Dynamic design of a nonlinear energy sink with NiTiNOL-steel wire ropes based on nonlinear output frequency response functions

A novel vibration isolation device called the nonlinear energy sink(NES)with NiTiNOL-steel wire ropes(NiTi-ST)is applied to a whole-spacecraft system.The NiTi-ST is used to describe the damping of the NES,which is coupled with the modified Bouc-Wen model of hysteresis.The NES with NiTi-ST vibration reduction principle uses the irreversibility of targeted energy transfer(TET)to concentrate the energy locally on the nonlinear oscillator,and then dissipates it through damping in the NES with NiTi-ST.The generalized vibration transmissibility,obtained by the root mean square treatment of the harmonic response of the nonlinear output frequency response functions(NOFRFs),is first used as the evaluation index to analyze the whole-spacecraft system in the future.An optimization analysis of the impact of system responses is performed using different parameters of NES with NiTi-ST based on the transmissibility of NOFRFs.Finally,the effects of vibration suppression by varying the parameters of NiTi-ST are analyzed from the perspective of energy absorption.The results indicate that NES with NiTi-ST can reduce excessive vibration of the whole-spacecraft system,without changing its natural frequency.Moreover,the NES with NiTi-ST can be directly used in practical engineering applications.

Uncertainty analysis of strain modal parameters by Bayesian method using frequency response function

Structural strain modes are able to detect changes in local structural performance, but errors are inevitably intermixed in the measured data. In this paper, strain modal parameters are considered as random variables, and their uncertainty is analyzed by a Bayesian method based on the structural frequency response function （FRF）. The estimates of strain modal parameters with maximal posterior probability are determined. Several independent measurements of the FRF of a four-story reinforced concrete flame structural model were performed in the laboratory. The ability to identify the stiffness change in a concrete column using the strain mode was verified. It is shown that the uncertainty of the natural frequency is very small. Compared with the displacement mode shape, the variations of strain mode shapes at each point are quite different. The damping ratios are more affected by the types of test systems. Except for the case where a high order strain mode does not identify local damage, the first order strain mode can provide an exact indication of the damage location.

Crack detection using a frequency response function in offshore platforms

Structural cracks can change the frequency response function (FRF) of an offshore platform. Thus, FRF shifts can be used to detect cracks. When a crack at a specific location and magnitude occurs in an offshore structure, changes in the FRF can be measured. In this way, shifts in FRF can be used to detect cracks. An experimental model was constructed to verify the FRF method. The relationship between FRF and cracks was found to be non-linear. The effect of multiple cracks on FRF was analyzed, and the shift due to multiple cracks was found to be much more than the summation of FRF shifts due to each of the cracks. Then the effects of noise and changes in the mass of the jacket on FRF were evaluated. The results show that significant damage to a beam can be detected by dramatic changes in the FRF, even when 10% random noise exists. FRF can also be used to approximately locate the breakage, but it can neither be efficiently used to predict the location of breakage nor the existence of small hairline cracks. The FRF shift caused by a 7% mass change is much less than the FRF shift caused by the breakage of any beam, but is larger than that caused by any early cracks.

Pilot study on the Non-Invasive Detectability of Femoral Neck Fractures with Frequency Response Functions

A suspicion of a femoral neck fracture is a frequently recurring situation, especially in nursing homes. For the clarification of such a suspicion normally imaging techniques are used. Such equipment is expensive and therefore is located in hospitals. In addition to the costs, a transport causes stress for the patient. This pilot study is devoted to the question whether the detection of a femoral neck fracture with vibration measurements is possible in principal. In such a case, the clarification could be done on-site by an ordinary person using much cheaper equipment. This would reduce the stress for the patient and save money. For this purpose vibration measurements on a dead body with intact, with partially fractured and with complete cut femoral neck have been performed. Two different methods for the vibration initiation have been investigated, the so called impact testing and the shaker testing. The frequency response function has been determined for all combinations on both sides of the body. It turned out that there is a clear difference in the frequency response functions of the fractured bone with respect to the intact bone when shaker testing is used. This indicates that the method could have the potential to be a cost-saving alternative to imaging techniques. However, in a next step a statistically reliable clinical survey on living persons needs to be done.

