HYBRID FREQUENCY-TIME DOMAIN METHODS FOR THE ANALYSIS OF COMPLEX STRUCTURAL SYSTEMS WITH DRY FRICTION DAMPING (original) (raw)
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A dynamic Lagrangian frequency–time method for the vibration of dry-friction-damped systems
Journal of Sound and Vibration, 2003
A new freq uen cy-time domain procedure, the dynamic Lagrangian mixed freq uency-time method (DLFT), is proposed to calculate the non-linear steady state response to periodic excitation of structural systems subject to dry friction damping. In this formulation, the dynamic Lagrangians are defined as the non-linear contact forces obtained from the eq uations of motion in the freq uency domain, with the adjunction of a penalization on the difference between the interface displacements calculate by the nonlinear solver in the frequency domain and those calculated in the time domain from the non-linear contact forces, thus accounting for Coulomb friction and non-penetration conditions. The dynamic Lagrangians allow one to solve for the non-linear forces between two points in contact without using artifacts such as springs. The new DLFT method is thus particularly well suited to handling finite element models of structures in frictional contact, as it does not req uire a special model for the contact interface. Dynamic Lagrangians are also better suited to frequency-domain friction problems than the traditional time-domain method of augmented Lagrangians. Furthermore, a reduction of the non-linear system to relative interface displacements is introduced to decrease the computation time. The DLFT method is validated for a beam in contact with a flexible dry friction element connected to ground, for frictional constraints that feature two-dimensional relative motion. Results are also obtained for a large-scale structural system with a large number of one-dimensional dry-friction dampers. The DLFT method is shown to be accurate and fast, and it does not suffer from convergence problems, at least in the examples studied.
TIME-SEGMENTED FREQUENCY-DOMAIN ANALYSIS FOR NON-LINEAR MULTI-DEGREE-OF-FREEDOM STRUCTURAL SYSTEMS
Journal of Sound and Vibration, 2000
This paper presents a new frequency-domain method to analyze physically non-linear structural systems having non-proportional damping. Single-and multi-degree-of-freedom (d.o.f.) systems subjected to time-dependent excitations are considered. A procedure to consider initial conditions, required by the methodology described, is discussed. The algorithm described here employs a time-segmented procedure in modal co-ordinates in the frequency domain; solution in each time-segment being obtained by an iterative process. The proposed methodology is validated by three examples. The procedure presented here can be employed as well to analyze structural systems with viscous and hysteretic damping or else with frequency-dependent damping properties.
Nonlinear Modal Analysis of Mistuned Periodic Structures Subjected to Dry Friction
Volume 7B: Structures and Dynamics, 2015
This paper deals with the dynamics of a cyclic system, representative of a bladed-disk subjected to dry friction forces, and exhibiting structural mistuning. The nonlinear complex modes are computed by solving the eigenproblem associated to the free response of the whole structure, and are then used to better understand the forced response to a traveling wave excitation. Similarly to the underlying linear system, the tuned model possesses pairs of modes that can be linearly combined to form traveling waves, unlike those of the mistuned structure. However, due to the nonlinearity, the modal properties are not constant but vary with the vibration amplitude in both cases. A qualitative analysis is also performed to assess the impact of the mistuning magnitude on the response, and suggests that further statistical investigations could be of great interest for the design of bladed disks, in terms of vibration mitigation and robustness.
Nonlinear vibration analysis of bladed disks with dry friction dampers
Journal of Sound and Vibration, 2006
In this work, a new model is proposed for the vibration analysis of turbine blades with dry friction dampers. The aim of the study is to develop a multiblade model that is accurate and yet easy to be analyzed so that it can be used efficiently in the design of friction dampers. The suggested nonlinear model for a bladed disk assembly includes all the blades with blade to blade and/or blade to cover plate dry friction dampers. An important feature of the model is that both macro-slip and micro-slip models are used in representing dry friction dampers. The model is simple to be analyzed as it is the case in macro-slip model, and yet it includes the features of more realistic micro-slip model. The nonlinear multidegree-of-freedom (mdof) model of bladed disk system is analyzed in frequency domain by applying a quasi-linearization technique, which transforms the nonlinear differential equations into a set of nonlinear algebraic equations. The solution method employed reduces the computational effort drastically compared to time solution methods for nonlinear systems, which makes it possible to obtain a more realistic model by the inclusion of all blades around the disk, disk itself and all friction dampers since in general system parameters are not identical throughout the geometry. The validation of the method is demonstrated by comparing the results obtained in this study with those given in literature and also with results obtained by time domain analysis. In the case studies presented the effect of friction damper parameters on vibration characteristics of tuned and mistuned bladed disk systems is studied by using a 20 blade system. It is shown that the method presented can be used to find the optimum friction damper values in a bladed disk assembly.
