Inverse Sub‐structuring Method for Multi‐coordinate Rigidly Coupled Product Transport System based on a Novel Shearing Probe Technique

The inverse sub‐structuring method can predict the component‐level frequency response functions (FRFs) of product (critical component) for product transport system from only measured system‐level FRFs, facilitating the cushioning packaging design. However, the FRFs of the coupling interface between product and vehicle are usually of extreme difficulty to be measured due to the limited accessible space. To overcome this difficulty, the authors suggested a so‐called FRF probe technique method in the previous study, which may be more suitable for the single‐coordinate coupled system. In practice, most of the product transport systems should be treated as multi‐coordinate coupled system. The aim of this paper is to derive a new FRF‐based inverse sub‐structuring method for multi‐coordinate rigidly coupled product transport system and develop a new shearing probe technique to obtain the difficult‐to‐monitor FRFs at the coupling interface, which will be validated by a lumped mass model and finite element models, respectively, showing perfect agreement. Finally, the experiment on a physical prototype of multi‐coordinate rigidly coupled product transport system is performed to further check the feasibility of the application prospect of the shearing probe technique for inverse analysis of product transport system. The method proposed in this study will provide the packaging designers an alternative method to monitor the integrity of product transport system. Copyright © 2017 John Wiley & Sons, Ltd.     

Inverse Sub‐structuring Method for Rigidly Coupled Product Transport System based on Frequency Response Function Testing Probe Technique

The inverse sub‐structuring method has been recently proposed and applied for inverse analysis of product transport system, to predict the component‐level frequency response functions (FRFs) and the coupling dynamic stiffness from only the system‐level FRFs. However, previous applications of this method were all developed based on the assumption that the components were coupled by flexible couplings. Actually, increasing more components are welded or bolted to construct a coupled system, which should be treated as rigidly coupled system. The aim of this paper is to derive a new FRF‐based inverse sub‐structuring method for the analysis of the dynamic characteristics of a two‐component coupled product transport system with rigid couplings. And then a so‐called FRF testing probe technique is proposed and applied to measure the difficult‐to‐monitor FRFs at the coupling interface. The developed method is 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 proposed method is an extension of previous inverse sub‐structuring method and may help to obtain the main controlling factors and contributions from the various structure‐borne paths for product transport system. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

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.     

Dynamic Characteristic Analysis of Refrigerator‐Truck Transport System by Using Inverse Substructure Method

This paper is a continuation of the previous research. The refrigerator‐truck system is treated as a two‐substructure multi‐coordinate coupled system, which is composed of a refrigerator substructure and a truck substructure coupled by numerous packaging units. Applying the two‐substructure multi‐coordinate coupled inverse substructure method to a product‐transport system, the paper makes an analysis of the dynamic characteristics for the refrigerator‐truck system. In order to validate the method in the refrigerator‐truck system, the measured system‐level frequency response functions (FRFs) were used to predict the substructure‐level FRFs that were compared with those directly measured and found to be in agreement in trend. To evaluate the vibration transmissibility of packaging units, the concepts of the vibration contribution, vibration contribution ratio, overall vibration contribution and overall vibration contribution ratio to product response through each packaging unit are introduced. The vibration contributions to the refrigerator through four coupling points almost coincide with each other in the whole frequency domain. However, the vibration contribution ratios are different at each frequency. The overall vibration contributions to the refrigerator through the frequency domain 10 to 50 Hz through four coupling points are respectively 9.4, 7.5, 9.8 and 11.2 mm/N, and the overall vibration contribution ratios are respectively 0.25, 0.20, 0.26 and 0.29. The vibration transmissibilities of four coupling points are similar. Copyright © 2014 John Wiley & Sons, Ltd.     

