Quasi-static modal analysis for reduced order modeling of geometrically nonlinear structures

2021 ◽  
pp. 116076
Author(s):  
Kyusic Park ◽  
M.S. Allen
Keyword(s):  
Modal Analysis ◽  
Reduced Order Modeling ◽  
Geometrically Nonlinear ◽  
Nonlinear Structures ◽  
Reduced Order

scholarly journals Reduced Order Modeling of Nonlinear Structures with Frictional Interfaces

2017 ◽  
pp. 427-450 ◽  
Author(s):  
Matthew R. W. Brake ◽  
Johann Groß ◽  
Robert M. Lacayo ◽  
Loic Salles ◽  
Christoph W. Schwingshackl ◽  
...  
Keyword(s):  
Reduced Order Modeling ◽  
Nonlinear Structures ◽  
Reduced Order

Reduced-Order Modeling of Two-Sided Frictional Interfaces

2007 ◽  
Author(s):  
Jason D. Miller ◽  
D. Dane Quinn
Keyword(s):  
Modal Analysis ◽  
Computational Efficiency ◽  
Order Approximation ◽  
Reduced Order Modeling ◽  
Original Model ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Overall Response

We consider a model describing the behavior of a two-sided interface allowing for both elasticity and microslip of the joint. A reduced-order approximation of this system is developed based on a decomposition of the original model into an elastic chain and a dissipative component equivalent to a series-series Iwan chain. The Iwan chain is then solved using a quasi-static complementarity formulation while the order of the elastic chain is reduced using modal analysis. The computational efficiency of the resulting reduced-order model is significantly increased, while the overall response of the interface to realistic forcing conditions is maintained.

Reduced Order Modeling Based on Complex Nonlinear Modal Analysis and its Application to Bladed Disks With Shroud Contact

2013 ◽  
Author(s):  
Malte Krack ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek ◽  
Christian Siewert ◽  
Andreas Hartung
Keyword(s):  
Modal Analysis ◽  
Limit Cycle ◽  
Large Scale ◽  
Computational Effort ◽  
Reduced Order Modeling ◽  
Forced Response ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Nonlinear Modal Analysis

The design of bladed disks with contact interfaces typically requires analyses of the resonant forced response and flutter-induced limit cycle oscillations. The steady-state vibration behavior can efficiently be calculated using the Multi-Harmonic Balance method. The dimension of the arising algebraic systems of equations is essentially proportional to the number of harmonics and the number of degrees of freedom (DOFs) retained in the model. Extensive parametric studies necessary e.g. for robust design optimization are often not possible in practice due to the resulting computational effort. In this paper, a two-step nonlinear reduced order modeling approach is proposed. First, the autonomous nonlinear system is analyzed using a Complex Nonlinear Modal Analysis technique based on the work of Laxalde and Thouverez [1]. The methodology in [1] was refined by an exact condensation approach as well as analytical calculation of gradients in order to efficiently study localized nonlinearities in large-scale systems. Moreover, a continuation method was employed in order to predict nonlinear modal interactions. Modal properties such as eigenfrequency and modal damping are directly calculated with respect to the kinetic energy in the system. In a second step, a reduced order model is built based on the Single Nonlinear Resonant Mode theory. It is shown that linear damping and harmonic forcing can be superimposed. Moreover, similarity properties can be exploited to vary normal preload or gap values in contact interfaces. Thus, a large parameter space can be covered without the need for re-computation of nonlinear modal properties. The computational effort for evaluating the reduced order model is almost negligible since it contains a single DOF only, independent of the original system. The methodology is applied to both a simplified and a large-scale model of a bladed disk with shroud contact interfaces. In contrast to [1], the contact constraints account for variable normal load and lift-off in addition to dry friction. Forced response functions, backbone curves for varying normal preload and excitation level as well as flutter-induced limit cycle oscillations are analysed and compared to conventional methods. The limits of the proposed methodology are indicated and discussed.

Reduced Order Modeling Techniques for Dynamic Analysis of Mistuned Multi-Stage Turbomachinery Rotors

2001 ◽  
Author(s):  
Ronnie Bladh ◽  
Matthew P. Castanier ◽  
Christophe Pierre
Keyword(s):  
Modal Analysis ◽  
Reduced Order Modeling ◽  
Stage Model ◽  
Reduced Order ◽  
Modal Data ◽  
Bladed Disk ◽  
Multi Stage ◽  
Modeling Techniques ◽  
Forced Responses ◽  
Stage Modeling

Recent findings indicate that structural interstage (stage-to-stage) coupling in multi-stage rotors can have a critical impact on bladed disk dynamics by altering significantly the flexibility of the disk. This affects local eigenfrequency veering characteristics, and thus a design’s sensitivity to mistuning. In response to these findings, two reduced order modeling techniques are presented that accurately capture structural interstage coupling effects, while keeping model sizes at practical levels. Both free and forced responses of an example two-stage rotor are examined using novel component-mode-based reduced order modeling techniques for mistuned multi-stage assemblies. Both techniques employ an intermediate multi-stage model constructed by component mode synthesis (CMS), which is further reduced by either: (a) partial secondary modal analyses on constraint-mode partitions; or (b) a full-scale secondary modal analysis on the entire multi-stage CMS model. The introduced techniques are evaluated using finite element results as a benchmark. The proposed reduced order modeling techniques are shown to facilitate accurate multi-stage modeling and analyses with or without blade mistuning, using only computationally inexpensive modal data from a cyclic disk sector and a single blade per stage. It is concluded that the most promising and practically feasible approach may be a combination of approaches (a) and (b), in which secondary modal analyses and truncations are first carried out on disk-blade constraint-mode partitions, followed by a tertiary modal analysis on the resulting multi-stage model. In conclusion, by alleviating the restriction to single-stage analyses, the presented multi-stage modeling techniques will enable engineers to analyze the dynamics of mistuned turbomachinery rotor assemblies with greater confidence.

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