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frequency response functions and modal analysis of general nonviscously damped dynamic systems with and without repeated modes

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2019年 120卷 744-764页

作者： Lin, R. M. Ng, T. Y. Nanyang Technol Univ Sch Mech & Aerosp Engn Singapore Singapore

This paper seeks to examine some important outstanding theoretical issues of general non-viscously damped vibration systems. Exact frequency response functions (FRFs) have been developed based on Cauchy's residue theorem for the case of repeated eigenvalues with arbitrary multiplicities. The new theory developed has not only extended the classical mode superposition principle, but also laid the necessary theoretical foundation for the modal analysis of nonviscously damped systems whose eigenvalues are nondistinct. Effective numerical methods for the computations of elastic and nonviscous modes are suggested. The unique feature, contribution and significance of nonviscous modes to FRFs have been examined and discussed. Since nonviscous modes are real and are hence similar in characteristics to structural rigid-body modes with zero frequency, a new and accurate method has been developed to lump their contributions to FRFs into a single artificial rigid-body mode, thereby eliminating the necessity of computing them which is numerically challenging. Traditional restrictions of symmetry have not been imposed on system matrices and neither state-space nor additional coordinates have been employed throughout theoretical development. Numerical examples are given to illustrate the new theory and methods developed in the paper. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Nonviscous damping frequency response functions

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frequency response functions for nonlinear convergent systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2007年第6期52卷 1159-1165页

作者： Pavlov, Alexey van de Wouw, Nathan Nijmeijer, Henk Norwegian Univ Sci & Technol Dept Engn Cybernet NO-7491 Trondheim Norway Eindhoven Univ Technol Dept Mech Engn NL-5600 MB Eindhoven Netherlands

Convergent systems constitute a practically important class of nonlinear systems that extends the class of asymptotically stable linear time-invariant systems. In this note, we extend frequency response functions defined for linear systems to nonlinear convergent systems. Such nonlinear frequency response functions for convergent systems give rise to nonlinear Bode plots, which serve as a graphical tool for performance analysis of nonlinear convergent systems in the frequency domain. The results are illustrated with an example.

关键词： convergent systems differential inclusions frequency response functions nonlinear systems performance analysis

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Structural damage detection method using frequency response functions

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STRUCTURAL HEALTH MONITORING-AN INTERNATIONAL JOURNAL 2014年第4期13卷 418-429页

作者： Bandara, Rupika P. Chan, Tommy H. T. Thambiratnam, David P. Queensland Univ Technol Sch Civil Engn & Built Environm Brisbane Qld 4000 Australia

Structural damage detection using measured dynamic data for pattern recognition is a promising approach. These pattern recognition techniques utilize artificial neural networks and genetic algorithm to match pattern features. In this study, an artificial neural network-based damage detection method using frequency response functions is presented, which can effectively detect nonlinear damages for a given level of excitation. The main objective of this article is to present a feasible method for structural vibration-based health monitoring, which reduces the dimension of the initial frequency response function data and transforms it into new damage indices and employs artificial neural network method for detecting different levels of nonlinearity using recognized damage patterns from the proposed algorithm. Experimental data of the three-story bookshelf structure at Los Alamos National Laboratory are used to validate the proposed method. Results showed that the levels of nonlinear damages can be identified precisely by the developed artificial neural networks. Moreover, it is identified that artificial neural networks trained with summation frequency response functions give higher precise damage detection results compared to the accuracy of artificial neural networks trained with individual frequency response functions. The proposed method is therefore a promising tool for structural assessment in a real structure because it shows reliable results with experimental data for nonlinear damage detection which renders the frequency response function-based method convenient for structural health monitoring.

