Inverse Sub‐Structuring Theory for Coupled Product Transport System Based On the Dummy Masses Method

It is of high importance to predict the components frequency response functions (FRFs) for obtaining the coupled product transport system's response. However, the components behaves much differently when coupled with another components compared with that in free state. Inverse sub‐structuring method has been recently proposed and applied for inverse analysis of the dynamical response of coupled product transport system. The component‐level FRFs and the coupling dynamic stiffness are all predicted from only the system‐level FRFs, facilitating the engineering design for product transport system. However, in most engineering application practices, the system‐level FRFs from coupling degrees of freedom may not be measured accurately because of the difficulties of vibration excitation and/or response measurement for the coupled interface between components within the limited accessible space. The aim of this paper is to develop a new FRF‐based indirect inverse sub‐structuring method for the analysis of the dynamic characteristics of a two‐component coupled product transport system without measuring system‐level FRFs at the coupling degrees of freedom. A so‐called dummy masses method is developed and applied for predicting the unmeasured FRFs at the coupling degrees of freedom, and the inverse sub‐structuring approach based on the dummy mass method is derived for inverse analysis of coupled product transport system, which is further verified by a lumped‐mass model, showing exact agreement. Finally, the experiment on a physical prototype of two‐substructure coupled product transport system is performed to further check the accuracy of the suggested method. The new method shows its great application prospect in coupled product transport system.     

基于频响函数辨识鼓筒-轮盘结合部连接参数的选点原则

基于频响函数的辨识方法被广泛用于识别结合部动态参数,其中如何选择频响数据是关键问题。本文针对结合部采用弹簧和阻尼器连接的鼓筒-轮盘模型提出了频响数据选取原则和对应于该原则的量化标准。具体选点原则为所选取的局部信噪比最高的频点所对应的模态对连接刚度的综合灵敏度应该最高。为了定量比较不同模态对连接刚度的综合灵敏度,建立了具体的量化指标和标准。理论分析表明本文所提出的频响数据选取原则和量化标准是有效的,具有一定的工程应用价值。     

Indirect Inverse Substructuring Theory for Coupling Dynamic Stiffness Identification of Complex Interface Between Packaged Product and Vehicle Transport System

Inverse substructuring method has been recently proposed and applied for inverse analysis of the dynamical response of product transport system. The component‐level frequency response functions (FRFs) and the coupling dynamic stiffness for facilitating the cushioning packaging design are all predicted from only the system‐level FRFs. However, the system‐level FRFs from coupling degree of freedoms may not be measured accurately because of the difficulties of vibration excitation and response measurement for the coupled interface between packaged product and vehicle within the limited accessible space. The aim of this paper is to develop a new FRF‐based indirect inverse substructuring method for the analysis of the dynamic characteristics of a three‐substructure coupled product transport system without measuring system‐level FRFs at the coupling degree of freedoms. By enforcing the dynamic equilibrium conditions at the coupling coordinates and the displacement compatibility conditions, a closed‐form analytical solution to inverse sub‐structuring analysis of multi‐substructure coupled product transport system is derived based on the relationship of easy‐to‐monitor component‐level FRFs and the system‐level FRFs at the coupling coordinates.. The proposed method is validated by a lumped mass‐spring‐damper model, and the predicted coupling dynamic stiffness is compared with the direct computation, showing exact agreement. Then, the FRF tests of a physical prototype of multi‐substructure coupled product transport system are performed to further check the accuracy of the suggested method. The method developed offers an approach to predict the unknown coupling dynamic stiffness from measured FRFs purely. The proposed method may help to obtain the main controlling factors and contributions from the various structure‐borne paths for product transport system. Copyright © 2014 John Wiley & Sons, Ltd.     

Expected position of the fatigue fracture plane by using the weighted mean principal Euler angles

The expected principal stress axes under multiaxial fatigue loading are determined by averaging the instantaneous Euler angles through suitable weight functions. Then, the fracture plane position is derived from such expected principal stress directions. Three weight functions based on stress parameters are discussed by comparing theoretical predictions with available test results related to six metallic materials under proportional and non-proportional loading. The fatigue fracture plane position under multiaxial loading may be established on the basis of the averaged direction of the maximum principal stress, with such a direction deduced by employing proper weight functions.     

