Semi-analytical formulation for the guided waves-based reconstruction of elastic moduli

In this study an inverse procedure based on the propagation of guided ultrasonic waves is proposed for the characterization of the elastic material constants of plates. The procedure consists of an optimization problem in which the discrepancy between the dispersion curves obtained through a semi analytical finite element (SAFE) formulation and numerical or experimental dispersion curves is minimized. The numerical dispersion curves were obtained from the application of the commercial finite element analysis software ANSYS. Finally experimental data were obtained by adopting a hybrid broadband laser/PZT ultrasonic set-up in a pitch-catch configuration. For both numerical and experimental data, the joint time-frequency analysis of the continuous wavelet transform was used.The optimization scheme proposed in this study is based on an improved version of the simplex search method. The scheme inputs an initial guess of the material parameters in the SAFE formulation. The values of these parameters are iteratively updated until the discrepancy between the SAFE-based group velocity dispersion curves and the numerical or experimental curves is minimized. The scheme is designed to minimize the discrepancy associated with the lowest symmetric and anti-symmetric order mode simultaneously.The validity of the SAFE method coupled to the inverse procedure scheme is tested to characterize the elastic material properties of a 2.54 mm thick aluminum plate. As the SAFE formulation is valid for waveguides of arbitrary cross-section the paper represents the first step toward the integration of an inversion scheme applicable into the SAFE algorithm to characterize the material properties of waveguides of complex geometries and various boundary conditions.     

Modeling the powder compaction process using the finite element method and inverse optimization

This paper focuses on studying and adapting modeling techniques using the finite element method to simulate the rigid die compaction of metal powders. First, it presents the implementation of the cap constitutive model into ABAQUS FE software using the closest point projection algorithm. Then, an inverse modeling procedure was proposed to alleviate the problems raised by the interpretation of the experimental tests and to more accurately determine the material parameters. The objective function is formed, based on the discrepancy in density data between the numerical model prediction and the experiment. Minimization of the objective function with respect to the material parameters was performed using an in-house optimization software shell built on a modified Levenberg?CMarquardt method. Thus, an integrated simulation module consisting of an inverse optimization method and a finite element method was developed for modeling the powder compaction process as a whole. The simulation and identification module developed was applied to simulate the compaction of some industrial parts. The results reveal that the maximum absolute error between densities is 2.3%. It corresponds to the precision of the experimental method.     

Modelling the plane strain compression test to obtain constitutive equations of aluminium alloys

Hot plane strain compression tests on 1050, 1198, 3003 and 3004 aluminium alloys have been conducted. Based on these experiments and on a set of internal type constitutive equations for hot working, the values of the parameters in the constitutive functions are determined. The constitutive equations proposed here, with the constitutive functions and material parameters associated, accurately reproduce the basic tests. The procedure used to fit the material parameters is improved, in comparison with classical slip line analysis, by using a finite element modelling of the plane strain compression test. It is demonstrated that accurate plane strain or three-dimensional large strain finite element analysis can be used to correct the friction and lateral spread effects. Furthermore, it is demonstrated from comparison with the experimental observations that microstructural parameters can be accurately determined from numerical modelling. The constitutive equations and finite element procedure proposed here can be useful for obtaining an improved analysis of hot rolling of aluminium alloys.     

Oscillation of a tilted circular pad on a droplet for the self-alignment process

The seesaw-oscillation of a small circular pad on a single droplet was studied both numerically and experimentally. The circular pad with a diameter of 2.0–3.8 mm onto a water or glycerol droplet with a volume of 1–10 μL, and a bottom substrate with a smaller diameter than that of the pad were used in the experiment. The pad was then tilted and then the tilting fixture was quickly removed. The pad alternately oscillated and then finally stabilized in a horizontal position. The numerical model considering the surface tension and the viscous force of the droplet was developed and calculated using the same configurations as those in the experiment. The experimental and numerical data showed good agreement not only in terms of the oscillating frequency and damping ratio but the transient motion of the circular pad and instantaneous droplet surface shape.     

Dynamic analysis of pseudoelastic SMA beam

The main goal of this work is to present a formulation of initial-boundary-value problem for the Bernoulli-Euler beam made of pseudoelastic shape memory alloy (SMA). The procedure of formulation of 1D constitutive relations based on the analysis of the proposed rheological model is presented in detail. The relationships to be obtained are of explicit type and were formulated within the notion of non-smooth mechanics using the so-called differential successions of constitutive equations. The system of partial differential equations is discretized with respect to spatial coordinates using the finite difference method. This procedure leads to the system of ordinary differential equations with respect to the time coordinate, which was solved using the Runge-Kutta method. The problem was coded within MATLAB system. A numerical example of a beam structure subjected to concentrated Heaviside-type loading was analysed.     

