粘弹性Timoshenko梁的动力学普遍方程及其动态特性分析

本文用直接力法在时域内推导了粘弹性Timoshenko梁的控制微分方程,它同时计及了材料的拉伸粘性和剪切粘性.为了测定标准线性固体的复模量和三参数,对有机玻璃(PMMA)和尼龙6(PCL)试件成功地应用了强迫振动梁技术.通过大量数值计算,对粘弹性Timoshenko梁的动力特性,特别是阻尼特性进行了分析.结果表明,材料粘性对结构的动力特性,尤其是对阻尼有较大影响。对于高粘性材料,其动力学性质用标准线性固体模型来描写是合适的.     

Bifurcations and chaos of the nonlinear viscoelastic plates subjected to subsonic flow and external loads

The subharmonic bifurcations and chaotic motions of the nonlinear viscoelastic plates subjected to subsonic flow and external loads are studied by means of Melnikov method. The critical conditions for the occurrence of chaotic motions are obtained. The chaotic features on the system parameters are discussed in detail. The conditions for subharmonic bifurcations are also obtained. For the system with no structural damping, chaotic motions can occur through infinite subharmonic bifurcations of odd orders. Furthermore, we confirm our theoretical predictions by numerical simulations. The theoretical results obtained here can help us to eliminate or suppress large nonlinear vibrations and chaotic motions of the nonlinear viscoelastic plates. Based on Melnikov method, complex dynamical behaviors of the nonlinear viscoelastic plates can be controlled by modifying the system parameters.     

Stability analysis of a single-walled carbon nanotube conveying pulsating and viscous fluid with nonlocal effect

For a single-walled carbon nanotube (CNT) conveying fluid, the internal flow is considered to be pulsating and viscous, and the resulting instability and parametric resonance of the CNT are investigated by the method of averaging. The partial differential equation of motion based on the nonlocal elasticity theory is discretized by the Galerkin method and the averaging equations for the first two modes are derived. The stability regions in frequency–amplitude plane are obtained and the influences of nonlocal effect, viscosity and some system parameters on the stability of CNT are discussed in detail. The results show that decrease of nonlocal parameter and increase of viscous parameter both increase the fundamental frequency and critical flow velocity; the dynamic stability of CNT can be enhanced due to nonlocal effect; the contributions of the fluid viscosity on the stability of CNT depend on flow velocity; the axial tensile force can only influence natural frequencies of the system however the viscoelastic characteristic of materials can enhance the dynamic stability of CNT. The conclusions drawn in this paper are thought to be helpful for the vibration analysis and structural design of nanofluidic devices.     

Optimal constrained layer damping with partial coverage

This paper deals with the optimal damping of beams constrained by viscoelastic layers when only one or several portions of the beam are covered. An efficient finite element model for dynamic analysis of such beams is used. The design variables are the dimensions and prescribed locations of the viscoelastic layers and the objective is the maximum viscoelastic damping factor. The method for non-linear programming in structural optimization is the so-called method of moving asymptotes.     

新型轻质复合材料夹芯结构振动阻尼性能研究进展

作为新一代先进轻质超强韧结构材料,复合材料格栅和点阵夹芯结构受到了国内外学者的广泛关注.目前关于该类结构材料的设计制备以及相关力学性能研究已取得了大量的研究成果.然而对该类结构振动阻尼性能的研究则处于起步阶段.该文综述了纤维增强树脂基复合材料简单层合结构以及各类夹芯结构振动阻尼性能的研究现状.首先阐述其阻尼机理, 然后分别概述了复合材料简单层合板的微观和宏观阻尼模型、复合材料粘弹性阻尼夹层结构和新型夹层结构的阻尼预报工作,最后总结归纳现有关于该类结构阻尼特性研究工作中已取得的成果和不足之处,并对其未来发展进行了展望.     

