Mixed finite element and differential quadrature method for free and forced vibration and buckling analysis of rectangular plates

This paper presents a combined application of the finite element method （FEM） and the differential quadrature method （DQM） to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.

Static and free vibration analyses of functionally graded porous variable-thickness plates using an edge-based smoothed finite element method

The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element(MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index(k) and maximum porosity distributions(U) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.

ANALYSIS OF DYNAMICAL BUCKLING AND POST BUCKLING FOR BEAMS BY FINITE SEGMENT METHOD

Based on the multi-rigid body discretization model, namely, finite segment model,a chain multi-rigid-body-hinge-spring system model of a beam was presented, then a nonlinear parametrically exacted vibration equation of multi-degrees of freedom system was established using the coordination transformation method, and its resonance fields were derived by the restriction parameter method, that is, the dynamical buckling analysis of the beam. Because the deformation of a beam is not restricted by the discrete model and dynamic equation, the post buckling analysis can be done in above math model. The numerical solutions of a few examples were obtained by direct integrated method, which shows that the mechanical and math model gotten is correct.

Prolonged simulation of near-free surface underwater explosion based on Eulerian finite element method

n the area of naval architecture and ocean engineering,the research about the underwater xplosion problem is of great significance.To achieve prolonged simulation of near-free surface underwater explosion,the underwater explosion transient numerical model is established in this paper based on compressible Eulerian finite element method(EFEM).Compared with Geers Hunter formula,EFEM is availably validated by simulating the free-field underwater xplosion case.Then,the bubble pulsation and flow field dynamic characteristics of the cases with different underwater explosive depth are compared in this work.Lastly,the height of the water hump and the pressure of flow flied are analyzed quantitatively through the simulation results.

An Effective Method for Free Vibration of Plate on Elastic Half Space

The vibration analysis of a plate on an elastic foundation is an important problem in engineering. It is the interaction of a plate with the three-dimensional half space and the plate is usually loaded from both the upper and lower surfaces. The contact pressure from the soil can not be predefined. According to Lamb's solution for a single oscillating force acting on a point on the surface of an elastic half space, and the relevant approximation formulae, a relation between the local pressure and the deflection of the plate has been proposed. Based on this analysis, the reaction of the soil can be represented as the deformation of the plate. Therefore, the plate can be separated from the soil and only needs to be divided by a number of elements in the analysis. The following procedure is the same as the standard finite element method. This is a semi-analytical and semi-numerical method. It has been applied to the dynamic analysis of circular or rectangular plates on the elastic half space, at low or high frequency vibration, and on rigid, soft or flexible foundations. The results show that this method is versatile and highly accurate.

Coupled Vibration Analysis of Vehicle-Bridge System Based on Multi-Boby Dynamics

For establishing the refined numerical simulation model for coupled vibration between vehicle and bridge, the refined three-dimensional vehicle model is setup by multi-body system dynamics method, and finite element method of dynamic model is adopted to model the bridge. Taking Yujiang River Bridge on Nanning-Guangzhou railway line in China as study background, the?refined numerical simulation model of whole vehicle and whole bridge system for coupled vibration analysis is set up. The dynamic analysis model of the cable-stayed bridge is established by finite element method, and the natural vibration properties of the bridge are analyzed. The German ICE Electric Multiple Unit (EMU) train refined three-dimensional space vehicle model is set up by multi-system dynamics software SIMPACK, and the multiple non-linear properties are considered. The space vibration responses are calculated by co-simulation based on multi-body system dynamics and finite element method when the ICE EMU train passes the long span cable-stayed bridge at different speeds. In order to test if the bridge has the sufficient lateral or vertical rigidity and the operation stability is fine. The calculation results show: The operation safety can be guaranteed, and comfort?index is “excellent”. The bridge has sufficient rigidity, and vibration is in good condition.

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

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.