Research on the iterative method for model updating based on the frequency response function

Model reduction technique is usually employed in model updating process. In this paper, a new model updat- ing method named as cross-model cross-frequency response function （CMCF） method is proposed and a new iterative method associating the model updating method with the mo- del reduction technique is investigated. The new model up- dating method utilizes the frequency response function to avoid the modal analysis process and it does not need to pair or scale the measured and the analytical frequency re- sponse function, which could greatly increase the number of the equations and the updating parameters. Based on the traditional iterative method, a correction term related to the errors resulting from the replacement of the reduction ma- trix of the experimental model with that of the finite element model is added in the new iterative method. Comparisons be- tween the traditional iterative method and the proposed itera- tive method are shown by model updating examples of solar panels, and both of these two iterative methods combine the CMCF method and the succession-level approximate reduc- tion technique. Results show the effectiveness of the CMCF method and the proposed iterative method .

Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates

This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.

A Contribution to the Analysis of Frequency Response and Impedance Measurements to Evaluation and Diagnosis of Power Transformers

This paper has an objective to show a developed quantitative criterion,based in two mathematical variables that explicit the deviation degree of a normal situation,applying simultaneously data from terminal impedances and frequency response.Based in more than 100-measured equipment,of different applications(step-up transformer,transmission transformer,etc.,),for a period of 10 years,the work presents some examples of practical application of this methodology in Brazilian Electrical System.

Analysis of Dynamic Cross Response between Spindles in a Dual Spindle Type Multi-Functional Turning Machine

In order to meet increasing demand for higher productivity and flexibility, recently many kinds of multi-functional machine tools, which are capable of multiple machining functions or different kinds of machining processes on one machine, have been developed and widely used in manufacturing industries. In this study, a multi-functional turning lathe, which has two spindles and two turrets so that multiple turning operations and various machining processes could be performed simultaneously, has been developed. Furthermore, the equations of correlation between whole responses and cross responses of the two spindles have been derived to examine to what extent the two spindles affect each other’s vibrations.

Tool Condition Monitoring Based on Nonlinear Output Frequency Response Functions and Multivariate Control Chart

Tool condition monitoring(TCM)is a key technology for intelligent manufacturing.The objective is to monitor the tool operation status and detect tool breakage so that the tool can be changed in time to avoid significant damage to workpieces and reduce manufacturing costs.Recently,an innovative TCM approach based on sensor data modelling and model frequency analysis has been proposed.Different from traditional signal feature-based monitoring,the data from sensors are utilized to build a dynamic process model.Then,the nonlinear output frequency response functions,a concept which extends the linear system frequency response function to the nonlinear case,over the frequency range of the tooth passing frequency of the machining process are extracted to reveal tool health conditions.In order to extend the novel sensor data modelling and model frequency analysis to unsupervised condition monitoring of cutting tools,in the present study,a multivariate control chart is proposed for TCM based on the frequency domain properties of machining processes derived from the innovative sensor data modelling and model frequency analysis.The feature dimension is reduced by principal component analysis first.Then the moving average strategy is exploited to generate monitoring variables and overcome the effects of noises.The milling experiments of titanium alloys are conducted to verify the effectiveness of the proposed approach in detecting excessive flank wear of solid carbide end mills.The results demonstrate the advantages of the new approach over conventional TCM techniques and its potential in industrial applications.

Response Characteristics of Load on Vessels in Waves

Considering the requirement of direct design and fatigue test for ships and floating structures by use of FEM technique, a computational procedure of spectral analysis for wave load on the hull surface is developed in this paper. The response of hydrodynamic pressure on the body surface to a designated sea state for ships and floating structures is calculated by use of the revised strip method with the hull bound perturbation flow concept. The spectral function of wave load for the defined point on the body surface can be determined from the Wiener-Khinhine theorem and the characteristic load value can be also obtained from spectral moment analysis. A container ship is taken as a computational example acid the sample of wave load with a certain probability and corresponding encountered frequency is provided.

