commercial software as a black box, and can use all kinds of elements available in commercial software to model unit cells with rather complicated microstructures, so the model may remain a fairly small scale. Several examples were carried out to demonstrate the simplicity and effectiveness of the new implementation.

9.

Free vibration of FGM Timoshenko beams with throughwidth delamination





LI ShiRong FAN LiangLiang《中国科学:物理学 力学 天文学(英文版)》,2014年第57卷第5期


Free vibration of functionally graded beams with a throughwidth delamination is investigated.It is assumed that the material property is varied in the thickness direction as power law functions and a single throughwidth delamination is located parallel to the beam axis.The beam is subdivided into three regions and four elements.Governing equations of the beam segments are derived based on the Timoshenko beam theory and the assumption of‘constrained mode’.By using the differential quadrature element method to solve the eigenvalue problem of ordinary differential equations governing the free vibration,numerical results for the natural frequencies of the beam are obtained.Natural frequencies of delaminated FGM beam with clamped ends are presented.Effects of parameters of the material gradients,the size and location of delamination on the natural frequency are examined in detail.

10.

Dynamic analysis of beamcable coupled systems using Chebyshev spectral element method





&prev_q=YiXin Huang" target="_blank">YiXin Huang &prev_q=Hao Tian" target="_blank">Hao Tian Yang Zhao《Acta Mechanica Sinica》,2017年第33卷第5期


The dynamic characteristics of a beam–cable coupled system are investigated using an improved Chebyshev spectral element method in order to observe the effects of adding cables on the beam. The system is modeled as a double Timoshenko beam system interconnected by discrete springs. Utilizing Chebyshev series expansion and meshing the system according to the locations of its connections, numerical results of the natural frequencies and mode shapes are obtained using only a few elements,and the results are validated by comparing them with the results of a finiteelement method.Then the effects of the cable parameters and layout of connections on the natural frequencies and mode shapes of a fixedpinned beam are studied.The results show that the modes of a beam–cable coupled system can be classified into two types,beam mode and cable mode,according to the dominant deformation.To avoid undesirable vibrations of the cable,its parameters should be controlled in a reasonable range,or the layout of the connections should be optimized.

11.

Elastically restrained BernoulliEuler beams applied to rotary machinery modelling





Tiago A.N.Silva Nuno M.M.Maia《Acta Mechanica Sinica》,2011年第27卷第1期


Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending,the authors deal with the free vibration of elastically restrained BernoulliEuler beams carrying a finite number of concentrated elements along their length.Based on Rayleigh's quotient,an iterative strategy is developed to find the approximated torsional stiffness coefficients,which allows the reconciliation between the theoretical model results and the experimental ones,obtained through impact tests.The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh's quotient but also on the mode shapes,considering the shape functions defined in branches.Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.

12.

Global asymptotical properties for a diffused HBV infection model with CTL immune response and nonlinear incidence





王绍利 冯新龙 何银年《数学物理学报(B辑英文版)》,2011年第31卷第5期


This article proposes a diffused hepatitis B virus (HBV) model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viralfree equilibrium and immunefree equilibrium of the model are obtained. Global stability of the positive equilibrium of the model is also considered. The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.

13.

Analytical modeling of sandwich beam for piezoelectric bender elements





周燕国 陈云敏 丁皓江《应用数学和力学(英文版)》,2007年第28卷第12期


Piezoelectric bender elements are widely used as electromechanical sensors and actuators.An analytical sandwich beam model for piezoelectric bender elements was developed based on the firstorder shear deformation theory(FSDT),which assumes a single rotation angle for the whole crosssection and a quadratic distribution function for coupled electric potential in piezoelectric layers,and corrects the effect of transverse shear strain on the electric displacement integration.Free vibration analysis of simply supported bender elements was carried out and the numerical results showed that,solu tions of the present model for various thicknesstolength ratios are compared well with the exact twodimensional solutions,which presents an efficient and accurate model for analyzing dynamic electromechanical responses of bender elements.

14.

Size effect of lattice material and minimum weight design 被引次数：1





Jun Yan WenBo Hu ZhenHua Wang ZunYi Duan《Acta Mechanica Sinica》,2014年第30卷第2期


The size effects of microstructure of lattice materials on structural analysis and minimum weight design are studied with extented multiscale finite element method（EMsFEM） in the paper. With the same volume of base material and configuration, the structural displacement and maximum axial stress of microrod of lattice structures with different sizes of microstructure are analyzed and compared.It is pointed out that different from the traditional mathematical homogenization method, EMsFEM is suitable for analyzing the structures which is constituted with lattice materials and composed of quantities of finitesized microrods.The minimum weight design of structures composed of lattice material is studied with downscaling calculation of EMsFEM under stress constraints of microrods. The optimal design results show that the weight of the structure increases with the decrease of the size of basic subunit cells. The paper presents a new approach for analysis and optimization of lattice materials in complex engineering constructions.

15.