Tactile Response Characterization of a Dynamic System Using Craig-Bampton Method

Vibrational characteristics in small horizontal axis wind turbine system are presented in this study with a system concept called tactile response and substructuring.The main focus is on managing the dynamic properties like vibration,noise,and harshness that occur during the operational mode.Tactile response is defined as the response of subsystem which is induced when a human body touches a vibrating system.Sub structuring is a computational method used to reduce the dynamic behavior of a large complex system with a smaller number of degrees of freedom without disturbing the mesh size of the model.Sub structuring has the ability to combine numerical results along with the experimental results.Combination of substructuring and tactile response is applied in this study.Mode shapes of the system are analyzed and results obtained are correlated within this study to provide better optimization of the results.Wind turbine excited with wind energy depends on wind speed.Torsional vibration has a significant role in determining dynamic properties.Torsional vibration is caused as a result of the rotation of the turbine blade and depends on wind speed.The study gives importance to investigating the ability to simulate the numerical method and tactile response to predict and improve dynamic properties.

Comparison of methods for vibration analysis of electrostatic precipitators

The paper presents two methods for the formulation of free vibration analysis of collecting electrodes of precipitators.The first,called the hybrid finite element method, combines the finit element method used for calculations of spring deformations with the rigid finite element method used to reflect mass and geometrical features,which is called the hybrid finite element method.As a result,a model with a diagonal mass matrix is obtained.Due to a specific geometry of the electrodes,which are long plates of complicated shapes,the second method proposed is the strip method which is a semi-analytical method.The strip method allows us to formulate the equations of motion with a considerably smaller number of generalized coordinates.Results of numerical calculations obtained by both methods are compared with those obtained using commercial software like ANSYS and ABAQUS.Good compatibility of results is achieved.

Analysis of the Behavior of a Square Plate in Free Vibration by FEM in Ansys

In the realization of mechanical structures, achieving stability and balance is a problem commonly encountered by engineers in the field of civil engineering, mechanics, aeronautics, biomechanics and many others. The study of plate behavior is a very sensitive subject because it is part of the structural elements. The study of the dynamic behavior of free vibration structures is done by modal analysis in order to calculate natural frequencies and modal deformations. In this paper, we present the modal analysis of a thin rectangular plate simply supported. The analytical solution of the differential equation is obtained by applying the method of separating the variables. We are talking about the exact solution of the problem to the limit values. However, numerical methods such as the finite element method allow us to approximate these functions with greater accuracy. It is one of the most powerful computational methods for predicting dynamic response in a complex structure subject to arbitrary boundary conditions. The results obtained by MEF through Ansys 15.0 are then compared with those obtained by the analytical method.

Free vibration analysis of laminated FG-CNT reinforced composite beams using finite element method

In the present study, the free vibration of laminated functionally graded carbon nanotube reinforced composite beams is analyzed. The laminated beam is made of perfectly bonded carbon nanotubes reinforced composite (CNTRC) layers. In each layer, single-walled carbon nanotubes are assumed to be unifonnly distributed (UD) or functionally graded (FG) distributed along the thickness direction. Effective material properties of the two-phase composites, a mixture of carbon nanotubes (CNTs) and an isotropic polymer, are calculated using the extended nile of mixture. The first-order shear deformation theory is used to formulate a governing equation for predicting free vibration of laminated functionally graded carbon nanotubes reinforced composite (FG?CNTRC) beams. The governing equation is solved by the finite element method with various boundary conditions. Several numerical tests are perfbnned to investigate the influence of the CNTs volume fractions, CNTs distributions, CNTs orientation angles, boundary conditions, length-to-thickness ratios and the numbers of layers on the frequencies of the laminated FG-CNTRC beams. Moreover, a laminated composite beam combined by various distribution types of CNTs is also studied.

GENERAL ANALYTIC SOLUTION OF DYNAMIC RESPONSE OF BEAMS WITH NONHOMOGENEITY AND VARIABLE CROSS-SECTION

In this paper, a new method, the step-reduction method, is proposed to investigate the dynamic response of the Bernoulli-Euler beams with arbitrary nonhomogeneity and arbitrary variable cross-section 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 cross-section 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 two unknowns which are independent of the numbers of elements divided. The present analysis can also be extended to the study of the vibration of such beams with viscous and hysteretic damping and other kinds of beams and other structural elements with arbitrary nonhomogeneity and arbitrary variable thickness.