Nonlinear oscillations of sigmoid functionally graded material plates moving in longitudinal direction

Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material （S-FGM） plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along the thickness direction. Based on the D＇Alembert＇s principle, a nonlinear equation of motion is derived for the moving S-FGM plates, where the von K^rm^n nonlinear plate theory is adopted. Utilizing the Galerkin method, the equation of motion is discretized and solved via the method of harmonic bal- ance. The approximate analytical solutions are validated through the adaptive step-size fourth-order Runge-Kutta method. Besides, the stability of the steady-state solutions is examined. The results reveal that the mode interaction behavior can happen between the first two modes of the moving S-FGM plates, leading to a complex nonlinear frequency response. It is further found that the power-law index, the longitudinal speed, the exci- tation amplitude, and the in-plane pretension force can significantly affect the nonlinear frequency-response characteristics of longitudinally traveling S-FGM plates.

Parametric characteristic of the random vibration response of nonlinear systems

Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density（PSD） and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.

Damage Detection of Offshore Jacket Structures Using Frequency Domain Selective Measurements

The development of damage detection techniques for offshore jacket structures is vital to prevent catastrophic events. This paper applies a frequency response based method for the purpose of structural health monitoring. In efforts to fulfill this task, concept of the minimum rank perturbation theory has been utilized. The present article introduces a promising methodology to select frequency points effectively. To achieve this goal, modal strain energy ratio of each member was evaluated at different natural frequencies of structure in order to identify the sensitive frequency domain for damage detection. The proposed methodology opens up the possibility of much greater detection efficiency. In addition, the performance of the proposed method was evaluated in relation to multiple damages. The aforementioned points are illustrated using the numerical study of a two dimensional jacket platform, and the results proved to be satisfactory utilizing the proposed methodology.

Sensibility to Changes of Vibrational Modes of Excited Electron： Sum Frequency Signals Versus Difference Frequency Signals

In this paper, we investigate a two electronic level system with vibrational modes coupled to a Brownian oscillator bath. The difference frequency generation （DFG） signals and sum frequency generation （SFG） signals are calculated. It is shown that, for the same model, the SFG signals are more sensitive than the DFG signals to the changes of the vibrational modes of the electronic two-level system. Because the SFG conversion efficiency can be improved by using the time-delay method, the findings in this paper predict that the SFG spectrum may probe the changes of the microstructure more effectively.

Exact Dynamic Modeling of PWM DC-to-DC Power Converters—Part II: Discontinuous Conduction Mode

This paper follows on from the first paper, Part I, where a general formulation of a describing function approach to frequency response determination of switched linear networks, such as PWM converters, was simplified and updated. The models assume a piecewise linear state space equation description of the system and results in a closed form solution for the sought after frequency response. In Part I, model derivation was demonstrated for the case of PWM converters operating in the continuous conduction mode (CCM). This operating mode does not feature any state dependent switching times. In this paper, Part II, frequency response models for any transfer function for PWM converters operating in discontinuous conduction mode (DCM) are derived based on the theory presented in Part I. This operating model features state dependent switching times. The describing function models developed are exact and therefore, in terms of accuracy, are to be preferred over averaged models which are widely used. The example of a boost dc-to-dc converter operating in DCM is simulated to obtain the control to output and input to output frequency responses and are compared with the models derived here. Excellent agreement between the simulated and model responses was found. Matlab code implementing the analytical models is also presented which the user can adapt for any other PWM converter topology. The models derived here may be used as a basis from which simplified models may be derived while still preserving required accuracy.