Optimization of sandwich structures with damping properties

Maximum viscoelastic damping characteristics of sandwich structures are designed using finite element and informative planning methods. Two basic design problems were considered: addition of a damping coating to a given homogeneous structure and building a sandwich structure subjected to a given set of constraints. The methods of complex eigenvalues and direct calculation of the frequency characteristics were used. Numerical examples of optimizing sandwich beams are presented for both design problems.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 5, pp. 653–656, September–October, 1993.     

Formulação numérica de estruturas compósitas amortecidas utilizando as teorias da Deformação Cisalhante de Primeira Ordem e de Alta Ordem

Composite materials have been used in the design of the aircrafts structures because their low weight and high mechanical strength. However, structures made in composite material are exposed to dynamical and/or static loading environments. Therefore, a major research effort is undertaken in the development of tools numerical for analysis and design of composite structures. This paper presents a numerical formulation of the composite structures using the Finite Element Method (FEM). The damped composite structures, using inserted viscoelastic devices, and undamped composite structures are formulated by FEM. Viscoelastic materials are applied as continuous layers inserted on composite structures. The intrinsic damping of the composite material is included in the studies, too. The First‐order (FSDT) and Higher‐order Shear Deformation (HSDT) theories are formulated. They are distinguished by order of the approximation functions used in the mechanical displacements field. Both theories are computationally implemented using the Serendipity finite element. This is a rectangular finite element with 8 nodes, 5 or 11 degrees of freedom per node. The results are compared with papers predictions. The advantages and disadvantages of using each theory in the modeling of composite (thin or thick) and thick sandwiches structures, including the intrinsic and the viscoelastic damping, are discusses.     

A model updating approach based on design points for unknown structural parameters

Finite element analysis has become an essential tool to estimate structural responses under static and dynamic loads. However, there are a lot of uncertainties in structural properties. For this reason, in many cases, the outcomes of the theoretical and experimental modal analyses do not match. Therefore, the analytical models of the structures need to be updated according to the experimental test results. The commonly used method to get parameters for model updating is experimental modal analysis which provides structural dynamic characteristic (natural frequencies, mode shapes and modal damping ratio). There are many methods available for the updating process. This study addresses an updating algorithm to modify the numerical models by using the design points for unknown structural properties. The proposed method aims to minimize the difference between the analytical and experimental natural frequencies by updating uncertain parameters for each mode and combine them to get an optimum solution. The algorithm is tested on a column and a 2D frame models. These models are investigated by taking the connection rigidity and elasticity modulus as unknown parameters. It is observed that the proposed algorithm gives better results for unknown structural properties compared to the initial values.     

On some regularities in dynamic response of cyclic periodic structures

The paper deals with cyclic periodic structures modelling bladed disk assemblies of blades with friction elements for vibration damping. These elements placed between adjacent blades reduce the vibration amplitudes by means of dry friction resulting from centrifugal forces acting on the elements and relative displacements of the blades. However, the application of these friction elements results in an additional dynamical coupling which together with mistuning of some system parameters (e.g., blade eigenfrequency or contact parameters) may cause localization of vibration. In the present paper a linear approximation of such a system is investigated. The structure composed of cyclic periodic cells modelled each as a clamped-free beam interacting with each other by means of viscoelastic elements of complex stiffness is applied for dynamic system analysis. In case of free vibrations as well as in case of steady-state dynamic response to a harmonic pressure field, a perfect periodic structure and the structures with periodically mistuned parameters (blade eigenfrequencies and contact parameters) are studied. Some regularities in the dynamic response of the systems with mistuning have been noticed. Despite the fact that only a linear approximation has been used, the results and conclusions can be applied for models which describe the blade interaction in a nonlinear way.     