Investigation of Frequency Response Function of Product‐Transport System Based on Multi‐coordinate Coupled Inverse Substructure Method

The product and vehicle, through a packaging, constitute a complex product‐transport system in logistics. It is very important to obtain the frequency response functions of the product‐transport system and its substructures for the design of product packaging. In this paper, the product‐transport system is treated as a two‐substructures multi‐coordinate coupled system. It is composed of a product substructure and a vehicle substructure, which are connected by a packaging structure consisting of many packaging units. The multi‐coordinate coupled inverse substructure method is developed and used to analyse the dynamic characteristics of the product‐transport system. To verify the validity of this method for the product‐transport system, the experiment of a physical prototype is conducted. The results show that the predicted substructure‐level frequency response functions are in accordance with the measured. Copyright © 2013 John Wiley & Sons, Ltd.     

获取界面响应不可测数据的频响探针关键技术研究

目的针对传统逆子结构理论在求解过程中界面响应难以实测的问题,提出一种利用频响探针技术来获取该界面响应的关键技术。方法首先基于该频响探针的动力学微分方程,从理论上推导了该频响探针技术的理论公式,然后对建立的二级单点刚性耦合系统进行了有限元数值验证,将利用频响探针技术预测得到的难测原点频响函数与有限元计算值进行比较,并将该预测值代入逆子结构理论公式中,得到了部件频响函数的预测值,将该预测值与有限元计算值进行了对比验证。结果预测值与有限元计算值高度吻合,验证了该理论的准确性。结论该频响探针关键技术在获取界面响应不可测数据方面,有很好的应用价值。     

Improved multi‐level Newton solvers for fully coupled multi‐physics problems

An algorithm is suggested to improve the efficiency of the multi‐level Newton method that is used to solve multi‐physics problems. It accounts for full coupling between the subsystems by using the direct differentiation method rather than error prone finite difference calculations and retains the advantage of greater flexibility over the tightly coupled approaches. Performance of the algorithm is demonstrated by solving a fluid–structure interaction problem. Copyright © 2003 John Wiley & Sons, Ltd.     

Acoustic modelling by BEM–FEM coupling procedures taking into account explicit and implicit multi‐domain decomposition techniques

The numerical modelling of interacting acoustic media by boundary element method–finite element method (BEM–FEM) coupling procedures is discussed here, taking into account time‐domain approaches. In this study, the global model is divided into different sub‐domains and each sub‐domain is analysed independently (considering BEM or FEM discretizations): the interaction between the different sub‐domains of the global model is accomplished by interface procedures. Numerical formulations based on FEM explicit and implicit time‐marching schemes are discussed, resulting in direct and optimized iterative BEM–FEM coupling techniques. A multi‐level time‐step algorithm is considered in order to improve the flexibility, accuracy and stability (especially when conditionally stable time‐marching procedures are employed) of the coupled analysis. At the end of the paper, numerical examples are presented, illustrating the potentialities and robustness of the proposed methodologies. Copyright © 2008 John Wiley & Sons, Ltd.     

多级刚性包装运输系统间接逆向子结构分析

目的针对各子部件耦合界面之间的系统水平频响函数难以测量,刚性耦合系统逆向子结构分析方法无法顺利应用的情况,提出多级系统间接分析方法。方法基于子结构理论,提出单点耦合和多点耦合系统的多级刚性耦合系统间接逆向子结构分析方法,然后建立相对应的集总参数模型,利用已知参数和公式获得部件频响函数直接计算值和预测值,最后将两者进行对比验证。结果部件频响函数直接计算值与预测值相吻合,验证了方法的准确性。结论提出的方法可为逆子结构理论在解决耦合界面频响函数难测问题时提供新思路,以及为在运输包装领域更广泛的应用提供更多的可能性。     

Elastic wave propagation in a 3‐D unbounded random heterogeneous medium coupled with a bounded medium. Application to seismic soil–structure interaction (SSSI)

We present a sub‐structuring method for the coupling between a large elastic structure, and a stratified soil half‐space exhibiting random heterogeneities over a bounded domain and impinged by incident waves. Both media are also weakly dissipative. The concept of interfaces classically used in sub‐structuring methods is extended to ‘volume interfaces’ in the proposed approach. The random dimension of the stochastic fields modelling the heterogeneities in the soil is reduced by introducing a Karhunen–Loéve expansion of these stochastic fields. The coupled overall problem is solved by Monte‐Carlo simulation techniques. A realistic example of a large industrial structure interacting with an uncertain stratified soil medium under earthquake is finally presented. This case study and others validate the presented methodology and its ability to handle complex mechanical systems. Copyright © 2002 John Wiley & Sons, Ltd.     

