基于随机等价线性化法的悬浮隧道锚索随机振动研究

为了得到悬浮隧道锚索在随机环境激励作用下的响应,建立了悬浮隧道锚索非线性随机振动方程,并在方程中考虑了锚索的垂度效应,随后采用随机等价线性化法对随机激励作用下锚索的振动响应进行了分析。研究结果表明:在零均值高斯白噪声环境激励作用下,锚索的跨中位移和速度均方根响应经过一定时间后将趋于定值,位移和速度的互相关函数趋于零;锚索的阻尼比越大,锚索跨中横向位移均方根响应越小;激励的功率谱密度强度越大,锚索跨中横向位移均方根响应越大;由于水体阻尼力的存在,悬浮隧道锚索的位移和速度均方根响应比空气中锚索的响应大幅减小。     

随机激励作用下悬浮隧道锚索的振动响应

为了研究水下悬浮隧道锚索在随机激励作用下的响应,考虑锚索的垂度效应,建立水下悬浮隧道锚索非线性随机振动方程,采用蒙特卡罗数值模拟法对随机激励作用下锚索的振动响应进行研究。研究结果表明:在零均值高斯白噪声激励作用下锚索的位移和速度均方根响应经过一定时间后将趋于定值;随着激励荷载均方根的增大,锚索位移和速度均方根响应也随之增大;由于水体阻尼力的作用,锚索的位移和速度均方根响应比空气中的锚索大幅减小。     

吊灯灯罩缓冲衬垫的随机振动仿真分析及实验验证

目的研究吊灯灯罩纤维模塑缓冲衬垫在随机振动激励下结构设计的合理性,及其对产品的保护性能。方法利用Ansys软件对吊灯灯罩纤维模塑缓冲衬垫包装件进行模态分析,获取包装件的固有频率和振型,将路面随机振动激励谱作用于纤维模塑缓冲衬垫包装件进行仿真分析,得到包装件的应力、应变云图和加速度功率谱密度响应曲线等,以此分析其结构设计的合理性以及对产品的保护性能,并进行实验验证。结果灯罩所受应力值远小于灯罩材料所能承受的最大屈服应力值(75 MPa),吊灯灯罩保存完好;有限元分析得到的结果与实测结果一致。结论纤维模塑缓冲垫结构设计合理,强度可满足保护产品的要求;利用有限元仿真分析解决纤维模塑缓冲包装制品的随机振动问题是可靠的,适用于动态环境下同类缓冲制品性能的研究,为缓冲包装产品性能预测、结构设计及优化提供有效分析手段。     

有界窄带激励柴油机轴系扭振系统主参数共振

研究柴油机轴系扭振强非线性系统在有界窄带激励下的主参数共振响应和稳定性问题。应用改进多尺度法得到在有界窄带随机激励下柴油机轴系扭振系统的幅频响应方程,导出系统的Ito随机微分方程。通过矩法得到系统随机均方响应的近似表达式,分析各个参数对柴油机轴系扭振系统主参数共振均方值的影响。结果表明,主参数共振稳态解稳定的充分必要条件与系统二阶矩稳定的充分必要条件是一样的;随着阻尼值的增大,系统主参数共振振幅的均方值减小;随着曲轴扭转刚度的减小,系统主参数共振的均方响应曲线的斜率增大;随着随机扰动强度的增大,系统时间响应曲线和相图变化微小。     

窄带随机激励带集中质量梁的主参激共振

以受窄带随机激励带集中质量柔性梁为研究对象,采用多尺度法导出系统单模态主参激共振调谐方程组,结合FPK方程分析了力-幅特性下联合概率密度随激励幅值所出现的随机跳跃现象,结果显示:在三值响应范围内存在一外扇形峰及一内火山口峰,随着激励幅值减小,外扇形峰减弱而内火山口峰增强,表明响应逐渐从非平凡稳态响应向平凡稳态响应跳跃。     

隔震结构非线性随机地震响应分析的复模态法

本对多自由度双线性滞变隔震结构在过滤白噪声地震激励下的随机响应问题进行了系统研究。首先建立了结构非线性运动方程；然后根据非线性随机振动理论对运动方程进行等效线性化；最后用复模态法获得了等效线性方程的解析解，将复杂的非线性随机响应问题简化为求解一元非线性代数方程问题，并给出了算例。从而建立了多自由度隔震结构非线性随机响应复模态分析的一整套计算方法。     

Transient random interaction of dam reservoir systems

A simple gravity dam-reservoir system is selected for studying the interaction of structure-fluid systems under nonstationary random excitation. For an idealized random excitation with a zero start and a white power spectrum, the transient response mean square for the structural displacement is obtained by a simple time domain approach. Using this transient solution the random interaction effect is examined in detail. This transient interaction effect is important because it simulates random and time dependent earthquake ground accelerations.     