Fractional In Situ Pad Conditioning in Chemical Mechanical Planarization

Material removal rate, shear force and variance of shear force during copper polishing are studied as a function of pad conditioning scheme: 0% in situ conditioning (i.e., basically the equivalent of ex situ conditioning) and fractional in situ conditioning variants (i.e., conditioning during the first 25, 50, 75 or 100% of the total polish time). Spectral analysis of raw shear force data is employed to help elucidate the fundamental physical phenomena during copper chemical mechanical planarization. Fast Fourier transform is performed to convert the shear force data from time domain into frequency domain. The energy distribution of copper polishing is quantified which sheds light on the effect of fractional in situ pad conditioning. Variance of shear force and spectral analysis indicate that pad micro-texture evolution ceases after 50% fractional conditioning, thereby indicating that in situ conditioning time can be reduced during a given polishing process thus extending pad life. This study shows that a combination of unique spectral fingerprinting and analysis of force variance can be used to monitor the effect of pad conditioning in real time. This work also underscores the importance of real-time detection and non-destructive method to extend pad life and consumable usage during CMP by optimizing the pad conditioning time.     

ACTIVE VIBRATION CONTROL OF A CAR BODY BASED ON EXPERIMENTALLY EVALUATED MODAL PARAMETERS

Active vibration control has been successfully tested for structures with simple geometry, such as beams and plates, by using modal controllers. Since the dynamical behaviour of a variety of mechanical structures can be expressed in terms of modal parameters, the application of modal control concepts can be extended to structures with more complex geometries. For such structures the evaluation of modal parameters from numerical calculations of local modes is complicated because the results strongly depend on proper boundary conditions of the truncated structure. Therefore, the modal data are identified by an experimental modal analysis. The transformation of the experimentally evaluated mode shapes into a closed analytical formulation and the extraction of modal input and output factors for sensors and actuators connect experimental modal analysis and modal control theory. The implementation of the input and output factors into a modal state-space formulation results in a modal filter for the point sensor array and a retransformation filter for the segmented actuator patches. In this study, PVDF foil is used for sensors and actuators. The modal controller is implemented on a digital controller board and experimental tests with the floor panel and centre panel of a car body are carried out to validate the proposed concept.     

Novel criteria for determination of material model parameters

Parameter identification problems have emerged due to the increasing demanding of precision in the numerical results obtained by finite element method (FEM) software. High result precision can only be obtained with confident input data and robust numerical techniques. The determination of parameters should always be performed confronting numerical and experimental results leading to the minimum difference between them. However, the success of this task is dependent of the specification of the cost/objective function, defined as the difference between the experimental and the numerical results. Recently, various objective functions have been formulated to assess the errors between the experimental and computed data (Lin et al., 2002 [36]; Cao and Lin, 2008 [14]; among others). The objective functions should be able to efficiently lead the optimisation process. An ideal objective function should have the following properties: (i) all the experimental data points on the curve and all experimental curves should have equal opportunity to be optimised; and (ii) different units and/or the number of curves in each sub-objective should not affect the overall performance of the fitting. These two criteria should be achieved without manually choosing the weighting factors. However, for some non-analytical specific problems, this is very difficult in practice. Null values of experimental or numerical models also turn the task difficult. In this work, a set of novel objective functions for constitutive model parameter identification are presented. One is a generalization of the work of Cao and Lin and it is suitable for all kinds of constitutive models and mechanical tests, including cyclic and Baushinger tests with null values.     

柔性立管内衬层的非线性力学行为分析

由于聚合物材料的黏弹性,柔性立管内衬层易发生蠕变而"嵌入"至骨架层沟槽中,这一现象可能造成立管结构完整性缺失和骨架层撕裂等安全隐患,但现有的分析理论及有限元模型中,对材料的性质均是做了简单的线性假设,并未考虑聚合物材料的非线性黏弹性特性。基于PA11的试验测试结果,分别采用时间硬化非线性本构模型和考虑时温影响的多重积分非线性本构模型来表征材料性质,并对比两种模型与试验数据拟合情况。根据内衬层与骨架层的真实结构建立二维有限元数值模型,采用两种理论模型进行结构的非线性蠕变行为分析及对比。结果表明：非线性蠕变本构模型能够在在非稳态阶段和存在温度梯度的条件下,更加准确地预测的结构关键部位应变和应力,可为柔性立管内衬层的设计及评估提供借鉴和参考。     

Creep simulation of adhesively bonded joints using modified generalized time hardening model

Creep behavior of double lap adhesively bonded joints was investigated using experimental tests and numerical analysis. Firstly, uniaxial creep tests were carried out to obtain the creep characteristics and constitutive parameters of the adhesive at different stress and temperature levels. Generalized time hardening model was used to predict the creep behavior of the adhesive. This model was modified to simulate the creep behavior at different stress and temperature levels. Secondly, the developed model was used to simulate the creep behavior of bonded joints using finite element based numerical analysis. Creep deformations of the joints were measured experimentally and good agreement was observed in comparison with the results obtained using numerical simulation. Afterward, stress redistribution due to the creep along the adhesively bonded joint was obtained numerically. It was observed that temperature level had a significant effect on the stress redistribution along the adhesive thickness.     

