Geometric nonlinear dynamic analysis of curved beams using curved beam element

Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the curved beam.Based on exact nonlinear strain-displacement relation,virtual work principle is used to derive dynamic equations for a rotating curved beam,with the effects of axial extensibility,shear deformation and rotary inertia taken into account.The constant matrices are solved numerically utilizing the Gauss quadrature integration method.Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system.The present results are compared with those obtained by commercial programs to validate the present finite method.In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation,comparison of the results of the present formulation with those of the ADAMS software are made.Furthermore,the present results obtained from linear formulation are compared with those from nonlinear formulation,and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.     

Elastodynamic analysis of low tension cables using a new curved beam element

In this paper, we address and overcome the difficulties associated with the use of the classic cable theory to treat low tension cables by developing a new three-noded locking-free nonlinear curved beam element. Based upon nonlinear generalized curved beam theory, large deformations and rotations in the new element are formulated in terms of Updated Lagrangian framework. Consistently coupled polynomial displacement fields are used to satisfy the membrane locking-free condition and the requirement of being able to recover the inextensible bending modes. Quintic transverse displacement interpolation functions are used to represent the bending deformation of the beam, while the axial and torsional displacement fields are derived by integration of the presumably linear membrane and torsional shear strain fields, which are coupled with the transverse displacement fields. Numerical results are presented to demonstrate the superior accuracy and the high convergence rate of the newly developed curved beam element. The stability and accuracy of the new element are further validated by experiments of an instrumented free-swinging steel cable experiencing slack and low tension. Good agreements in cable position and tension are observed between the experimental results and the finite element predictions.     

Analysis of curved beams using a new differential transformation based curved beam element

Differential transformation method is used to obtain the shape functions for nodal variables of an arbitrarily non-uniform curved beam element including the effects of shear deformation considering axially functionally graded material. The proposed shape functions depend on the variations in cross-sectional area, moment of inertia, curvature and material properties along the axis of the curved beam element. The static and free vibration of axially functionally graded tapered curved beams including shear deformation and rotary inertia are studied through solving several examples. Numerical results are presented for circular, parabolic, catenary, elliptic and sinusoidal beams (both forms—prime and quadratic) with hinged-hinged, hinged-clamped and clamped-clamped and clamped-free end restraints. Three general taper types (depth taper, breadth taper and square taper) for rectangular cross section are studied. Out of plane vibration is studied and the lowest natural frequencies are calculated and compared with the published results. Out of plane buckling is investigated for circular beams due to radial load.     

螺旋压缩弹簧应力松弛特性试验分析及其应用

本文通过应力松弛试验、理论推导及数值模拟研究了高温下螺旋压缩弹簧的应力松弛规律,并利用加速模型对工况下弹簧应力松弛服役寿命做出预测.首先,根据螺旋压缩弹簧的结构特点搭建了弹簧应力松弛连续动态测试装置,该装置不仅避免了传统测试方法存在的缺陷,而且能够保证试验过程中位移载荷恒定,并实时监测载荷变化.本文以某飞机舱门单锁机构...     

Buckling analysis of discretely stiffened composite curved panels under compression and shear

An analytical method for the buckling discretely thin-wall stiffened composite curved panels under compression and shear is presented by use of finite strip-element method.In the report a simplified scheme for complex displacement functions is developed. It enables that computation to be performed in real number algebra easily. And a simple and easy way to satisify the boundary conditions is introduced.Numerical results are given and are in good agreement with available data.     

钢管混凝土拱稳定分析的三维退化层合曲梁单元

为计算钢管混凝土拱的屈曲荷载,本文在文[1]三维退化梁单元的基础上,采用等效数值积分法,构造,出120－20结点三维退化层合曲梁单元,并考虑几何非线性影响,给出用于层合梁或拱线弹性稳定性分析的有限元列式,最后,以绍兴轻纺大桥为工程背景,计算出轻纺大枯钢管混凝土拱面内及面外屈曲的稳定系数。     

Finite element analysis of the secondary buckling of a flat plate under uniaxial compression

Uemura and Byon (Int. J. Non-Linear Mech. 13, 1–14, 1978) presented experimental results and a numerical analysis about the secondary buckling of clamped flal plates under uniaxial compression. However, their numerical analysis is based upon an inconsistent flat plate finite element and it does not take into account the important influence of antisymmetric imperfections.This paper presents and discusses F.E.M. results obtained by two computer codes using very different approaches, and compares these results with the experimental ones.     