Dynamic Analysis of Nonproportional Damping Structural Systems Time and Frequency-Domain Methods
2001
Structural systems composed of structural elements with different characteristics as NPP and soil and fluid-structure interaction systems present considerable nonproportional damping. The assumption of uncoupled modal equations with assumed modal damping ratios can lead to substantial errors in the dynamic analysis results of those systems. Therefore that assumption is not anymore accepted by the nuclear industry. Appropriate and more rigorous methods for the dynamic analysis of structural systems with nonproportional damping should be developed. In this paper pseudo-force mode superposition methods are developed which consider the nonproportional damping effect through a pseudo-force term in the RHS of the modal equations. These equations are then iteratively solved. The methods presented are considered in time and frequency-domain. The frequency-domain version is very suitable for the analysis of systems with hysteretic damping and frequency-dependent properties. Examples of time ...
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
Journal of Sound and Vibration, 2009
A method for modal analysis of non-linear and non-conservative mechanical systems is proposed. In particular, dry-friction non-linearities are considered although the method is not restricted to these. Based on the concept of complex non-linear modes, eigensolutions are written as generalized Fourier series and the eigenproblem is then formulated in the frequency-domain. An alternating frequency-time domain method is used for the calculation of implicit non-linear forces. A two degrees-of-freedom example featuring dry-friction illustrates the method and highlights the effects of dissipation on modal parameters. The stabilizing effects of friction in presence of negative damping in the system are also addressed.
2019
High cyclic fatigue (HCF) is by far the main source of failure of bladed disks in turbomachinery applications. In order to reduce the vibration amplitudes, dry friction damping has been widely used in the design of bladed disks in different forms such as; blade root joints, shrouds, solid dampers and etc. This will make the dynamic analysis of bladed disks more challenging due to presence of nonlinear interactions between contacting surfaces. The purpose of the current study is to develop an efficient and highly compact reduced order model (ROM) for nonlinear dynamics of bladed disks subjected to different sources of friction damping. The developed ROM consists of two steps: first, representing the kinematics of the contact nodes lying on adjacent friction interfaces in terms of relative displacements between the node pairs. Afterwards, performing the Craig-Bampton Component Mode Synthesis (CBCMS) on the full-order model already transformed into relative coordinates. Implementation ...
Non-linear modal analysis for bladed disks with friction contact interfaces
A method for non-linear modal analysis of mechanical systems with contact and friction interfaces is proposed. It is based on a frequency domain formulation of the dynamical system's equations of motion. The dissipative aspects of these non-linearities result in complex eigensolutions and the modal parameters (natural frequency and modal damping) can be obtained without any assumptions on the external excitation. The generality of this approach makes it possible to address any kind of periodic regimes, in free and forced response. In particular, stability analysis in flutter applications can be performed. Applications for the design of friction ring dampers for blisks and for the dynamical simulation of bladed disk with dovetail attachment are proposed. Finally, we propose a study of dynamical behaviour coupling with the calculation of fretting-wear at the interfaces based on non-linear modal characterization.
MULTI-MODE ANALYSIS OF BEAM-LIKE STRUCTURES SUBJECTED TO DISPLACEMENT-DEPENDENT DRY FRICTION DAMPING
Journal of Sound and Vibration, 1997
A multi-mode analysis of a beam-like structure undergoing transverse vibration and subjected to a displacement-dependent friction force is conducted. The system model uses a ramp configuration to increase the normal force of the dry friction damper proportional to the beam's transverse displacement. The system is studied by using harmonic balance as an approximate analytical solution and then by using a time integration method. Interesting findings include the appearance of internal resonance peaks when multiple beam modes are considered. Also, as with the earlier single-degree-of-freedom study, two dynamic response solutions exist at certain parameter values. It is found that the ability to control the amplitude of the response is a function of the frequency range considered. In general, near modal resonance peaks, the amplitude of the response decreases with increasing ramp angle. However, in an ''overlapping'' region between resonance peaks, the amplitude of the response actually increases with increasing ramp angle. It is also found that the damping contribution from the displacement-dependent dry friction damper is ''linear structural-like'' in nature and relatively insensitive to the amplitude of the response. This result suggests that in the case of turbine or compressor blades, this type of damping arrangement may be effective in the suppression of flutter.