热冲压硼钢B1500HS高温本构方程的研究

硼钢的高温本构方程是热冲压数值模拟不可缺少的数学模型,它反映了流动应力与应变、应变速度以及温度之间的依赖关系。为了研究热冲压硼钢B1500HS高温时的流变力学行为,采用Gleeble 1500D热模拟试验机,在600～900℃温度区间,分别以0.01 s–1、0.1 s–1、1.0 s–1、10 s–1的应变速度对硼钢B1500HS试样进行等温单向拉伸试验,计算得到各相应测试条件下的正应力—应变曲线。采用包含变形激活能和变形温度的双曲正弦形式修正的Arrhenius关系来描述硼钢奥氏体组织的热激活变形行为。通过对试验数据进行拟合回归分析,得到与应变量相关的各材料参数,以及与应变速度、变形温度相关的流变应力关系式。试验结果显示,流动应力随着变形温度的降低而增大,随着形变速度的升高而增大。计算结果表明:流变应力关系式的计算结果与试验数据的吻合度较好。     

Nonlinear Numerical Prediction of a Rotor–Bearing System Using Damped Flexure Pivot Tilting Pad Gas Bearings

Flexure pivot tilting pad gas bearings with pad radial compliance (FPTPGB-Cs) and metal mesh dampers (MMDs) in parallel (FPTPGB-C-MMDs) have been considered for application to high-speed and high-performance turbomachinery because of their advantages of high effective damping level and adequate compliance with variations in rotor geometry or misalignment. Although the dynamic coefficients of FPTPGB-C-MMDs have been predicted using the linear method, a nonlinear study is urgently needed for their high nonlinear behavior. A nonlinear numerical investigation on the rotor–bearing system supported by FPTPGB-C-MMDs is presented in this study by using the time domain orbit simulation method that couples rotor motion equations, the unsteady Reynolds equation, and pad motion (considering MMDs) equations. The nonlinear predictions are verified by the prediction and experimental results of a published paper.FPTPGB-C-MMDs can effectively suppress the subsynchronous vibrations compared with the rotor system supported by FPTPGB-Cs. The prediction results show that a high damper mesh density has a more positive effect on improving the stability of the rotor system by reducing the subsynchronous vibrations. Investigation shows that MMDs can improve the ability of the rotor system to sustain the effect of destabilizing forces. A high damper mesh density can sustain large destabilizing forces. The simulation results also indicate that low pad radial stiffness or preload leads to high amplitudes of subsynchronous vibrations. A small clearance results in an increase in critical speed and its synchronous amplitude. Moreover, large clearance results in a wide speed range that leads to the occurrence of subsynchronous vibrations with large amplitudes.     

基于连续介质损伤力学的7075铝合金高温成形极限理论预测与数值仿真

开展7075铝合金高温单向拉伸试验和成形极限试验,获得了不同温度和应变率的应力-应变曲线和成形极限曲线。结果表明,在较高的温度和应变率时7075铝合金的强度减小、成形性提高。为描述7075铝合金高温损伤演化过程,提出一种改进的连续介质损伤模型,并建立了耦合损伤的多轴统一黏塑性本构模型。基于试验结果,运用NSGAII遗传算法标定了模型中的参数,标定后的本构模型可以很好地预测7075铝合金的高温热力行为和极限应变。通过有限元软件Abaqus的用户材料子程序VUMAT,该本构模型被编入到Abaqus软件中进行数值仿真计算。结果表明,仿真获得的成形极限曲线和应变场分布与试验和理论结果吻合度好,进一步证明了所建立的耦合损伤的多轴本构模型的正确性及其在高温成形极限有限元仿真中的适用性。     

THE EXTENDED KALMAN FILTER IN THE FREQUENCY DOMAIN FOR THE IDENTIFICATION OF MECHANICAL STRUCTURES EXCITED BY SINUSOIDAL MULTIPLE INPUTS

A modal parameter identification method applied to mechanical structures excited by correlated sinusoidal multiple inputs was developed. The algorithm is based on the same formulation of the extended Kalman filter, applied as a system parameter identifier in the frequency domain to mechanical structures subject to excitations characterised by an inherently high degree of correlation. The algorithm was validated by using simulated data on a multi-degree-of-freedom system. The tests demonstrate that the proposed technique is of practical application value. The method is devoted to the identification of the modal parameters of supporting structures of rotating machinery, using data obtained during the normal operation of the machines. Nonetheless, it can have an interest for more general applications in the field of the experimental modal analysis. This study was undertaken in the framework of the BRITE EURAM III project MODIAROT (MOdel based DIAgnosis of ROTors in power plants).     