Stability and subcritical dynamics of structures with spatially disordered travelling parametric excitation

Spatially periodic travelling loading may lead sometimes to parametric excitation of structures. However, random spatial nonuniformity of the loading pattern, which leads in time domain to fluctuations of the excitation frequency, makes this phenomenon less severe. This effect is considered for the case of a single-mode resonant response. Using stochastic averaging, stability boundaries are found both with respect to probability and in the mean square; subcritical response to an external broadband random excitation is also obtained.     

斜拉索风致随机振动的计算机模拟

斜拉索是斜拉桥的主要受力构件之一,由于其柔度大、质量小、阻尼小和自振频率低等特点,对风荷载比较敏感,在风载作用下极易发生振动,因此有必要对这种结构风振响应进行研究。通过在斜拉索有限元模型上导入随机风荷载,用计算机模拟斜拉索的风振响应,为进一步研究风振响应的控制打下基础。该方法可以节省研究成本,提高研究效率,对斜拉桥的设计具有一定的参考意义。     

Dynamic characterization of the thickness-tapered laminated plant fiber-reinforced polymer composite plates

Evolution of the laminated woven natural fiber fabric-reinforced polymer composite structures makes a way to the development of the non-uniform laminated composite structures in order to achieve the stiffness variation throughout the structure. An attempt is made in this work to carry out the experimental and numerical investigations on the dynamic characteristics of the thickness-tapered laminated woven jute/epoxy and woven aloe/epoxy composite plates. The governing differential equations of motion for the thickness-tapered laminated composite plate are developed using the h-p version FEM based on higher order shear deformation theory. The validation of the present finite element formulation is carried out by comparing the natural frequencies obtained using the finite element formulation with those natural frequencies determined experimentally. The developed model is further validated with the available literature works on tapered composite plate to confirm the efficiency of h-p version FEM. This work also explores the study of the vibrational characteristics of composite plates under the influence of plant fiber’s transverse isotropic material characteristics and porosity associated with plant fiber composites through the elastic constants evaluated in the author’s previous work. Also the influences of aspect ratios, ply orientations, and taper angles under various end conditions on the natural frequencies of the woven jute/epoxy composite plate are studied using the present finite element formulation. The forced vibration response of the thickness-tapered laminated woven jute/epoxy composite plate under the harmonic force excitation is carried out considering CFCF and CFFF end conditions.     

Numerical solutions of Fokker-Planck equation of nonlinear systems subjected to random and harmonic excitations

A new approach for an efficient numerical implementation of the path integral (PI) method based on non-Gaussian transition probability density function (PDF) and the Gauss-Legendre integration scheme is developed. This modified PI method is used to solve the Fokker-Planck (FP) equation and to study the nature of the stochastic and chaotic response of the nonlinear systems. The steady state PDF, periodicity, jump phenomenon, noise induced changes in joint PDF of the states are studied by the modified PI method. A computationally efficient higher order, finite difference (FD) technique is derived for the solution of higher-dimensional FP equation. A two degree of freedom nonlinear system having Coulomb damping with a variable friction coefficient subjected to Gaussian white noise excitation is considered as an example which can represent a bladed disk assembly of turbo-machinery blades. Effects of normal force and viscous damping on the mean square response are investigated.     

液压源管路系统随机压力脉动可靠性研究

将液压源管路系统的压力脉动近似为平稳随机过程。在频响特性的基础上,计算了随机白噪声泵源流量脉动激励下管路终端压力脉动的均方差。分别采用首次超越破坏和疲劳累积破坏准则,对液压源终端管路随工作时间的可靠度变化历程进行了仿真,得到了泵源脉动幅值对管路系统可靠性的影响。结果表明,小于额定压力10%的压力脉动评估方法不能满足液压系统安全性要求。本文提出的基于可靠性的液压管路系统耐随机压力脉动的评估方法,为液压系统的动强度安全性评估和设计提供了新的参考和指导     

薄壁板在随机声载荷作用下的振动响应谱估算

针对飞行器薄壁结构声疲劳问题，研究了具有多模态的薄壁板结构在声载荷作用下振动响应谱的估算方法。基于正交模态法，采用结合受纳函数描述结构模态和声场空间压力分布的耦合关系，建立动态响应计算模型。为与试验结果进行对比，选取具有固支边界的金属薄壁板作为研究对象，以试验测得的噪声载荷作输入，计算了该结构的振动响应谱，估算了均方应力，并将计算结果与试验数据进行比较和讨论。     

Effect of constrained layers on vibrational characteristics of a composite sandwich system��A finite element based critical investigation

The main aim of this paper is to investigate the effect of various constrained layers (viscoelastic layer (VEL), electro-rheological fluid (ERF), and magneto-rheological fluid (MRF)) over natural frequency and the damping loss factor with two different fiber orientations (0° and 90°) for a Graphite/Epoxy (GR/E) composite sandwich shaft disc system. The finite element technique is used to investigate the natural frequency and loss factor for various combinations. Furthermore, the vibrational characteristics of the composite sandwich shaft disc system are compared with those of the base structure without constrained layers. The study shows that introducing various constrained layers reduces the magnitude of natural frequency by up to 80%. The results also show that GR/E composite with 90° fiber orientation acquires the highest frequency reduction. Among the proposed layers, VEL has the highest damping loss factor.     

