Nonlinear dynamic buckling and stability of autonomous structural systems

A general approach for the nonlinear dynamic buckling and stability of dissipative or nondissipative structural systems governed by autonomous ordinary differential equations (ODEs) is presented. Geometrically imperfect systems with or without symmetric imperfections, as well as statically stable systems, which, in addition to a monotonically rising (stable) equilibrium path exhibit an unstable complementary path, are considered. The role of the dynamic buckling mechanism of the basin of attraction of a stable equilibrium point (on the prebuckling path), as well as the inset (stable) and outset (unstable) manifolds of a saddle (on a physical or complementary unstable path), are comprehensively explained. A static energy criterion for determining dynamic buckling loads for vanishing (but nonzero) damping and lower bound estimates of exact dynamic buckling loads are presented. Metastability, loading discontinuity and chaos-like phenomena are also revealed. The analysis is supplemented by two illustrative models of practical engineering importance.     

Dynamic buckling of a simple geometrically imperfect frame using Catastrophe Theory

This paper deals with nonlinear static and dynamic buckling of a geometrically imperfect two-bar frame due to initially crooked bars, which is subjected to an eccentrically applied load at its joint. The analysis is facilitated by considering the frame (being a continuous system) as one degree-of-freedom (1-DOF) system with generalized coordinate unknown the column axial force and then by employing catastrophe theory. Through a local analysis via Taylor's expansion of the nonlinear equilibrium equation of the frame, one can classify the total potential energy (TPE) function of the frame to the canonical form of the corresponding TPE function of the seven elementary Thom's catastrophes. Using energy criteria static catastrophes are extended to the corresponding dynamic catastrophes of undamped frames under step loading (autonomous systems) by conveniently determining the dynamic singularity and bifurcational sets. Numerical examples associated with static and dynamic fold catastrophes demonstrate the efficiency and reliability of the present approach.     

NON-LINEAR CONTROL OF BUCKLED BEAMS UNDER STEP LOADING

The present paper studies a strategy for the active non-linear control of the oscillations of simply supported buckled beams, in order to mitigate the effects of dynamic loading on the vibration amplitudes and prevent dangerous instability phenomena. First, an analysis of the symmetric non-linear behaviour of the structure without any control system is carried out. In order to control the non-linear vibrations of the beam, an active tendon control system is adopted. A control method based on non-linear optimal control using state feedback is developed and the solution of the non-linear optimal control problem is obtained by representing system non-linearities and performance indices by power series with the help of algebraic tensor theory. In this work, general polynomial representations of the non-linear control law are obtained up to the fifth order. This solution procedure is employed to analyse the influence of the resulting non-linear control laws on the dynamic behaviour of a buckled beam under a lateral step load. This arch-like structural system is highly non-linear and under compressive lateral loading may suffer snap-through buckling. This may cause undesirable stresses and/or displacements, leading as a rule to a failure of the structural system. So, special attention is given to the determination of the potential of the present control methodology for efficiently limiting extreme state responses and preventing the snap-through buckling. Numerical results indicate that the control algorithm can effectively increase the load-carrying capacity of the buckled beam without demanding large control forces. Also, this study can be used as a basis for the non-linear control of more complex structures and for the design of control systems.     

Dynamics of structural systems with various frequency-dependent damping models

The aim of this paper is to present the dynamic analyses of the system involving various damping models. The assumed frequency-dependent damping forces depend on the past history of motion via convolution integrals over some damping kernel functions. By choosing suitable damping kernel functions of frequency-dependent damping model, it may be derived from the familiar viscoelastic materials. A brief review of literature on the choice of available damping models is presented. Both the mode superposition method and Fourier transform method are developed for calculating the dynamic response of the structural systems with various damping models. It is shown that in the case of non-deficient systems with various damping models, the modal analysis with repeated eigenvalues are very similar to the traditional modal analysis used in undamped or viscously damped systems. Also, based on the pseudo-force approach, we transform the original equations of motion with nonzero initial conditions into an equivalent one with zero initial conditions and therefore present a Fourier transform method for the dynamics of structural systems with various damping models. Finally, some case studies are used to show the application and effectiveness of the derived formulas.     

基于有限元方法的塔机桁架结构屈曲分析

以塔式起重机的金属结构为主要研究对象,借助有限元平台,从简单杆件的分析入手获得了可行的线性屈曲与非线性屈曲分析的方法与流程,进而以此为基础从不同侧面对塔机桁架结构的屈曲问题进行了详细分析.研究结果表明：考虑载荷偏心和初始位移非线性屈曲分析的结果要比线性特征值屈曲分析的结果更符合实际状态.在塔机上计算时只考虑5％的载荷偏心就使结果比原来小了33％,而在实际情况中由于小车轨道不平、风载荷等原因引起的载荷偏心可能会更严重.     