被动约束层阻尼圆柱壳振动和阻尼分析的一种新矩阵方法

基于线弹性薄壳理论和线粘弹性理论,考虑粘弹性层的剪切耗能作用和各层间的相互作用力,导出了被动约束层阻尼层合圆柱壳在谐激励作用下的一阶常微分矩阵控制方程．然后,借助作者提出的齐次扩容精细积分技术建立了一种新的矩阵方法,并利用该方法研究了层合圆柱壳的振动特性和阻尼特性．该方法与已提出的以位移及其导数作为状态向量的传统传递矩阵法的根本区别在于,控制方程中的状态向量中包含了层合壳的全部位移和整合内力变量,因此,可以方便地适用于各种位移和内力边界条件以及部分环状覆盖约束层阻尼圆柱壳的动态分析．数值算例与解析解和有限元解的结果比较有力说明了该方法的正确性和有效性．     

Exact bounds for the sensitivity analysis of structures with uncertain-but-bounded parameters

Based on interval mathematical theory, the interval analysis method for the sensitivity analysis of the structure is advanced in this paper. The interval analysis method deals with the upper and lower bounds on eigenvalues of structures with uncertain-but-bounded (or interval) parameters. The stiffness matrix and the mass matrix of the structure, whose elements have the initial errors, are unknown except for the fact that they belong to given bounded matrix sets. The set of possible matrices can be described by the interval matrix. In terms of structural parameters, the stiffness matrix and the mass matrix take the non-negative decomposition. By means of interval extension, the generalized interval eigenvalue problem of structures with uncertain-but-bounded parameters can be divided into two generalized eigenvalue problems of a pair of real symmetric matrix pair by the real analysis method. Unlike normal sensitivity analysis method, the interval analysis method obtains informations on the response of structures with structural parameters (or design variables) changing and without any partial differential operation. Low computational effort and wide application rang are the characteristic of the proposed method. Two illustrative numerical examples illustrate the efficiency of the interval analysis.     

关于分数阶Maxwell淤泥模型及其在水波衰减问题中的应用

分数阶Maxwell模型可用来模拟粘弹性的海床淤泥．与传统的有理分式模型相比,分数阶Maxwell模型可以用更少的自由参数,较好地描述某些真实淤泥的流变特性．将该分数阶Maxwell模型用于研究淤泥与自由表面水波的相互作用,并得到了线形单色波的衰减率．从水波衰减率曲线中可观测到淤泥层的共振现象,共振时衰减率将达到峰值．对于线形单色波,其衰减率还可表示为各模态衰减率之和,从而可研究某一模态的运动对水波衰减的影响．模态分析表明,当某一模态运动引发共振时,总衰减率由该模态的模态衰减率决定．     

Bending analysis of elastically connected Euler–Bernoulli double-beam system using the direct boundary element method

Double and multiple-Beam System (BS) models are structural models that idealize a system of beams interconnected by elastic layers, where beam theories are assumed to govern the beams and elastic foundation models are assumed to represent the elastic layers. Many engineering problems have been studied using BS models such as double and multiple pipeline systems, sandwich beams, adhesively bonded joints, continuous dynamic vibration absorbers, and floating-slab tracks. This paper presents for the first time a direct Boundary Element Method (BEM) formulation for bending of Euler–Bernoulli double-beam system connected by a Pasternak elastic layer. All of the mathematical steps required to establish the direct BEM solution are addressed. Discussions deriving explicit solutions for double-beam fundamental problem are presented. Integral and algebraic equations are derived where influence matrices and load vectors of double-beam systems are explicitly shown. Finally, numerical results are presented for differing cases involving static loads and boundary conditions.     

小垂度粘弹性索非线性响应及振动主动控制

研究具有初始应力的小垂度粘弹性索的非线性动态响应及振动主动控制。在假定索材料的本构关系为一般微分本构类型的基础上,建立小垂度粘弹性索的运动微分方程;应用Galerkin方法将其转化为可用Runge-Kutta数值积分方法求解的一系列三阶非线性常微分方程。在仅考虑面内的横向振动及忽略非线性的情况下得到了连续状态空间中的状态方程,将状态方程离散为差分方程形式,并用矩阵指数来逐步近似状态转移矩阵;基于二次性能指标的最小化得到了最优的控制力与状态向量。最后通过数值仿真研究说明了粘性参数对索动态响应的影响。     