有界窄带激励下的电磁开关系统主共振分析

以电磁开关系统为研究对象,研究电路与磁路耦合系统在有界窄带激励下的强非线性振动问题。建立电磁开关强非线性系统在有界窄带激励下的随机微分方程。应用改进的多尺度法得到系统的幅频响应方程,对窄带激励下系统主共振的稳定性进行计算,并分析系统各参数对系统主共振均方值的影响。结果表明,增大阻尼系数可以减小系统主共振的均方值;增大激励电压可以增大系统主共振的均方值;增大电阻可以减小系统主共振的均方值;增大随机扰动强度,极限环变化不大。     

弱非线性系统在白噪声激励下均方响应的优化

本文研究了具有硬弹簧或软弹簧的弱非线性振动系统在白噪声激励下位移均方响应的优化问题。利用摄动法求得了位移响应谱与激励谱之间的关系。根据阻尼最小二乘可行方向法,以质量 m_2在某频率范围内的位移均方响应为目标函数,对阻尼与刚度系数进行了最良选择,在计算机上实现了这种优化。     

随机激励作用下硬涂层薄板振动有限元分析及减振预估

硬涂层减振是一项新兴的阻尼减振技术,硬涂层复合结构在随机激励载荷作用下的振动特性建模与分析方法还未开展研究。将有限元建模方法和虚拟激励法(pseudo excitation method, PEM)相结合,实现了随机激励作用下硬涂层悬臂薄板结构振动建模及减振性能预估。首先,基于等效单层法创建了双面涂敷硬涂层的薄板结构振动特性有限元模型,得到了基础激励作用下包含涂层材料阻尼和剩余等效黏性阻尼的复合板结构的运动方程。接着,利用虚拟激励法,将平稳随机激励载荷谱转化为简谐激励,得到了硬涂层薄板结构在随机激励作用下的响应功率谱密度的求解方法。最后,以双面涂敷NiCrAl硬涂层材料的45#钢悬臂板为实例进行研究,利用所研发的方法计算了涂层板结构的固有频率及随机基础激励作用下的振动响应,并与试验数据进行对比校验。进一步,分析了涂层厚度、储能模量和损耗因子对悬臂板振动特性的影响。结果表明,适当增加上述涂层参数量值可有效提高硬涂层的减振效果。     

热处理软点对圆锯片模态参数和刚度的影响

圆锯片己经被广泛应用于切割石材、木材、钢材等工程中。热处理作为圆锯片加工中重要的一道工序,热处理的质量对圆锯片的使用性能有很大的影响。热处理缺陷导致圆锯片产生软点,使得圆锯片的固有频率及刚度发生变化。本文采用有限元分析了热处理软点对圆锯片的模态参数以及刚度的影响。通过改变软点的弹性模量、软点直径大小以及软点的位置,分析了圆锯片的固有频率以及径向和切向刚度的变化规律。结果表明软点的存在降低了圆锯片的固有频率,软点直径越大,固有频率越小,软点距离中心越近,固有频率越小。软点的弹性模量越小,圆锯片的固有频率越小。软点的存在使得圆锯片的径向刚度和切向刚度都有所减小。     

Stochastic critical stress intensity factor response of single edge notched laminated composite plate using displacement correlation method

Abstract

The second-order statistics of critical stress intensity factor (SIF) of single edge notched fiber reinforced composite plates with random system properties and subjected to uniaxial tensile loadings is investigated. This paper is an extension of reference (Lal and Kapania, 2013) by the present authors by considering more number of input random system parameters for higher accuracy. A C⁰ finite element method based on a higher-order shear deformation plate theory using displacement correlation method via isoparametric quarter point element is proposed for basic formulation. A stochastic finite element method using first-order perturbation technique and Monte Carlo simulation (MCS) is employed to examine the mean, coefficient of variance, and probability density faction of critical first mode SIF. The effect of different fiber orientations, crack length, plate thickness, a number of layers, and the lamination schemes with random system properties on the statistics of SIF of single edge crack laminated composite plate is evaluated. The tensile failure load is predicted using Hashin’s failure criteria. The present approach is validated with results available in literature and by employing independent MCS.     

Free vibration of composite cylindrical panels with random material properties

Virtually in all structural systems, and in particular composites, there are uncertainties in the system parameters because of practical bounds on the quality control. In the present work the effect of variations in the mechanical properties of laminated composite cylindrical panels on its natural frequency has been obtained by modeling these as random variables. The transverse shear and rotatory inertia effects have been included in the governing equations. A perturbation approach is presented to obtain the mean and variance of the random natural frequencies. The effects of thickness ratios, edge support conditions and standard deviation of material properties on response of shallow square panels have been investigated. Results have been obtained by employing the finite element method. The approach has been validated by comparison of results with other approaches.