Control Method for Multiple‐Input Multiple‐Output Non‐Gaussian Random Vibration Test

A control method for multi‐input multi‐output non‐Gaussian random vibration test based on an improved zero‐memory nonlinear transformation and an inverse system method is proposed. Compared with the classic zero‐memory nonlinear transformation method, the improved one can overcome the defect of the dynamic range loss. The inverse system method is put forward in order to control the kurtoses and the spectra for multi‐input multi‐output non‐Gaussian random vibration test simultaneously. The main idea of inverse system method is to generate the Gaussian reference response signals first from the reference spectra, and the improved zero‐memory nonlinear transformation method is utilized to obtain the non‐Gaussian reference response signals with the reference kurtoses, then the continuous and stationary coupled driving signals can be derived from the relationship between the inputs and outputs of the test system. Thus, the difficulty in generation of driving signals in multi‐input multi‐output non‐Gaussian random vibration test can be overcome. The matrix power control algorithm is introduced for the spectrum control, and a kurtosis control algorithm is set up similarly. A simulation example and an experimental test are provided in the paper, and the results illustrate the effectiveness and feasibility of the proposed control method. Copyright © 2017 John Wiley & Sons, Ltd.     

多部件耦合包装系统逆子结构分析一般性理论

建立多部件耦合包装系统动力学模型,建立其动力学分析的一般逆子结构方法,得到从系统水平传函反向计算各耦合部件水平传函及部件间耦合动刚度的理论公式,采用集总参数模型数值校验了所建立理论的正确性。研究结论为复杂系统动力学特性分析提供了一种新的技术方法。     

Application of the Inverse Substructure Method in the Investigation of Dynamic Characteristics of Product Transport System

Product, packaging and vehicle constitute a complex product transport system in logistics. It is very difficult to obtain accurately the dynamic response of a product transport system under the action of environmental vibration and shock. In this paper, product transport system is treated as a two substructure‐coupled system composed of product system (including critical element) and vehicle connected by packaging and its fixing (location pattern, securing, etc.); the inverse substructure method is applied to the analysis of the dynamic characteristics of the system. For verification of the validity of the inverse substructure method for product transport system, a typical lumped mass model is taken as an example for numerical validation. To check out the accuracy of the method, we completed the experiment, and the predicted substructure‐level frequency response functions are in overall agreement with those measured. The sensitivity of the method to measurement error is also made. To study the influences of the product parameters, packaging and its fixing, we investigated the effects of the coupling stiffness, mass ratio, frequency parameter ratio and damping on the dynamic response of critical element. Reducing the coupling static stiffness of product–vehicle interface can effectively lower the response of critical element, especially when the coupling stiffness is less than the stiffness of product and vehicle. Copyright © 2011 John Wiley & Sons, Ltd.     

产品-包装-运载体系统动态特性研究

为缓冲防震系统的设计与评估提供一种新的结构动态分析方法,将复杂耦合结构系统的动态逆子结构分析方法应用于运输包装工程中.从系统分析的角度建立用于确定"产品-包装-运载体"在系统与部件水平的动态特性的实验技术理论.通过对一个集总参数模型实例在系统水平的传递函数的计算,验证了所建立理论的有效性.     

A new coupling technique for the combination of wavelet‐Galerkin method with finite element method in solids and structures

In this paper, a coupling technique is developed for the combination of the wavelet‐Galerkin method (WGM) with the finite element method (FEM). In this coupled method, the WGM and FEM are respectively used in different sub‐domains. The WGM sub‐domain and the FEM sub‐domain are connected by a transition region that is described by B‐spline basis functions. The basis functions of WGM and FEM are modified in the transition region to ensure the basic polynomial reconstruction condition and the compatibility of displacements and their gradients. In addition, the elements of FEM and WGM are not necessary to conform to the transition region. This newly developed coupled method is applied to the stress analysis of 2D and 3D elasticity problems in order to investigate its performance and study parameters. Numerical results show that the present coupled method is accurate and stable. The new method has a promising potential for practical applications and can be easily extended for coupling of other numerical methods. Copyright © 2017 John Wiley & Sons, Ltd.     