On the qualitative analysis of nonlinear resonant modes in multidimensional structures

The resonant behavior of multidimensional structures simulated via strongly nonlinear dynamic systems has been studied. The energy balance principle has been applied for the qualitative analysis of these systems. The number of potential nonlinear resonant modes under periodic polyharmonic force and parametric excitation has been estimated. The dynamic effects have been investigated and examples have been provided.     

The analytical solution of the buckling of composite truncated conical shells under combined external pressure and axial compression?

The objective of this research is determining the buckling load of composite truncated conical shells under external loading by theoretical and numerical methods. The boundary conditions are assumed to be clamped. At first, basic equations and stability relations of conical shells were derived. The analysis is carried out using Donnel-type stability equations for thin cross-ply conical shells. By applying Galerkin??s method, these equations are converted to a system of ordinary time dependent differential equations. Ritz method is employed for finding the dynamic stability load. Finally, the critical static and dynamic buckling loads and the corresponding wave numbers have been found analytically. Then comparison of results is considered. Results of analytical calculations are compared with numerical results and with other researchers?? analytical results. The effects of geometric parameters, the cone semi-vertex angle, number of layers and material of fibers on buckling loads are discussed.     

Chaotic responses of curved plate under sinusoidal loading

In the present investigation, the nonlinear dynamic buckling of a curved plate subjected to sinusoidal loading is examined. By the theoretical analyses, a highly nonlinear snap-through motion of a clampedfreeclampedfree plate and its effect on the overall vibration response are investigated. The problem is reduced to that of a single degree of freedom system with the Rayleigh-Ritz procedure. The resulting nonlinear governing equation is solved using Runge-Kutta (RK.-4) numerical integration method. The snap-through boundaries, which vary with different damping coefficient and linear circular frequency of the flat plate are studied and given in terms of force and displacement. The relationships between static and dynamic responses at the start of a snap-through motion are also predicted. The analysis brings out various characteristic features of the phenomenon, i.e. l) small oscillation about the buckled position-softening spring type motion, 2) chaotic motion of intermittent snap-through, and 3) large oscillation of continuous snap-through motion crossing the two buckled positions-hardening spring type. The responses of buckled plate were found to be greatly affected by the snap-through motion. Therefore, better understanding of the snap-through motion is needed to predict the full dynamic response of a curved plate.     

Loading rate effects of high damping seismic isolation rubber bearing on earthquake responses

This paper investigates the effects of the loading rates of high damping seismic isolation rubber bearing on earthquake responses. For this purpose, a seismically isolated system is formulated by the Runge-Kutta numerical algorithm with nonlinear rate model of high damping rubber bearing to carry out the seismic time history response analysis. Results, of the seismic time history response analyses using both the present parameter equations and Fujita's equations are compared with those of pseudo dynamic tests. From these results it is confirmed that the parameter equations of high damping rubber bearing should be obtained by tests with the loading rate equivalent to the isolation frequency as close as possible.     

Static and dynamic buckling analyses of spherical sandwich caps

For some ranges of sandwich shell parameter the axisymmetric and asymmetric buckling curves for spherical sandwich caps under a uniform hydrostatic pressure are similar to those for the corresponding homogeneous caps. In the first part of this investigation two methods are presented to obtain the buckling curves for the sandwich caps directly from the buckling curves for the homogeneous caps without going through any buckling analysis.In the second part of the investigation the axisymmetric dynamic snap-through buckling behavior of the sandwich cap under a uniform step pressure is studied. The numerical results show that the dynamic buckling curve for the sandwich cap is similar to that for the homogeneous cap. Moreover, the methods of estimating buckling loads presented for the static buckling analysis are also applicable to the dynamic buckling analysis.     

Plane vibration characteristics of multired externally pressurized oil journal bearings

Externally pressurised oil journal bearings are often subjected to dynamic loading and vibration. A theoretical analysis of the dynamic behaviour of orifice compensated bearings is presented and a design procedure outlined. The analysis assumes that the journal undergoes plane harmonic vibration about its mean steady state position in the absence of shaft rotation. The lubricant is assumed to be isovicous and incompressible. Stiffness and damping characteristics are presented.     

Dynamic instability analysis of stiffened shell panels subjected to partial edge loading along the edges

The dynamic instability characteristics of stiffened shell panels subjected to partial in-plane harmonic edge loading are investigated in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners, respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover, the new formulation for the beam element requires five degrees of freedom per node as that of shell element. The method of Hill's infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented through convergence and comparison with the published results from the literature. The effects of parameters like loading type and shell geometry are considered in the dynamic instability analysis of stiffened panels subjected to non-uniform in-plane harmonic loads along the boundaries. The tension buckling aspect of the stiffened panels are also considered and the dynamic stability behavior due to tensile in-plane edge loading is studied for the concentrated load.     