Vibration analysis of two-dimensional structures using micropolar elements

Based on the micropolar theory(MPT),a two-dimensional(2 D)element is proposed to describe the free vibration response of structures.In the context of the MPT,a 2 D formulation is developed within the ABAQUS finite element software.The user-defined element(UEL)subroutine is used to implement a micropolar element.The micropolar effects on the vibration behavior of 2 D structures with arbitrary shapes are studied.The effect of micro-inertia becomes dominant,and by considering the micropolar effects,the frequencies decrease.Also,there is a considerable discrepancy between the predicted micropolar and classical frequencies at small scales,and this difference decreases when the side length-to-length scale ratio becomes large.

Identification of hydrodynamic coefficients from experiment of vortex-induced vibration of slender riser model

One of the challenges in predicting the dynamic response of deepwater risers under vortex-induced vibration （VIV） is that it runs short of believable fluid loading model. Moreover, the hydrodynamic loading is also difficult to be measured directly in the VIV experiments without disturbing the fluid field. In the present work, by means of a finite element analysis method based on the experimental data of the response displacements, the total instantaneous distributions of hydrodynamic forces together with the hydrodynamic coefficients on the riser model with large aspect ratio （length/ddiameter） of 1750 are achieved. The steady current speeds considered in the experiments of this work are ranging from 0.15 rn/s to 0.60 m/s, giving the Reynolds Number between 2400 and 9600. The hydrodynamic coefficients are evaluated at the fundamental frequency and in the higher order frequency components for both in-line and cross-flow directions. It is found that the Root-Mean Squared hydrodynamic forces of the higher order response frequency are larger than those of the fundamental response frequency. Negative lift or drag coefficients are found in the numerical results which is equivalent to the effect of fluid damping.

Structural finite element model updating using incomplete ambient vibration modal data

This paper presents an effective approach for updating finite element dynamic model from incomplete modal data identified from ambient vibration measurements.The proposed method is based on the relationship between the perturbation of structural parameters such as stiffness and mass changes and the modal data measurements of the tested structure such as measured mode shape readings.Structural updating parameters including both stiffness and mass parameters are employed to represent the differences in structural parameters between the finite element model and the associated tested structure.These updating parameters are then evaluated by an iterative solution procedure,giving optimised solutions in the least squares sense without requiring an optimisation technique.In order to reduce the influence of modal measurement uncertainty,the truncated singular value decomposition regularization method incorporating the quasi-optimality criterion is employed to produce reliable solutions for the structural updating parameters.Finally,the numerical investigations of a space frame structure and the practical applications to the Canton Tower benchmark problem demonstrate that the proposed method can correctly update the given finite element model using the incomplete modal data identified from the recorded ambient vibration measurements.

液压蓄能式竖向隔震装置性能试验及隔震参数分析

提出一种由液压油缸和蓄能器组成的新型竖向隔震装置,用于建筑结构竖向隔震.首先,介绍液压蓄能式竖向隔震装置的工作原理,并建立了非线性刚度模型和阻尼耗能模型.其次,开展了频率相关性、位移幅值相关性的反复加载试验,测得液压蓄能式竖向隔震装置的竖向刚度和阻尼耗能性能参数.试验结果表明,隔震装置的竖向刚度呈现非线性变化,理论值和实测试验值误差在±3%以内;隔震装置的滞回曲线饱满,具有较强的耗能性能,阻尼特性为速度相关型,试验结果与理论计算值吻合.最后,利用有限元方法建立不同竖向刚度和阻尼系数的竖向隔震结构数值分析模型,研究了在竖向地震作用下,隔震装置参数对结构隔震效果的影响.结果表明,隔震结构竖向刚度降低会导致竖向位移响应增大,而竖向加速度响应减小;通过调节阻尼调节阀可有效控制隔震结构在地震作用下的竖向位移,从而实现良好的隔震效果.