Forced torsional oscillations of multilayered solids

A new approach is proposed for obtaining the dynamic elastic response of a multilayered elastic solid caused by a forced torsional oscillation inside the solid. The elastodynamic Green’s function of the center of rotation and a point load method are used to solve the problem. The solution of the center of rotation for multilayered solids is obtained by solving a set of simultaneous linear algebraic equations using the boundary conditions for the singularity and for the layer interfaces. The solution of the forced torsional oscillation is formulated by integrating the Green’s function over the contact area with unknown surface traction. The dual integral equations of the unknown surface traction are established by considering the boundary conditions on the contact surface of the multilayered solid, which can be converted into a Fredholm integral equation of the second kind and solved numerically.     

铆接界面端三维奇异性应力场的研究

针对铆接结构的特点,应用特征函数扩展技术分析柱坐标下接触界面端的应力奇异性问题。建立了柱坐标下圆柱体端面接触边缘附近的三维渐近位移场和应力场渐近表达式,并根据铆钉/被铆接件接触界面端的位移和应力边界条件,建立一个非线性特征方程组。据此方程组可求解界面端邻域的应力奇异性指数、位移和应力角分布函数的数值解。通过与有限元方法计算结果相对比,验证了该方法的有效性。分析了平头、沉头以及半圆头铆钉构成的铆接结构的应力奇异性问题,考察了铆钉材料、几何形式和摩擦系数对接触界面端应力奇异性指数和应力场角分布的影响。     

参数振动系统频响特性研究

采用矩阵谱分解中常用的Sylvester理论和Fourier级数展开法,推导了单自由度参数振动系统的频响函数,并得到了系统外激励共振条件。在此基础上,以直齿轮副参数振动系统为例仿真了系统的频响特性,并讨论了系统参数稳定性、时变参数以及阻尼的影响。结果表明,参数振动系统的频响特性主要有以下一些特点:(1)系统具有多个频响函数,分别对应于多频响应中的各个频率成分;(2)系统存在多个外激励共振区。除了外激励频率等于系统固有频率的共振区外,当激励频率等于系统固有频率与参数激励频率的组合值时,同样存在共振现象;(3)参数振动系统共振响应时,主导频率成分为系统固有频率;(4)阻尼使得频响函数峰值有明显下降,而对非共振区的频响曲线影响不大。     

移动分布荷载下层状粘弹性体系的动力响应分析

以粘弹性Burgers模型模拟沥青面层,建立了路面结构层状粘弹性体系模型。利用积分变换和传递矩阵法,并结合广义Duhamel积分,推导出了移动分布荷载作用下层状粘弹性体系动力响应的解析解。利用样条插值函数开发了计算奇异、振荡函数多重无穷积分的计算程序,完成了动力响应从波数-频率域到时间-空间域的转化,与已有文献数据和有限元结果进行了比较,显示出了较好的一致性。结合算例分析了移动分布荷载作用下层状粘弹性体系的振动特性。结果表明,粘弹性解大于弹性解,Burgers模型能反映沥青路面变形的滞后现象,层状粘弹性体系的垂向位移随行车速度和Burgers模型材料参数的增加而减小。     

Model-based contact fatigue design of surface engineered titanium gears

In order to fully realise the potential of advanced surface engineering in the automotive sector, a contact mechanics model has been developed based on modern theories of multi-layered surface contact, taking into account the multi-layered structure, real surface roughness and friction effects. With this model, the performance of surface engineered titanium automotive gears can be successfully predicted thus making possible the design of optimised surface engineering systems to meet particular engineering demands within the shortest possible time and with least cost. This paper presents the predictive contact fatigue design of Ti6Al4V based gears in racing car engines using the developed contact mechanics model for the real rough multilayered surface systems. Evaluation of the effectiveness of the predictive design is carried out through cam rig tests of real gears, simulating the in-service loading conditions. Good agreement between theoretical prediction and service performance has been achieved. By way of example, the present paper demonstrates a number of major steps towards designing dynamically loaded titanium automotive gears.     