Exact Dynamic Modeling of PWM DC-to-DC Power Converters—Part I: Continuous Conduction Mode

A general approach is presented by which the exact frequency response of any transfer function of switched linear networks can be determined. This is achieved with a describing function approach using a state space equation formulation. This work presents a somewhat simplified set of equations to one previously given by one of the authors. To demonstrate application of the general formulation, the frequency responses of switched networks used as PWM DC-to-DC converters operating in continuous conduction mode (CCM) under voltage mode control are derived. (The accompanying paper, Part II, will present results for converters operating in discontinuous conduction mode (DCM)). From the general sets of equations developed here, both the control to output and input source variation to output frequency responses are derived. The describing function approach enables exact frequency response determination, even at high frequencies where the accuracy using average models may be compromised. Confirmation of the accuracy of the derived models is provided by comparing the responses with those obtained using the commercial simulator PSIM on a PWM boost converter. The magnitude and phase responses are shown to match perfectly over the full range of frequencies up to close to half the switching frequency. Matlab code that implements the models is given such that the user can easily adapt for use with other PWM converter topologies.

Regularized automatic frequency response function acquisition of a milling robot operating in a high-dimensional workspace

Because robotic milling has become an important means for machining significant large parts,obtaining the structural frequency response function(FRF)of a milling robot is an important basis for machining process optimization.However,because of its articulated serial structure,a milling robot has an enormous number of operating postures,and its dynamics are affected by the motion state.To accurately obtain the FRF in the operating state of a milling robot,this paper proposes a method based on the structural modification concept.Unlike the traditional excitation method,the proposed method uses robot joint motion excitation instead of hammering excitation to realize automation.To address the problem of the lack of information brought by motion excitation,which leads to inaccurate FRF amplitudes,this paper derives the milling robot regularization theory based on the sensitivity of structural modification,establishes the modal regularization factor,and calibrates the FRF amplitude.Compared to the commonly used manual hammering experiments,the proposed method has high accuracy and reliability when the milling robot is in different postures.Because the measurement can be performed directly and automatically in the operation state,and the problem of inaccurate amplitudes is solved,the proposed method provides a basis for optimizing the machining posture of a milling robot and improving machining efficiency.

基于NOFRF裂纹转子非线性频谱分析

建立了裂纹转子非线性逼近模型,论述了非线性输出频域响应函数(NOFRF)及其非线性频谱分析理论,基于该理论对裂纹转子系统的各阶NOFRF进行了仿真分析,该分析结果说明了裂纹转子系统新频域成份是如何产生的,对裂纹转子的超谐波成份和亚共振现象进行了解释,并进行了试验分析,结果表明了高阶NOFRF比一阶对转子裂纹深度更敏感,为裂纹转子的精确故障诊断提供了理论基础。

基于NARMAX模型和NOFRF结构损伤检测的实验研究

非线性输出频率响应函数是由Volterra级数发展而来的频域概念,可方便在频域对非线性系统进行分析,它是频率的一维函数.本文主要介绍了利用NARMAX模型以及NOFRF对结构进行损伤检测的方法,并利用实验研究证实了该损伤检测方法的可行性.另外,由于系统非线性特性可用来做结构损伤检测,且具有对系统状态比较敏感的优点,而基于NOFRF的损伤检测方法是利用非线性方法来分析系统的状态,该方法提取出的特征属于非线性特征,所以该损伤检测方法可以用来做结构损伤检测,且具有对系统状态比较敏感的优点.

IMPROVEMENT ACCURACY OF SYSTEM IDENTIFICATION BASED ON MORLET WAVELET

A time frequency de-noising method is presented in the frequency response function （FRF） preprocessing based on the continuous wavelet transform. Morlet wavelet is employed to construct a filter bank to reduce the noise. The filter bank is a finite impulse response （FIR） linear phase filter thus maintaining phase consistency. A modified Morlet base function is proposed to meet the time frequency resolution by using transient excitation. Numerical simulation is conducted using a Group for Aeronautical Research and Technology in Europe （GARTEUR） aircraft model excited by the transient input. The white noise is added to the simulated data. Results show that the accuracy of the system identification is improved. The estimated error of the mode damping is decreased by 30% compared with that obtained from the noise-corrupted signal.