用Adomian分解法求解分数阻尼梁的解析解

利用Adomian分解法, 得到了由任意阶分数微分描述的具有阻尼特性的黏弹性连续梁的解析解．解中包含了任意的初始条件和零输入．为了更明确的分析, 假定初始条件是奇次的,输入受力是针对某种特定梁的特殊过程．分别考虑了两种简单情况下梁的响应:阶跃激励和脉冲激励．然后在系统的不同组参数条件下绘制了梁的位移图,并且讨论了梁在不同微分阶数下响应情况．     

基于正交试验法和数值仿真的环形降压槽结构优化

降压槽存在相互矛盾的阻力和粘损特性均受各结构参数的影响,合理的结构参数选择一直是降压槽设计的难点问题.环形降压槽结构优化设计涉及到多因素多水平问题,数值仿真和正交试验设计方法相结合可以有效地减少对实验的依赖和试验次数.对环形降压槽进行结构参数化建模,建立了幂律流体在降压槽环空流道流动的数值仿真模型,可完成不同结构降压槽性能的数值仿真分析;制定了降压槽3因素3水平的多指标正交试验,采用极差和方差分析方法对试验的结果进行了分析,并用综合平衡的方法确定最优的降压槽结构参数组合.最终得到了各结构参数对降压槽的粘损和阻力性能的影响规律以及最优的结构参数,可为环形降压槽的设计和改进提供有价值的参考.     

New symmetry preserving method for optimal correction of damping and stiffness matrices using measured modes

Measured and analytical data are unlikely to be equal due to measured noise, model inadequacies, structural damage, etc. It is necessary to update the physical parameters of analytical models for proper simulation and design studies. Starting from simulated measured modal data such as natural frequencies and their corresponding mode shapes, a new computationally efficient and symmetry preserving method and associated theories are presented in this paper to update the physical parameters of damping and stiffness matrices simultaneously for analytical modeling. A conjecture which is proposed in [Y.X. Yuan, H. Dai, A generalized inverse eigenvalue problem in structural dynamic model updating, J. Comput. Appl. Math. 226 (2009) 42-49] is solved. Two numerical examples are presented to show the efficiency and reliability of the proposed method. It is more important that, some numerical stability analysis on the model updating problem is given combining with numerical experiments.     

Modeling of the multi-cable supported arch and a novel technique to investigate the natural vibratory characteristics

A fully analytical model of the multi-cable supported arch (MSA) is presented and a parametric study of the structural parameters on the planar natural vibratory characteristics is performed. Unlike the existing models, the structure is modeled with the idea “dividing the whole into parts, assembling the parts to whole” to simulate the stayed cable erection construction of the arch bridge. The global MSA under both the cantilever state and the closed state is divided into a series of chained cable-arch substructures along the span direction, The Hamilton principle is used to build the model of each substructure, in which the cable and arch segment are defined in local and global Cartesians, respectively. By assembling the equations of all substructures through the match conditions and boundary conditions, the global equation is established. Also, the global characteristic equation is determined by the transferring of coefficients vectors of substructures and some coordinate transformations. In each substructure, the interaction between the cable and the arch segment are isolated and the mutual effects are considered in the connected matrix of the coefficients vectors. The unification of the substructures converts to the transferring of the arch segments. This substructure transferring technique (STT), which is compared and verified by the finite element method (FEM), is able to effectively acquire the frequencies and the modes. The results show the sag-to-span ratios and inclined angles of the cables play significant role on the veering phenomenon in some specific intervals. Local and global modes exist simultaneously in the frequency spectrum, the involved resonant zone and veering area is needed to avoid in the parametrical design for structural safety.     

小曲率粘弹性索非线性随机稳定性分析

基于Kelvin粘弹性材料本构模型,研究小曲率粘弹性索在窄带随机激励作用下的非线性随机稳定性及均方响应。首先建立小曲率粘弹性索数学模型;然后提出一种确定粘弹性索均方响应及概率渐近稳定性方法;给出了系统均方稳定对激励带宽、幅值、中心频率等要求;给出系统的稳定区域;最后讨论了材料粘性、波速比及介质阻尼对系统不稳定区域的影响。