电磁辅助支承被动阻尼减振与主动阻尼减振的比较

对基于电磁执行器的一种新型支承结构--电磁辅助支承的被动阻尼减振和主动阻尼减振进行比较.首先通过各自的数学模型分析其阻尼减振的不同机理,然后在一四自由度电磁辅助支承转子系统中进行验证,并取得较好的实验效果.通过比较可知,在被动阻尼控制中电磁执行器仅提供负的动刚度和随转速变化的动阻尼;而主动阻尼控制则可以根据需要提供正负刚度和固定或变化的阻尼;且在相同的静态励磁电流下,主动减振效果优于被动减振,但前者结构复杂,造价较高,而后者实施容易.     

Analysis of load application on idler roller bearing of belt conveyor in different dynamic models

The work presents an analysis of the loading conditions of an idler roller journal bearing of a belt conveyor based on different dynamic models (linear and nonlinear with elastic and frictional elements). It is established using computer simulation that the correct choice of the elastic and viscous characteristics of the damping components used in the support bearing design makes it possible to substantially reduce the dynamic loads on the latter.     

Post-buckling stability of orthotropic, linear elastic, rectangular plates under biaxial loads

The potential energy function in a neighborhood of the buckling point for a biaxially loaded, linear elastic, orthotropic, simply supported, rectangular plate is obtained from a perturbation analysis. The perfect system has two independent bifurcation parameters, the loads. The postbuckling behavior is stable, and a good estimate is found for the post-buckling deflection of the plate in terms of the loads. The orthotropic constitutive equation interacts with the biaxial loading to cause a bimodal buckling point for certain combinations of loads; this point is also stable. Away from the bimodal point, the equilibrium surface is described as a cusp cylinder. At the bimodal point, the equilibrium surface is a double cusp.     

Buckling of rectangular plates with various boundary conditions loaded by non-uniform inplane loads

In the present paper, buckling loads of rectangular composite plates having nine sets of different boundary conditions and subjected to non-uniform inplane loading are presented considering higher order shear deformation theory (HSDT). As the applied inplane load is non-uniform, the buckling load is evaluated in two steps. In the first step the plane elasticity problem is solved to evaluate the stress distribution within the prebuckling range. Using the above stress distribution the plate buckling equations are derived from the principle of minimum total potential energy. Adopting Galerkin's approximation, the governing partial differential equations are converted into a set of homogeneous linear algebraic equations. The critical buckling load is obtained from the solution of the associated linear eigenvalue problem. The present buckling loads are compared with the published results wherever available. The buckling loads obtained from the present method for plate with various boundary conditions and subjected to non-uniform inplane loading are found to be in excellent agreement with those obtained from commercial software ANSYS. Buckling mode shapes of plate for different boundary conditions with non-uniform inplane loadings are also presented.     

复合材料加筋板在剪切载荷下的屈曲特性研究

通过对复合材料薄壁加筋板结构进行剪切载荷下的屈曲试验研究,得到结构的屈曲模态、屈曲失稳载荷以及破坏形式,并通过有限元方法对结构的屈曲进行数值分析,分析得到的复合材料薄壁加筋板结构的屈曲模态和试验结果一致,屈曲载荷与试验结果吻合较好.试验还发现复合材料薄壁加筋板结构有较高的后屈曲承载能力,后屈曲过程中由于桁条脱胶会造成屈曲模态的变化.还分析了筋条的连续性对屈曲载荷的影响.     

Effects of Joint Controller on Analytical Modal Analysis of Rotational Flexible Manipulator

Modal analysis is a fundamental and important task for modeling and control of the flexible manipulator. However, almost all of the traditional modal analysis methods view the flexible manipulator as a...     

双壁碳纳米管转动阻尼特性和承载能力的计算分析

基于分子动力学方法对双壁碳纳米管转动的阻尼特性和承载能力进行了计算分析。针对双壁碳纳米管的组成结构和物理模型,使用经验势函数描述双壁碳纳米管管间交互作用势和交互作用力。提出碳纳米管转动阻尼特性与承载能力的分析方法。得到双壁碳纳米管阻尼系数与纳米管的长度、半径以及初始角速度的定量关系。研究纳米管的承载能力以及不同载荷下双壁碳纳米管的阻尼特性,为双壁碳纳米管的工作稳定性分析和工程化应用研究奠定基础。     

仿形刀架机液伺服控制系统动态特性仿真

为保证液压仿形机床的加工质量,仿形刀架的动态特性应满足一定的要求,建立了仿形刀架机液伺服控制系统的数学模型,运用Matlab／Simulink软件构建了该试验系统的仿真模型,并采用阶跃信号对其动态特性进行了仿真分析。通过仿真分析探讨了系统主要参数活塞行程、阻尼和切削负载力对试验系统性能的影响,得出了系统的变化特性曲线及相应的结论。