Sensitivity analysis of frequency response functions of composite sandwich plates containing viscoelastic layers

In the scope of structural dynamics, sensitivity analysis is a very useful tool in a number of numerical procedures such as parameter identification, model updating, optimal design and uncertainty propagation. In this paper the formulation of first-order sensitivity analysis of complex frequency response functions (FRFs) is developed for composite sandwich plates composed by a combination of fiber-reinforced and elastomeric viscoelastic layers, in arrangements that are frequently used for the purpose of noise and vibration attenuation. Although sensitivity analysis is a well known numerical technique, the main contribution intended for this study is its extension to viscoelastic structures, which are characterized by frequency- and temperature-dependent material properties and, thus, require particularly adapted analytical and numerical procedures. Due to the fact that finite element discretization has become the most used method for dynamic analysis of complex structures, the sensitivity analysis addressed herein is based on such models, being computed from the analytical derivatives of the FRFs with respect to a set of design parameters, such as fiber orientations and layer thicknesses. Also, a procedure for evaluating the sensitivity of the FRFs with respect to temperature of the viscoelastic material is suggested. After discussion of various theoretical aspects, including a parameterization scheme of the structural matrices with respect to the design variables, first-order response derivatives are calculated for a composite plate with inherent structural damping, and for a composite sandwich plate with a viscoelastic core. The results are compared to those obtained from first-order finite-difference approximations.     

Inverse Sub‐Structuring Method for Multi‐Coordinate Coupled Product Transport System

A new high‐accuracy transfer function is selected, and an inverse sub‐structuring method is developed for the analysis of the dynamic characteristics of a three‐sub‐structure coupled product transport system. The closed‐form analytical solution to inverse sub‐structuring analysis of multi‐coordinate coupled multi‐ sub‐structure product transport system is derived. The proposed method is validated by a lumped mass spring damper model; the predicted frequency response functions (FRFs) of sub‐structures and the coupling stiffness, in addition to the most concerned system‐level FRF, are compared with the direct computations, showing exact agreement. Then, FRF tests of a physical prototype of the multi‐coordinate coupled product transport system with three sub‐structures are performed to further check the accuracy of the suggested method. The method developed offers an approach to predict the unknown sub‐structure‐level FRFs and coupling stiffness purely from system‐level FRFs. The suggested method may help obtain the main controlling factors and contributions from the various structure‐borne paths for the product transport system, which may certainly facilitate the cushioning packaging design. Copyright © 2013 John Wiley & Sons, Ltd.     

基于不完备频响函数辨识结合部等效参数的研究

研究了输出信息不完备情况下结合部等效动力学参数的辨识问题,阐述了一种较为通用的结合部等效动力学参数辨识方法.首先采用实验与有限元法相结合,辨识出试验中难以获取的频响函数,构造出完备频响函数.然后通过完备频响函数,运用迭代算法辨识出结合部等效动力学参数.在辨识过程中,建立损失函数模型,将问题转化为求解损失函数的最小值问题.该方法不需要求出模态参数,所以同样适用于大阻尼系统或者模态密集系统的结合部参数辨识.由于只需部分易测的频响函数,所以具有很好的工程应用性.最后通过算例验证了本方法具有很高的辨识精度.     

Tangent operators,sensitivity expressions,and optimal design of non-linear elastica in contact with applications to beams

The tangent operator and design sensitivity expressions for non-linear elastica subject to frictionless unilateral contact are derived and computed via the finite element method. The sensitivity computations are then combined with a numerical programming package to create an optimal design environment. To exemplify the optimal design environment, a beam's contact surface is contoured to minimize bending stress. This work combines the research on the sensitivity analysis of non-linear elastic bodies subject to constraints, finite strain non-linear elastic beam analysis and contact analyses. The analysis is valid for any smooth contact surface; and specialized for the case in which the surface is represented by a cubic spline. The direct differentiation method is utilized to perform the sensitivity analysis. In an example problem, the sensitivity analysis is verified by finite difference computations and then combined with a numerical optimization program to design the stop profile of a valve.     

A meshless local Petrov–Galerkin method for large deformation contact analysis of elastomers

A meshless method based on the local Petrov–Galerkin formulation is applied to the large deformation contact analysis of elastomeric components. Trial functions are constructed using the radial-basis function (RBF) coupled with a polynomial-basis function. The plane stress hypothesis and a pressure projection method are employed to overcome the incompressibility or nearly incompressibility in the plane stress and plane strain problems, respectively. Two different sets of equations are used for the nodes on the contact surface and nodes not on the contact surface, respectively, which is based on the meshless local Petrov–Galerkin method (MLPG) establishing equations node by node. Numerical results for several examples show that the present method is effective in dealing with large deformation contact problems.     