Modeling of system dynamics of a slewing flexible beam with moving payload pendulum

When a tower crane is handling payload via rotation and moving the carriage simultaneously the jib structure and the payload can be modeled as a system consisting of a slewing flexible clamed-free beam with the spherical payload pendulum that moves along the beam. The present work completes the dynamic modeling of the system mentioned above. The clamed-free beam attached to a rotating hub is modeled by Euler–Bernoulli beam theory. The payload is modeled as a sphere pendulum of point mass attached to via massless inextensible cable the carriage moving on the rotating beam. Non-linear coupled equations of motion of the in- and out-of-plane of the beam and the payload pendulum are derived by means of the Hamilton principle. Some remarks are made on the equations of motion.     

Design of a metastructure for vibration isolation with quasi-zero-stiffness characteristics using bistable curved beam

Nonlinear Dynamics - This work designs and analyzes a metastructure-based vibration isolation model to improve small-scale equipment's isolation effectiveness under low-frequency excitations....     

Modeling and analysis of an axially acceleration beam based on a higher order beam theory

In this paper, a higher order model equation is presented for an axially accelerating beam. Based on a new kinematic frame of the beam and continuum mechanics theory, the coupled governing equations of nonlinear vibration for axially accelerating beam are obtained with the aid of the generalized Hamilton principle. The governing equations take into account the characteristic of the material, the shear strain, the rotation strain and the effect of longitudinally varying tension due to the axial acceleration. The equations are decoupled into a nonlinear partial-integro-differential equations when the transverse nonlinear vibration is small. For the principal parametric resonances, the steady-state frequency responses are obtained by the multiple scales method. The stable and unstable interval are analyzed for the trivial and nontrivial steady-state response. Effects of the system parameters on the amplitude have been investigated. The results show that the material parameter (i.e, in-plane Poisson ratio) has a significant effect on the amplitude and the nonlinear vibration behavior type. The amplitude decrease with the growth of the in-plane Poisson ratio. The total potential energy has play a very important role in determining the amplitude of frequency response according to model analysis. Lastly, comparisons among the analytical solutions and numerical solutions are made and good agreements for the amplitude are found.     

Response of a finite beam in contact with a tensionless foundation under symmetric and asymmetric loading

In this work a general analytical model is developed for the static response of a beam resting on a tensionless elastic foundation subjected to a lateral point load. This load may either be located at the center of the beam or may be offset. An analytical/numerical solution is obtained to the governing equations; this solution makes no assumption about either the contact area or the kinematics associated with the transverse deflection of the beam. This is in contrast to previous work in which, for an infinite beam (where the load is symmetric by definition), implicit assumptions about the contact area and the response kinematics were made. Because these assumptions are dropped, the contact behavior differs in several fundamental ways from its infinite counterpart. Specifically, it is shown that (i) the contact area is a sensitive function of the beam length and that this function may change nonmonotonically, (ii) the contact area may depend on the magnitude of the load, (iii) asymmetric loads, which cannot exist in the infinite problem, have a dramatic influence the contact area for the finite system. These features are demonstrated with specific examples and explained in terms of the fundamental physics of the system. The implications for these behaviors are also discussed.     

On the elastoplastic cyclic analysis of plane beam structures using a flexibility-based finite element approach

This paper presents the extension of a flexibility-based large increment method (LIM) for the case of cyclic loading. In the last few years, LIM has been successfully tested for solving a range of non-linear structural problems involving elastoplastic material models under monotonic loading. In these analyses, the force-based LIM algorithm provided robust solutions and significant computational savings compared to the displacement-based finite element approach by using fewer elements and integration points. Although in cyclic analysis a step-by-step solution procedure has to be adopted to account for the plastic history, LIM will still have many advantages over the traditional finite element method. Before going into the basic idea of this extension, a brief discussion regarding LIM governing equations is presented followed by the proposed solution procedure. Next, the formulation is specified for the treatment of the elastic perfectly plastic beam element. The local stage for the beam behavior is discussed in detail and the required improvement for the LIM methodology is described. Illustrative truss and beam examples are presented for different non-linear material models. The results are compared with those obtained from a standard displacement method and again highlight the potential benefits of the proposed flexibility-based approach.     

Convergence analysis of a finite element method based on different moduli in tension and compression

When analyzing materials that exhibit different mechanical behaviors in tension and compression, an iterative approach is required due to material nonlinearities. Because of this iterative strategy, numerical instabilities may occur in the computational procedure. In this paper, we analyze the reason why iterative computation sometimes does not converge. We also present a method to accelerate convergence. This method is the introduction of a new pattern of shear modulus that was strictly derived according to the constitutive model based on the bimodular elasticity theory presented by Ambartsumyan. We test this procedure with a numerical example concerning a plane stress problem. Results obtained from this example show that the proposed method reduces the cost of computation and accelerates the convergence of the solution.     

