Modal Identification of Non-Linear Structures and the Use of Modal Model in Structural Dynamic Analysis (original) (raw)
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Mechanical Systems and Signal Processing, 2011
Engineering structures seldom behave linearly and, as a result, linearity checks are common practice in the testing of critical structures exposed to dynamic loading to define the boundary of validity of the linear regime. However, in large scale industrial applications, there is no general methodology for dynamicists to extract nonlinear parameters from measured vibration data so that these can be then included in the associated numerical models. In this paper, a simple method based on the information contained in the frequency response function (FRF) properties of a structure is studied. This technique falls within the category of single-degree-of-freedom (SDOF) modal analysis methods. The principle upon which it is based is effectively a linearisation whereby it is assumed that at given amplitude of displacement response the system responds at the same frequency as the excitation and that stiffness and damping are constants. In so doing, by extracting this information at different amplitudes of vibration response, it is possible to estimate the amplitude-dependent 'natural' frequency and modal loss factor. Because of its mathematical simplicity and practical implementation during standard vibration testing, this method is particularly suitable for practical applications. In this paper, the method is illustrated and new analyses are carried out to validate its performance on numerical simulations before applying it to data measured on a complex aerospace test structure as well as a full-scale helicopter.
Nonlinear analysis of the forced response of structural elements
The Journal of the Acoustical Society of America, 1974
A general procedure is presented for the nonlinear analysis of the forced response of structural elements to harmonic excitations. Internal resonances (i.e., modal interactions) are taken into account. All excitations are considered, with special consideration given to resonant excitations. The general procedure is applied to clamped-hinged beams. The results reveal that exciting a higher mode may lead to a larger response in a lower interacting mode, contrary to the results of linear analyses. Subject Classification: 40.30, 40.22. Recently, Nayfeh t• and Atluri •a applied versions of the method of multiple scales, in place of harmonic balance, to the study of beam vibrations. Three versions 281
Forced harmonic response analysis of nonlinear structures using describing functions
AIAA Journal, 1993
The dynamic response of multiple-degree-of-freedom nonlinear structures is usually determined by numerical integration of the equations of motion, an approach which is computationally very expensive for steady-state response analysis of large structures. In this paper, an alternative semianalytical quasilinear method based on the describing function formulation is proposed for the harmonic response analysis of structures with symmetrical nonlinearities. The equations of motion are converted to a set of nonlinear algebraic equations and the solution is obtained iteratively. The linear and nonlinear parts of the structure are dealt with separately, the former being represented by the constant linear receptance matrix [a], and the latter by the generalized quasilinear matrix [A] which is updated at each iteration. A special technique that reduces the computation time significantly when the nonlinearities are localized is used with success to analyze large structures. The proposed method is fully compatible with standard modal analysis procedures. Several examples dealing with cubic stiffness, piecewise linear stiffness, and coulomb friction type of nonlinearities are presented in the case of a ten-degree-of-freedom structure.
As the main source of local nonlinearities, joints can lead to drastic changes in dynamic behavior of structures in a global scale. Finite element (FE) models often lack these nonlinearities and are incapable of representing nonlinear behavior. Therefore, the identification of nonlinear dynamic mechanical properties of the joint is necessary, in order to develop a faithful FE model of the structure. In the present work, dynamic parameters of a nonlinear joint are identified using an optimum equivalent linear frequency response function of the structure. A test rig, which includes a beam that can produce cubic stiffness spring characteristic as a nonlinear joint, is built, and nonlinear dynamic characteristics of the beam are identified. In addition to hardening behavior related to cubic stiffness, softening effects were also observed in some measured modes in which further investigation attributed that behavior to the presence of a bolt in the test rig.
Assessment of structural nonlinearities employing extremes of dynamic responses
Journal of Vibration and Control, 2016
A range of methodologies exist for estimating nonlinear responses of structural systems using numerical simulations. However, efforts in relation to experimental methods in this regard still warrant further investigation. This paper presents an approach for assessing structural nonlinearities using the extremes of dynamic responses of the structural system under consideration. The approach allows revisiting and parameter tuning of theoretical models of structures based on experimental studies. A single degree of freedom system was excited in this study using broadband input excitations and the output dynamic responses were measured using different devices. The type and extent of experimentation required for implementation of the presented technique was investigated along with the effects of the estimates of the measured variables and the effects related to different measurement devices.