Calculation of stress intensity factors for functionally graded materials by using the weight functions derived by the virtual crack extension technique

The weight function method provides a powerful approach for calculating the stress intensity factors for a homogeneous cracked body subjected to mechanical loadings. In this paper, the basic equations of weight function method for mode I and mixed mode crack problems in a two-dimensional functionally graded crack system are derived based on the Betti’s reciprocal theorem. The weight functions derived by the virtual crack extension technique are further used to calculate the stress intensity factors of functionally graded materials (FGMs). The practicability and accuracy of this proposed method has been confirmed by the comparison with theoretical or numerical solutions available in the literatures. On account that the repeated extractions of the distributions of normal stress and shear stress in the uncracked component along the prospective crack line under different loadings can be avoided using the method presented in this paper, this method can be potentially used for optimal design for FGMs under multiple-load cases.     

高温接触热阻的有限元模拟方法

基于多点接触理论建立了高温接触热阻的计算模型及其有限元格式,模型的基本尺寸取自表面粗糙度测量时的特征尺寸,该模型能有效模拟界面粗糙度、界面压力、界面温度和间隙填料热导率等参数对界面接触热阻的影响,同时也考虑了高温环境下材料热导率随温度变化的特点以及通过界面间隙的辐射换热效应。在此基础上,针对影响接触热阻的若干主要参数进行了研究。数值算例表明：该文所建立的有限元计算模型及其计算方法不仅能有效地模拟不同条件下高温接触热阻的变化规律,也为进行高温接触热阻研究提供了一种新途径。     

Multilayered optical memory with bits stored as refractive index change. I. Electromagnetic theory

With the Lippman-Schwinger equation, dyadic Green's functions, and the vector coherent transfer function method, an electromagnetic theory of a waveguide multilayered optical memory is first developed for the static case, from which a theory describing a conventional multilayered optical memory with bits stored as a refractive index change is also derived. In addition, the formulas for readout signals and cross talk are given, and some problems of numerical calculations are discussed. The theories can be used effectively for optimum design of a multilayered optical memory with bits stored as a refractive index change.     

用幂基多项式拟合频向函数的几点技巧

提出了用幂基多项式拟合频响函数的几点技巧。运用幂基多项式和最小二乘法对频响函数拟合的计算公式进行了推导,得到了用于问题求解的线性代数方程组,为改善该方程组系统矩阵的条件数,对频率变量和系数矩阵进行了规范化处理;频率变量被规范化到0＝－1的无量纲正实数区域,两个相关矩阵的每列模长被规范为1。然后用奇异值分解的方法求解该方程组,得到拟合频响函数所用的幂基多项式的系数。最后,根据幂基多项式的系数,求出系统的极点和留数,从而识别出系统的模糊态参数,文中给出了一个悬臂梁模拟算例,结果表明本文算法具有较好的计算精度。     

基于实测频响函数主成分的在役网架损伤识别方法

鉴于从实际网架动测中得到的频响函数已受到噪声的污染,会使模态分析出现较大的误差,提出了基于实测频响函数和主成分分析的网架损伤识别方法:用网架实测的频响函数数据作为损伤识别的基本变量,建立损伤识别矩阵,通过主成分分析和变量重构对频响函数进行减消噪处理,利用重构的频响函数前几阶主成分,在低维空间中对损伤信息进行分析、提取,并通过多元控制图,来识别网架的损伤。该方法不需要模态参数,避开了模态参数误差所引起的损伤识别不准问题,不需建立力学模型,对网架边界约束条件和结构型式没有特别的限制。为了验证该方法的可靠性,在试验室完成了足尺网架模型在不同损伤情况下动测试验。结果表明,所提出的损伤识别方法简便可行,结果可靠,尤其对噪声环境下和具有一定非线性网架的损伤识别有良好的适应性。     

Antiplane problem of curvilinear cracks in bonded dissimilar materials

A general solution to the antiplane problem of curvilinear cracks in bonded dissimilar materials is provided. The analysis is based upon the Hilbert problem formulation and the technique of analytical continuation. To illustrate the use of the present approach, detailed results are given for a single circular-arc crack lying along the interface between dissimilar materials. The expressions of the complex potentials are derived explicitly in both the unit disk and the surrounding medium. Both the stress intensity factors and contact stress are provided in an explicit form and the former are verified by comparison with existing ones. The effect of material and geometrical parameters upon the contact stress and stress intensity factors has also been discussed and shown in graphic form.