Computational simulation of three-dimensional neck propagation in polymeric specimens under tension and hybrid identification of constitutive equation

The three-dimensional neck propagation behavior of a glassy polymer under tension, which obeys a constitutive equation based on the molecular chain network theory, was investigated numerically. An experimental observation of tension in polycarbonate (PC) specimens was performed. A hybrid identification procedure of the parameters in the constitutive equation was developed by employing the least mean squares method with an evaluation function which is defined by the square of the difference of the computational and experimental results for nominal stress at specific deformation stages. Application of the proposed procedure to PC led to a very smooth convergence process and accurate results. The validity of the results was also examined through a comparison of the calculated lateral contractions of the specimens at different points in different stages of the deformation with those obtained by experiments.     

橡胶主簧的数值建模分析与实验验证

橡胶主簧作为液压悬置的主要承力部件,其刚度特性直接影响液压悬置的性能.分析了橡胶类材料的本构模型,通过实验方法测得橡胶材料的本构模型参数,建立了橡胶主簧的有限元数值分析模型.数值计算结果与实验数据相吻合,说明该模型是有效实用的.     

Characterisation and modelling of viscoelastically damped sandwich structures

A passive damping technique with viscoelastic materials is analysed in the present work. Concretely, the constrained layer damping (CLD) configuration, also known as viscoelastically damped sandwich structure, is considered. For an efficient dynamical analysis of viscoelastically damped structures, an accurate material characterisation and suitable mathematical models are necessary for reproducing the real material behaviour. With this aim, a CLD structure has been characterised in the frequency domain by means of experimental tests, considering both homogenised and multilayered approaches. The material-parameter extraction procedure is presented, and mathematical models are reviewed. For the homogenised characterisation, a mathematical model based on the Ross et al. model has been proposed, whereas for the multilayered characterisation, the constraining layers have been considered as linear elastic, and the viscoelastic core has been represented by a four-parameter fractional derivative model. Both material models have been considered for defining both homogenised and layered multimaterial numerical models by the finite element method. The numerical models have been validated by correlating the numerical and the experimentally measured dynamic responses. Both numerical models have reproduced the experimental dynamic response accurately for the bandwidth considered herein.     

Numerical simulation for abrasive water jet machining based on ALE algorithm

In dealing with fluid impact and large deformation problems by traditional Lagrange grid, calculation failure often happens due to grid distortion. An abrasive water jet machining model is created to simulate the whole stage by software LS-DYNA from the jet into the nozzle to the workpiece material removal process using ALE (Arbitrary Lagrange–Euler) algorithm. The mesh for the abrasive and water is based on the ALE formulation, while the target mesh applies the Lagrange formulation. The effect of jet penetration is implemented by coupling the grids of ALE and Lagrange. The jet traverse speed is achieved by definition of the movement of ALE grid to reduce the mesh domain. The abrasive constitutive equations are also presented in this paper. The uniform mixture for abrasive and water is achieved by definition of volume percentage of the two materials in the initial ALE elements. Simulation results give the relationships between processing parameters and the cutting depth. The good agreement between simulation results and experimental data verifies the correctness of the simulation.     

Semi-analytical derivation of approximate non-linear eigenvalues and eigenvectors for general non-linear MDOF systems

This work introduces a novel theoretical formulation for the evaluation of approximate eigenvalues and eigenvectors for general non-linear MDOF systems using the so-called “approximate non-linear mode evaluation” (ANME) method. The approach is based on analytically derived quasi-linear expressions which relate the change in modal parameters to physical non-linear elements that can be added anywhere in the system. Subject to assuming that the change in the mode shape is small, expressions for non-linear eigenvalues and eigenvectors become fully determined for a general MDOF system, even within typical experimental constraints. The errors arising from this assumption can be minimized via an iterative procedure. Preliminary results indicate that the rate of convergence is quite fast for systems with medium to high damping but more effort is required for lightly damped systems. The derived expressions provide a theoretical basis for observations made by previous researchers from an inspection of their experimental and/or numerical results: these indicate that an invariant relationship exists between a non-linear eigenvalue and its associated modal response.