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.     

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.     

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.     

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.     

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.     

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.     

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.     

一种针对含非线性子结构多点耦合运输包装系统的解耦方法

目的 考虑到运输包装系统耦合形式复杂,包装材料及包装结构具有非线性特性,不容易测量局部物理参数,需要对传统逆向子结构方法进行优化,使之能够求解非线性多点耦合系统中子结构的动态响应特性。方法 使用描述函数法将非线性的运输包装系统线性化,测量其在若干特定振动幅值下的频率响应函数;之后,应用逆向子结构方法和参数识别方法,计算包装件的模态参数;最后,拟合包装件模态参数与振动幅值之间的关系,构建函数来描述包装件的动态响应特性。结果 在集总参数模型中,解耦预测值与实际值吻合;在有限元模型中,对响应峰值的预测误差小于5%,对响应跳跃现象所在频率的预测误差小于3%。结论 该研究将传统逆向子结构方法的应用范围拓展到了非线性多点耦合系统,对复杂运输包装系统动力学模型的构建和防振包装的设计具有指导意义。     

A coupled approach of optimization,uncertainty analysis and configurational mechanics for a fail‐safe design of structures

In this contribution, a novel method for a fail‐safe optimal design of structures is proposed, which is a coupled approach of optimization employing a genetic algorithm, the structural analysis conducted in the framework of fracture mechanics and uncertainty analysis. The idea of fail‐safe structures is to keep their functionality and integrity even under damage conditions, for example, a local failure of substructures. In the present work, a design concept of a substructure exhibiting a damage accumulating function due to the application of crack arresters is introduced. If such a substructure is integrated within a system of coupled substructures, it will accumulate the damage arising from the boundary conditions change induced by the failure of certain neighbouring structural elements and hinder further damage escalation. The investigation of failure of the damage accumulating substructure is introduced within a finite element framework by a combination of discrete fracturing and configurational mechanics based criteria. In order to design a structure, which will fail safely according to a predefined scenario, uncertainties are taken into account. The developed approach optimizes the configuration of crack arresters within the damage accumulating substructure so that the uncertain crack propagation is hindered and only a local failure of this element occurs. Copyright © 2016 John Wiley & Sons, Ltd.     

Modeling of the dynamic characteristics of two‐bolt‐joints

Abstract

In this paper, a method to identify the damping and stiffness properties of bolted joints from a substructure synthesis scheme is presented. The easily measured frequency response functions of substructures and the assembled structure are the only data needed in this method. A synthesis formula used to predict the frequency response functions of two‐bolt‐joint structures is proposed. The formula makes use of the extracted properties of a single‐bolt‐joint. Some experiments with two free‐free steel beams jointed with one or two bolts are made to check this method. The close correlation between predicted and measured results demonstrates that this method is acceptable.     

运输包装系统随机振动频域分析

为了研究包装件在实际流通环境振动特性下的振动规律,以车辆、包装件构成的六自由度运输包装系统为基础,构建了在以白噪声为输入的路面不平激励下的振动模型,建立了路面不平激励的数学模型、运输车辆以及包装件的动力学模型。借助Matlab/Simulink仿真技术,对运输包装系统随机振动进行了频域分析,得到了内装产品及易损零件随机振动加速度响应的幅值频谱和功率谱密度。仿真结果表明了随机振动强弱程度与频率的关系,全面反映了随机振动规律,为缓冲包装设计提供了理论依据。     

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.     

Statistical modelling of predicted non‐stationary vehicle vibrations

This paper describes a method to predict the vertical vibrations of road vehicles from measured pavement profiles. It discusses the limitations of current methods used for analysing and simulating vehicle vibrations and shows that more accurate characterization and simulation of the transport environment must take into account the non‐stationary nature of road vehicle vibrations. Vertical vibrations for typical transport vehicles under various operating conditions and pavement profiles are predicted using a computer model of the vehicle characteristics and analysed to produce the spectral and statistical characteristics. The paper also presents an improved method to compute the vibration intensity by using a dynamic segmentation data reduction technique. The effectiveness of the procedure to characterize the non‐stationarity of random vehicle vibrations is demonstrated. Finally, the paper deals with the statistical distribution of the vibration intensity and demonstrates how it can be adapted to a technique for the simulation the non‐stationary nature of random vehicle vibrations. Copyright © 2002 John Wiley & Sons, Ltd.     

Analysis of in‐flight vibration of a twin‐engine turbo propeller aircraft

A data recorder was utilized to record in‐flight vibration of a twin engine turbo propeller (feeder) aircraft. The data recorded produced power spectral density (PSD) profiles which are currently used in laboratory settings to drive vibration tables in order to simulate a particular vehicle type. Overall Grms values were averaged and compared to previous research studies. The data collected from this research study could be utilized for packaging research when developing products and packages that will pass through a distribution cycle which includes transportation via a feeder aircraft. One example of this type of distribution cycle is the small parcel shipping environment. The PSD profiles which were analyzed from this research could simulate in‐flight aircraft vibration of the aircraft chassis in a laboratory environment. This will enable further research in the air transport environment. Copyright © 2009 John Wiley & Sons, Ltd.     