VIBRATION SUPPRESSION OF A FLEXIBLE PIEZOELECTRIC BEAM USING BP NEURAL NETWORK CONTROLLER





Zhicheng Qiu Xiangtong Zhang Chunde Ye《Acta Mechanica Solida Sinica》,2012年第4期


This paper aims at modeling and developing vibration control methods for a flexible piezoelectric beam. A collocated sensor/actuator placement is used. Finite element analysis (FEA) method is adopted to derive the dynamics model of the system. A back propagation neural network (BPNN) based proportionalderivative (PD) algorithm is applied to suppress the vibration. Simulation and experiments are conducted using the FEA model and BPNNPD control law. Experimental results show good agreement with the simulation results using finite element modeling and the neural network control algorithm.

16.

A novel implementation algorithm of asymptotic homogenization for predicting the effective coefficient of thermal expansion of periodic composite materials





Yongcun Zhang Shipeng Shang Shutian Liu《Acta Mechanica Sinica》,2017年第33卷第2期


Asymptotic homogenization (AH) is a general method for predicting the effective coefficient of thermal expansion (CTE) of periodic composites. It has a rigorous mathematical foundation and can give an accurate solution if the macrostructure is large enough to comprise an infinite number of unit cells. In this paper, a novel implementation algorithm of asymptotic homogenization (NIAH) is developed to calculate the effective CTE of periodic composite materials. Compared with the previous implementation of AH, there are two obvious advantages. One is its implementation as simple as representative volume element (RVE). The new algorithm can be executed easily using commercial finite element analysis (FEA) software as a black box. The detailed process of the new implementation of AH has been provided. The other is that NIAH can simultaneously use more than one element type to discretize a unit cell, which can save much computational cost in predicting the CTE of a complex structure. Several examples are carried out to demonstrate the effectiveness of the new implementation. This work is expected to greatly promote the widespread use of AH in predicting the CTE of periodic composite materials.

17.

On the homogenization of metal matrix composites using strain gradient plasticity





Reza Azizi Christian F.Niordson Brian Nyvang Legarth《Acta Mechanica Sinica》,2014年第30卷第2期


The homogenized response of metal matrix composites（MMC） is studied using strain gradient plasticity.The material model employed is a rate independent formulation of energetic strain gradient plasticity at the micro scale and conventional rate independent plasticity at the macro scale. Free energy inside the micro structure is included due to the elastic strains and plastic strain gradients. A unit cell containing a circular elastic fiber is analyzed under macroscopic simple shear in addition to transverse and longitudinal loading. The analyses are carried out under generalized plane strain condition. Micromacro homogenization is performed observing the HillMandel energy condition,and overall loading is considered such that the homogenized higher order terms vanish. The results highlight the intrinsic sizeeffects as well as the effect of fiber volume fraction on the overall response curves, plastic strain distributions and homogenized yield surfaces under different loading conditions. It is concluded that composites with smaller reinforcement size have larger initial yield surfaces and furthermore,they exhibit more kinematic hardening.

18.

ACTIVE VIBRATION CONTROL OF FINITE LSHAPED BEAM WITH TRAVELLING WAVE APPROACH 被引次数：1





Chunchuan Liu Fengming Li Wenhu Huang《Acta Mechanica Solida Sinica》,2010年第23卷第5期


In this paper, the disturbance propagation and active vibration control of a finite Lshaped beam axe studied. The dynamic response of the structure is obtained by the travelling wave approach. The active vibration suppression of the finite Lshaped beam is performed based on the structural vibration power flow. In the numerical calculation, the influences of the near field effect of the error sensor and the small error of the control forces on the control results are all considered. The simulation results indicate that the structural vibration response in the medium and high frequency regions can be effectively computed by the travelling wave method. The effect of the active control by controlling the power flow is much better than that by controlling the acceleration in some cases. And the control results by the power flow method are slightly affected by the locations of the error sensor and the small error of the control forces.

19.

Finite element modeling of acoustic scattering from an encapsulated microbubble near rigid boundary





黄蓓 张艳丽 章东 龚秀芬《中国物理 B》,2010年第19卷第5期


This article proposes a finite element model(FEM) for predicting the acoustic scattering from an encapsulated microbubble near rigid boundary.The validity of the model is first examined by comparing the acoustic nonlinear response of a free microbubble with that obtained by the Church model.Then this model is used to investigate the effect of the rigid boundary on acoustic scattering signals from microbubble.The results indicate that the resonance frequency decreases while the oscillation amplitude increases as the microbubble approaches the rigid boundary.In addition,the fundamental component of the acoustic scattering signal is enhanced compared with that of the free microbubble.

20.

Atomistic simulation of free transverse vibration of graphene,hexagonal SiC,and BN nanosheets





DanhTruong Nguyen MinhQuy Le ThanhLam Bui HaiLe Bui《Acta Mechanica Sinica》,2017年第33卷第1期


Free transverse vibration of monolayer graphene, boron nitride (BN), and silicon carbide (SiC) sheets is investigated by using molecular dynamics finite element method. Eigenfrequencies and eigenmodes of these three sheets in rectangular shape are studied with different aspect ratios with respect to various boundary conditions. It is found that aspect ratios and boundary conditions affect in a similar way on natural frequencies of graphene, BN, and SiC sheets. Natural frequencies in all modes decrease with an increase of the sheet's size. Graphene exhibits the highest natural frequencies, and SiC sheet possesses the lowest ones. Missing atoms have minor effects on natural frequencies in this study.