关键词： Structural damage detection pattern recognition artificial neural networks principal component analysis frequency response functions damage quantification

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High-frequency response functions for composite plate monitoring with ultrasonic validation

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AIAA JOURNAL 2005年第11期43卷 2431-2437页

作者： Park, G Rutherford, AC Wait, JR Nadler, B Farrar, CR Claytor, TN Los Alamos Natl Lab Los Alamos NM 87545 USA

frequency response functions (FRF) measured by piezoelectric macrofiber composite (MFC) actuators/sensors are used to detect subsurface delamination in a composite plate. The plate is impacted to seed damage in the form of ply delamination. Then, the MFC-based active-sensing system exerts an excitation into the plate and measures the subsequent responses. Traditional piezoceramic materials are also mounted in comparable locations on the plate to compare their performances. FRF and damage indicator features are derived from the measured signals and used to assess the condition of the plate. Validation of the delamination is completed using an ultrasonic C-scan method. The effective area of observed damage is well correlated to the damage indicator feature.

关键词： frequency response functions Piezoelectric Sensors Piezo Actuators Statistical Distributions SHM Composite Structures Ultrasonic Testing Lamb Waves Projectiles Piezoelectric Materials

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Linear viscoelastic behavior of asphalt mixes from dynamic frequency response functions

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INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS 2020年第7期44卷 1019-1031页

作者： Carret, Jean-Claude Di Benedetto, Herve Sauzeat, Cedric Univ Lyon LTDS UMR CNRS 5513 ENTPE Rue M Audin F-69518 Vaulx En Velin France

In the small strain domain, asphalt mixes (AM) have a linear viscoelastic (LVE) behavior that is strongly dependent on frequency and temperature. The maximum ratio of modulus values can be up to 1000, and traditional elastic analyses are not pertinent. The possibility to characterize AM from frequency response functions (FRFs) was studied. A new optimization process using the finite element method (FEM) has been developed to back-calculate the LVE properties of AM from FRFs. The numerical optimization process was applied to a reference material with averaged LVE properties determined from tension-compression tests performed on a wide variety of AM types. The LVE properties were modeled considering the 3-Dim version of the model 2S2P1D (2 Springs, 2 Parabolic elements, and 1 Dashpot). Reference FRFs for the considered reference material were obtained from FEM simulations. Three different configurations that may be of interest for practical tests were studied at five different temperatures. The proposed numerical optimization method consists in performing separate optimizations at each temperature to obtain the LVE properties for the considered temperature. Then values obtained at each temperature are considered to optimize 2S2P1D and Williams Landel Ferry (WLF) Equation constants to simulate the global LVE behavior of the material. The accuracy of the process was assessed regarding both the calculated FRFs and the complex modulus evaluation. Results indicate that the proposed optimization process converges almost perfectly towards the reference FRFs. The simulated complex modulus values are also in very good agreement with the values of the reference material.

关键词： asphalt mixes complex modulus finite element method frequency response functions linear viscoelasticity optimization process

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A modified surface spline for expansion and smoothing of frequency response functions

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART G-JOURNAL OF AEROSPACE ENGINEERING 1996年第G1期210卷 77-92页

作者： Waters, TP Lieven, NAJ Department of Aerospace Engineering University of Bristol

Measured frequency response functions (FRFs) are becoming more widely used to correlate finite element (FE) models with test structures. However, most model updating techniques require measured data at every degree of freedom (DOF) in the FE model, a necessity that is rarely met by experiment. Furthermore, the sensitivity of updating techniques to noise measurement demands experimental data of the highest attainable quality, and often beyond. A modified surface spline is presented which can expand measured FRFs to unmeasured DOFs and also apply smoothing to reduce noise contamination.

关键词： frequency response functions finite element models modified surface spline noise contamination

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Measurement of frequency response functions using periodic excitations, corrupted by correlated input/output errors

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2001年第6期50卷 1753-1760页

作者： Pintelon, R Schoukens, J Free Univ Brussels Dept ELEC Brussels Belgium

The frequency response function (FRF) of a system is often measured by taking the ratio of the output to the input Fourier coefficients of the steady-state response of the system to a periodic excitation. Generator noise, common noise disturbances picked up by the acquisition channels of the measurement device, and an external feedback loop, cause a correlation between the input/output errors of such an FRF measurement. This paper quantifies the bias error and the variance of the FRF measurement due to correlated input/output errors.