基于逆子理论的洗衣机运输系统动态特性分析

目的获取产品运输包装系统各部件的动态特性。方法采用多级系统分布解耦法,结合二级刚性耦合系统逆子结构理论,推导由产品、车辆部件水平和系统水平频响传函预测关键部件频响传函的理论公式。搭建电机-洗衣机-车辆三级刚柔耦合运输系统,对理论方法进行验证。结果通过在线实验验证,基于理论预测得到的关键部件频响传函和测试值相吻合。结论研究结果为产品运输包装设计和优化提供了参考依据。     

道路不平顺激励下车辆运输非线性包装系统动力学响应

目的研究运输车辆-非线性包装系统耦合系统在路面脉冲激励下的隔振特性。方法整体考虑路面-运载工具-缓冲包装材料-物品之间耦合的非线性振动传递模型,建立基于二分之一系统的五自由度路面脉冲激励下车辆-非线性包装系统运动分析理论模型,推导得到系统动力学方程并求解。依据结果比较考虑车辆-非线性包装系统耦合及不考虑两者耦合对运输包装件的影响,从而得知考虑车辆-非线性包装件系统耦合系统下包装件最大竖向位移是不考虑两者耦合情况下的1.25倍左右,并分别对隔振材料非线性因素及路面不平顺因素对包装件的影响进行分析。结果在车辆运输过程中,隔振材料的非线性因素及路面不平顺因素对包装件系统的响应会产生一定的影响。结论对于精确进行被动隔振设计和隔振效果评价具有积极意义。     

基于频响函数的逆子结构方法误差分析

目的 通过分析随机误差在基于试验频响函数(FRFs)的逆子结构分析方法中的传递,得出随机误差对预测结果的影响规律,为基于逆子结构方法分析复杂结构的动态特性提供参考价值.方法 对获得的系统频响函数施加不同程度(1％,5％,10％)的随机误差,对比分析各个耦合系统频响函数对预测子结构频响函数的影响.结果 对耦合系统频响函数施加随机误差后,采用逆子结构方法对耦合系统解耦后预测的子结构频响函数严重偏离真实值,尤其是共振频率附近,所施加的随机误差在预测子结构频响函数中甚至被放大了数十倍,导致预测结果不可靠;且耦合系统耦合点处的频响函数对预测结果的影响最大.结论 通过分析明确了系统频响函数所携带的随机误差对预测结果的影响规律,且这些误差将随着矩阵的求逆运算被放大,且交叉耦合系统频响函数对预测结果的影响最为显著.     

A FETI‐DP method for the parallel iterative solution of indefinite and complex‐valued solid and shell vibration problems

The dual‐primal finite element tearing and interconnecting (FETI‐DP) domain decomposition method (DDM) is extended to address the iterative solution of a class of indefinite problems of the form ( K ?σ² M ) u = f , and a class of complex problems of the form ( K ?σ² M +iσ D ) u = f , where K , M , and D are three real symmetric matrices arising from the finite element discretization of solid and shell dynamic problems, i is the imaginary complex number, and σ is a real positive number. A key component of this extension is a new coarse problem based on the free‐space solutions of Navier's equations of motion. These solutions are waves, and therefore the resulting DDM is reminiscent of the FETI‐H method. For this reason, it is named here the FETI‐DPH method. For a practically large σ range, FETI‐DPH is shown numerically to be scalable with respect to all of the problem size, substructure size, and number of substructures. The CPU performance of this iterative solver is illustrated on a 40‐processor computing system with the parallel solution, for various σ ranges, of several large‐scale, indefinite, or complex‐valued systems of equations associated with shifted eigenvalue and forced frequency response structural dynamics problems. Copyright © 2005 John Wiley & Sons, Ltd.     

The dynamic behaviour of stacked shipping units during transport. Part 1: model validation

This paper deals with the dynamic behaviour of stacked packaging units when subjected to vertical vibrational inputs as experienced in transport vehicles. Although the vibrational performance of single‐unit packaging systems has been thoroughly studied, the behaviour of stacked packaging units is not fully understood. The complexity of the problem is compounded when the effects of vertical restraints are taken into account. The paper presents the development of a numerical computer model designed to predict the dynamic response of stacked package systems when subjected to vertical vibrational excitation. Provisions have been made to account for the effects of vertical restraint tension and stiffness. In addition, a physical model representative of a generic stacked packaging system has been developed to assist in validating the numerical model. The paper includes results from preliminary experiments in which the frequency response functions of the models were evaluated and compared. The validity of the numerical model in the time domain was tested using random burst excitation signals. These preliminary experiments reveal that, when the effects of frictional damping are taken into account, the numerical model can be used to generate reasonably accurate predications of the dynamic behaviour of the equivalent physical system. Copyright © 2004 John Wiley & Sons, Ltd.