Parametric identification of structural nonlinearities from measured frequency response data
Mechanical Systems and Signal Processing, 2011
Most engineering structures include nonlinearity to some degree. Depending on the dynamic conditions and level of external forcing, sometimes a linear structure assumption may be justified. However, design requirements of sophisticated structures such as satellites require even the smallest nonlinear behavior to be considered for better performance. Therefore, it is very important to successfully detect, localize and parametrically identify nonlinearity in such cases. In engineering applications, the location of nonlinearity and its type may not be always known in advance. Furthermore, in most of the cases, test data will be incomplete. These handicaps make most of the methods given in the literature difficult to apply to engineering structures. The aim of this study is to improve a previously developed method considering these practical limitations. The approach proposed can be used for detection, localization, characterization and parametric identification of nonlinear elements by using incomplete FRF data. In order to reduce the effort and avoid the limitations in using footprint graphs for identification of nonlinearity, describing function inversion is used. Thus, it is made possible to identify the restoring force of more than one type of nonlinearity which may co-exist at the same location. The verification of the method is demonstrated with case studies.
A method of non-linear modal identification from frequency response tests
Journal of Sound and Vibration, 1992
A theoretical and experimental study of non-linear systems governed by Duffing's equation is presented in this study. The non-linear mode concept is applied to analyze the steady state responses of non-linear systems driven by a harmonic force. In the experimental context, the present modal identification method permits one to obtain the non-linear modal parameters from frequency response tests. By comparison with other methods, the proposed methods appear very interesting in regard to computational time, formulation, and they necessitate fewer computer resources. An experimental work on the steady state response of a beam with local non-linear stiffness is reported to justify the methods. Many aspects of theoretical results, such as the dependence of resonance frequency on the amplitude of vibration and the downward and upward jump phenomena are observed experimentally. The experimental results are in good agreement with theoretical predictions based upon the non-linear modal superposition approach. Recently, the identification of non-linear systems has received considerable attention; parametric and non-parametric techniques have been studied intensively by many authors. 497
A new method for harmonic response of non-proportionally damped structures using undamped modal data
Journal of Sound and Vibration, 1987
A method of calculating the receptances of a non-proportionally damped structure from the undamped modal data and the damping matrix of the system is presented. The method developed is an exact method. It gives exact results when exact undamped receptances are employed in the computation. Inaccuracies are due to the truncations made in the calculation of undamped receptances. Numerical examples, demonstrating the accuracy and speed of the method when truncated receptance series are used are also presented. Advantages of the method over classical methods are discussed, and it is concluded that the method is most advantageous when used for a structure with frequency and/or temperature dependent damping properties, or when the non-proportional part of the damping is local. The technique suggested can easily be applied to structural modification problems if there is no additional degree-of-freedom due to the modifying structure.
Study of Non-Linear Behavior of Vibrating System
Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. In the case of the real structures a linear model will be insufficient to describe the dynamic behavior correctly. It thus appears natural to introduce non-linear models of structures which are able to predict the dynamic behavior of the real structures. This seminar includes study of non-linear vibrations, it different types and various applications. Here the vibratory behavior of an absorber of vibration related to a system subjected to a harmonic load, in the presence of uncertainties on the design parameters is optimised. The total system is modeled by two degrees of freedom (2 dof) with a shock absorber and a generalized non-linear stiffness. one proposes to optimize the vibratory behavior of an absorber of vibration related to a system subjected to a harmonic load, in the presence of uncertainties on the design parameters. The total system is modelled by two degrees of freedom (2 dof) with a shock absorber and a generalized non-linear stiffness. The resolution is carried out in the temporal field according to a traditional diagram. It is a question of seeking the optimal responses envelopes of the deterministic and stochastic case and this for the non-linear displacements, phases and forces.