Modeling and dynamics analysis of Zika transmission with contaminated aquatic environments

Nonlinear Dynamics - Since the outbreak in Brazil, Zika has received the worldwide attention. Zika virus is mainly transmitted via the bites of Aedes mosquito. Recently, experimental evidence...     

Stress and finite-strain analysis of a circular ring under diametral compression

Using a moiré, large-strain analysis method, a complete solution is shown in this paper of the fields of strain and stress for a circular ring subjected to diametral compression between two flat platens. The isotheticsu andv, obtained using 1000-lines-per-inch gratings, were differentiated photographically by the shifting technique (moiré-of-moiré) to determine ?u/?x, ?v/?y, ?u/?y and ?v/?x. Using the exact finite strain-displacement relationship, the Eulerian strains ? _x ^E , ? _y ^E and γ _xy ^E were computed. From these, the principal Eulerian strains were obtained. These results were verified with the isochromatics obtained from a large-deformation photoelasticity analysis. The ring was made of a polyurethane rubber which exhibits a linear relationship between natural strain and a newly introduced concept of “natural stress”. The Eulerian strains were converted to natural strains, and from these natural stresses were computed using the newly developed concept. Results are presented graphically for the whole field of the ring.     

Influence of spring dynamics and friction on a spring-actuated cam system

Summary  The paper investigates two important aspects, friction and spring motion, of the dynamics of a spring-actuated cam system. The characteristics of the friction on the camshaft are analyzed using the nonlinear pendulum experiment, while the parameters of the friction model are estimated using the optimization technique. The analysis reveals that the friction of the camshaft depends on stick–slip, Stribeck effect and viscous damping. Spring elements are found to have much influence on the dynamic characteristics. Hence, they are modeled as four-degrees-of-freedom lumped masses with equivalent springs. The lumped masses and equivalent springs are obtained to match the static stiffness and natural frequency of the actual spring. The appropriateness of the derived friction and spring model are verified by its application to a vacuum circuit-breaker mechanism of the cam-follower type. Received 23 March 2000; accepted for publication 21 November 2000     

Modeling and analysis of the transmission dynamics of tuberculosis without and with seasonality

A deterministic model of tuberculosis without and with seasonality is designed and analyzed into its transmission dynamics. We first present and analyze a tuberculosis model without seasonality, which incorporates the essential biological and epidemiological features of the disease. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium coexists with one or more stable endemic equilibria when the associated basic reproduction number is less than unity. The statistical data of tuberculosis (TB) cases show seasonal fluctuations in many countries. Then, the extension of our TB model by incorporating seasonality is developed and the basic reproduction ratio is defined. Parameter values of the model are estimated according to demographic and epidemiological data in Cameroon. The simulation results are in good accordance with the seasonal variation of the reported cases of active TB in Cameroon.     

Effect of aspect ratio on triaxial compression of multi-sphere ellipsoid assemblies simulated using a discrete element method

Here, we present a numerical investigation of the mechanical behavior of ellipsoids under triaxial compression for a range of aspect ratios. Our simulations use a multi-sphere approach in a three-dimensional discrete element method. All assemblies were prepared at their densest condition, and triaxial compression tests were performed up to extremely large strains, until a critical state was reached. The stress–strain relationship and the void ratio–strain behavior were evaluated. We found that the stress–dilatancy relationship of ellipsoids with different aspect ratios could be expressed as a linear equation. In particular, the aspect ratio influenced the position of the critical state lines for these assemblies. Particle-scale characteristics at the critical state indicate that particles tend to be flat lying, and the obstruction of particle rotation that occurs with longer particles affects their contact mechanics. Lastly, anisotropic coefficients related to aspect ratio were investigated to probe the microscopic origins of the macroscopic behavior. A detailed analysis of geometrical and mechanical anisotropies revealed the microscopic mechanisms underlying the dependency of peak and residual strengths on aspect ratio.     

Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting

A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting. The effects of two geometrical parameters on the first band gap of this periodic beam are investigated by the generalized differential quadrature rule (GDQR) method. The GDQR method is also used to calculate the forced vibration response of the beam and voltage of each piezoelectric layer when the beam is subject to a sinusoidal base excitation. Results obtained from the analytical method are compared with those obtained from the finite element simulation with ANSYS, and good agreement is found. The voltage output of this periodic beam over its first band gap is calculated and compared with the voltage output of the uniform piezoelectric beam. It is concluded that this periodic beam has three advantages over the uniform piezoelectric beam, i.e., generating more voltage outputs over a wide frequency range, absorbing vibration, and being less weight.