基于试验数据的频响函数综合法概述

利用子结构方法对舰艇上复杂隔振系统进行建模分析时,因子结构的复杂性而无法准确获取其动力学模型,一种解决办法是采用试验测得的子结构频响函数数据进行基于频响函数的子结构综合。为提高子结构频响函数测试结果的精度和基于试验数据的频响函数综合结果的精度,采用频响函数综合算法、子结构频响函数测试误差的消除方法、子结构转角自由度频响函数的测试、频响函数数据的测试及影响因素等几个方面进行总结,并采用基于试验数据的频响函数综合法对一复杂隔振系统进行建模分析,得到较好的效果。可在进行实际隔振系统的子结构测试和综合时提供参考。     

A coupling of multi‐zone curved Galerkin BEM with finite elements for independently modelled sub‐domains with non‐matching nodes in elasticity

When the different parts of a structure are modelled independently by BEM or FEM methods, it is sometimes necessary to put the parts together without remeshing of the nodes along the part interfaces. Frequently the nodes do not match along the interface. In this work, the symmetric Galerkin multi‐zone curved boundary element is a fully symmetric formulation and is the method used for the boundary element part. For BEM–FEM coupling it is then necessary to interpolate the tractions in‐between the non‐matching nodes for the FEM part. Finally, the coupling is achieved by transforming the finite element domains to equivalent boundary element domains in a block symmetric formulation. This system is then coupled with a boundary element domain with non‐matching nodes in‐between. Copyright © 2004 John Wiley & Sons, Ltd.     

Real‐time Reliability Evaluation for an Individual Product Based on Change‐point Gamma and Wiener Process

Reliability evaluation based on degradation data has received significant attentions in recent years. However, existing works often assume that the degradation evolution over time is governed by a single stochastic process, which may not be realistic if change points exist. Here, for cases of degradation with change points, this paper attempts to capture the degradation process with a multi‐phase degradation model and find the method to evaluate the real‐time reliability of the product being monitored. Once new degradation information becomes available, the evaluation results are adaptively updated through the Bayesian method. In particular, for a two‐stage degradation process of liquid coupling devices (LCDs), a model named as change‐point gamma and Wiener process is developed, after which issues of real‐time reliability evaluation and parameters’ estimation are addressed in detail. Finally, the proposed method is illustrated by a case study of LCDs, and the corresponding results indicate that trustful evaluation results depend on the fitting accuracy in cases of multi‐phase degradation process. Copyright © 2013 John Wiley & Sons, Ltd.     

A simple dynamical scale‐coupling method for concurrent simulation of hybridized atomistic/coarse‐grained‐particle system

We propose a simple method for dynamical coupling of two sub‐systems with different characteristic scales described with different theoretical models, such as the fine‐scale sub‐system with the atomistic model (AM) such as the empirical inter‐atomic potential and the coarse‐scale sub‐system with the coarse‐grained particle (CGP) method, in a concurrent hybrid simulation scheme. Naive coupling of the different‐scale sub‐systems results in reflection of high wavenumber waves at the interface because of the differences in the phonon Brillouin‐zone and in the dispersion relation. To solve the problem, the present scale‐coupling method introduces (virtual) extra atoms and particles for the AM and the CGP sub‐systems, respectively, beyond the atom–particle interface, and uses the extra atoms and the particles to mutually transfer information of the waves between the two sub‐systems and to suppress the artificial reflection of the incident wave in the whole wavenumber range. As the algorithm in the present scale‐coupling method is local in time and space, it is applicable to hybrid systems with any interface shape at low computation and memory requirement. Accuracy of the present scale‐coupling method is compared with that of the existing methods for a simple model system. The hybrid AM‐CGP simulation of indentation of a graphene nano‐drum using the present scale‐coupling method is performed to demonstrate its accuracy and usefulness through its comparison with the fully atomistic results. Copyright © 2010 John Wiley & Sons, Ltd.