一种多层组合梁自由振动分析的混合有限元法

基于截面等效,提出了多层组合梁的二维分析模型。使用混合能变分原理,以包含频率函数的节点位移及其能量对偶的应力分量为单元节点未知量,引入混合元对梁长方向进行离散,建立动力学状态空间控制方程;接着引入微分求积法(Differential Quadrature Method,DQM)对控制方程进行梁高度方向的离散,求得组合梁在不同轴力与边界条件下的动力学方程。以混凝土-木材组合梁、波形钢腹板梁和钢-混组合梁为例进行验证。该方法基于二维理论,可为梁理论提供假设依据和误差分析的基准。

大跨度公铁两用斜拉-悬索协作体系桥断索动力响应

研究大跨度公铁两用斜拉-悬索协作体系桥在极端作用下发生断索时桥梁结构及桥上列车的动力响应,以G3铜陵长江公铁大桥为研究对象,建立全桥有限元模型;研究各个位置斜拉索、吊索断裂后桥梁结构的动力响应;研究在列车-桥梁耦合振动作用下,各断索组合工况中桥梁及列车的动力响应.结果表明:斜拉-悬索协作体系桥具有较高的结构刚度及安全冗余;在单根斜拉索、吊索断索后,可保持列车通行;在吊索区域单侧发生4根以上断索,可导致连续断索破坏;在斜拉索-吊索交替及斜拉索区域,单侧断索达到8根也不会发生连续断索破坏;断索动力放大系数取2.0合理,但仅对断索位置附近剩余吊索和斜拉索具有工程应用价值;当断索发生时,若列车经过,列车竖向加速度会发生突变,但仍在安全范围内;剩余斜拉索与吊索动应力增加主要来自于主梁作用,列车作用占比不超过13%.

悬臂同轴双转子系统不平衡耦合振动抑制试验研究

针对悬臂同轴双转子系统不平衡耦合振动突出问题,以某开式转子发动机输出端双转子系统为研究对象,对悬臂双转子系统振动耦合机理进行了理论推导、仿真分析和试验研究。首先,采用有限元法(FEM)建立了双转子系统等效动力学模型和耦合动力学方程,分析了悬臂同轴双转子系统耦合振动机理;然后,利用有限元软件对双转子系统进行了模态分析、临界转速分析以及不平衡响应分析,建立了自敏感系数概念以定量评价系统对不平衡振动的敏感度和耦合状态;最后,根据实际结构设计了悬臂同轴双转子实验台,进行了不同转速比下的不平衡振动抑制实验,并结合实验结果对仿真结果进行了验证。研究结果表明:模拟仿真提出的自敏感系数可作为双转子系统实际振动测点布置和不平衡振动抑制策略的理论依据;通过应用先平衡内转子后平衡外转子的不平衡振动分步抑振策略,可使双转子系统不平衡振动降幅达80%以上。该研究对双转子系统传感器测点布局和系统耦合振动抑制具有一定的指导意义。

基于现场实测反演的地铁运行诱发邻近结构振动预测

准确预测地铁运行引起的拟建结构振动具有重要的理论意义和工程应用价值。目前现场实测主要用于验证数值模拟的准确性,较少直接用于数值模型校准。为解决拟建结构振动预测难的问题,提出了基于地下室建成前地表振动实测和有限元模拟的地铁运行诱发振动频域反演预测方法。首先,开展了地下室建成前地铁运行引起的场地振动实测,然后由隧道-分层地基有限元模型计算场地振动传递函数。结合传递函数原理和地表实测反演得到振源。随后,将反演振源输入含地下室结构的有限元模型,开展振动预测分析。结果表明,预测的地下室振动与实测结果吻合良好,提出的方法可为地铁运行引起拟建结构振动的准确预测提供重要的支撑。