关键词： frequency response functions linear systems system identification

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Crack identification in curvilinear beams by using ANN and ANFIS based on natural frequencies and frequency response functions

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NEURAL COMPUTING & APPLICATIONS 2012年第7期21卷 1629-1645页

作者： Saeed, R. A. Galybin, A. N. Popov, V. Wessex Inst Technol Southampton SO40 7AA Hants England

This paper presents different artificial intelligence (AI) techniques for crack identification in curvilinear beams based on changes in vibration characteristics. Vibration analysis has been performed by applying the finite element method (FEM) to compute natural frequencies and frequency response functions (FRFs) for intact and damaged beams. The analysis reveals the changes in natural frequencies and amplitudes of FRFs of the beams for cracks of different sizes at different locations. These changes are used as input data for single and multiple artificial neural networks (ANN) and multiple adaptive neuro-fuzzy inference systems (ANFIS) in order to predict the size of the crack and its location. To avoid large models, the principal component analysis (PCA) approach has been carried out to reduce the computed FRFs data. The analysis of different techniques shows that the average prediction errors in the multiple ANN models is less than those in the single ANN model and in the multiple ANFIS. It is shown that the cracks longer than 5 mm can be located with satisfactory accuracy, even if the input data are corrupted with various level of noise. Multiple ANFIS is adopted to construct a more reliable and less sensitive model for noise excitation.

关键词： Curvilinear beam Crack identification Natural frequency frequency response functions Artificial neural network Adaptive neuro-fuzzy inference systems

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Identification of an open crack in a beam using an a posteriori error estimator of the frequency response functions with noisy measurements

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EUROPEAN JOURNAL OF MECHANICS A-SOLIDS 2009年第1期28卷 75-85页

作者： Faverjon, B. Sinou, J-J. Ecole Cent Lyon Equipe Dynam Struct & Syst CNRS Lab Tribol & Dynam SystUMR 5513 F-69134 Ecully France Univ Paris 06 CNRS ENS Cachan LMT CachanUMR 8535 F-94235 Cachan France

This paper presents a robust damage assessment technique for the nondestructive detection and size estimation of open cracks in beams. The damage detection, based on the constitutive relation error updating method, is used for the identification of the crack's location and size in a simply-supported beam. The transverse open crack is modeled through the introduction of the flexibility due to the presence of the crack, i.e. by reducing the second moment of area of the element at the crack's location. This identification algorithm is illustrated through numerical examples involving different positions and sizes of a transverse open crack. We show that the detection of damage and the identification of the crack's size and position can be achieved with satisfactory precision, even if 20% noise has been added to the simulations and less than 5% of all displacements have been measured. (C) 2008 Elsevier Masson SAS. All rights reserved.

关键词： Crack Damage detection and identification frequency response functions Noisy measurements

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Semi-analytic solution of three-dimensional temperature distribution in multilayered materials based on explicit frequency response functions

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2018年 118卷 208-222页

作者： Zhang, Haibo Wang, Wenzhong Zhang, Shengguang Zhao, Ziqiang Beijing Inst Technol Sch Mech Engn Beijing 100081 Peoples R China

Multilayer coatings have been widely using in a wide range of applications, including industrial, biological and electrical areas, and the thermal distribution in a multilayered material is of great interest. In present paper, the frequency response functions (FRFs) of temperature field under unit point heat flux are derived through thermal conduction equation. The unknown coefficients in the FRFs are assembled in a linear system of matrix equations according to the heat input and continuity condition of heat flux and temperature at each interface;then the coefficients are solved and expressed recursively. Based on the closed-form solution of FRFs, a fast semi-analytical method (SAM) is developed to solve the three-dimensional steady state heat conduction in arbitrary multilayered materials, and there are no limits on the number or the thickness of layers. The temperature fields under different kinds of heat flux in multilayered coatings are studied. Moving heat flux and convection on the surface are also considered. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Multilayered materials Heat conduction frequency response functions Moving heat flux

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