Nonlinear Reduced Order Models for the Structural Dynamics of Combustor Systems With Prestress and Friction

2014 ◽  
Vol 10 (1) ◽  
Author(s):  
Chulwoo Jung ◽  
Bogdan I. Epureanu ◽  
Sanghum Baik ◽  
Marcus B. Huffman
Keyword(s):  
Coulomb Friction ◽  
Convex Surface ◽  
Contact Stiffness ◽  
Reduced Order Models ◽  
Order Model ◽  
Transient Dynamic Analysis ◽  
Reduced Order ◽  
Require Time ◽  
Flow Induced Vibrations ◽  
Transition Piece

An efficient methodology to capture the nonlinear responses of combustor systems with prestress and Coulomb friction is developed. The combustor systems experience wear at the interfaces between components due to flow-induced vibrations. In particular, wear has been observed at the interface between the transition piece and the hula seal, and at the interface between the hula seal and the liner. These interfaces are prestressed, and their vibratory response has a softening nonlinearity caused by Coulomb friction combined with microslip. In addition, the contact between the hula seal and the transition piece is that between a convex surface and a concave surface. Hence, geometric nonlinearity of the contact stiffness in the normal direction is present also. These phenomena are hard to capture by full-order finite element (FE) approaches because they require time marching or harmonic balancing of very large models. To address this issue, we develop reduced order models (ROMs) which are specifically designed to capture Coulomb friction (combined with micro- and macroslip). To demonstrate the proposed approach, a simplified hula seal is placed between two very rigid plates (which relate to the transition piece and the liner). For validation, contact elements are used to model the interface between the plates and the hula seal. Transient dynamic analysis (TDA) in ansys is applied to the full-order model. The model is shown to exhibit softening nonlinearity and microslip at all levels of prestress. To show that ROMs for this system are possible (i.e., they exist), we use proper orthogonal decomposition (POD) to show that the dynamics is dominated by a low number of spatial coherences. For a variety of frequency ranges and prestress levels, we show that a single such coherence is dominant. Next, low order models are proposed and their parameters are identified. A systematic method to identify these parameters is developed. Particular attention is paid to the amount of calculations needed for obtaining these parameters. Finally, the ROMs are validated by comparing their predictions with results from TDA for the full-order model. We show that these ROMs can accurately predict the nonlinear response of the system.

Nonlinear Reduced-Order Models for the Structural Dynamics of Combustor Systems With Pre-Stress and Friction

2013 ◽  
Author(s):  
Chulwoo Jung ◽  
Bogdan I. Epureanu ◽  
Sanghum Baik ◽  
Marcus B. Huffman
Keyword(s):  
Coulomb Friction ◽  
Convex Surface ◽  
Contact Stiffness ◽  
Reduced Order Models ◽  
Order Model ◽  
Transient Dynamic Analysis ◽  
Reduced Order ◽  
Require Time ◽  
Flow Induced Vibrations ◽  
Transition Piece

An efficient methodology to capture the nonlinear responses of combustor systems with pre-stress and Coulomb friction is developed. The combustor systems experience wear at the interfaces between components due to flow-induced vibrations. In particular, wear has been observed at the interface between the transition piece and the hula seal, and at the interface between the hula seal and the liner. These interfaces are pre-stressed, and their vibratory response has a softening nonlinearity caused by Coulomb friction combined with micro-slip. In addition, the contact between the hula seal and the transition piece is that between a convex surface and a concave surface. Hence, geometric nonlinearity of the contact stiffness in the normal direction is present also. These phenomena are hard to capture by full order finite element approaches because they require time marching or harmonic balancing of very large models. To address this issue, we develop reduced order models (ROMs) which are specifically designed to capture Coulomb friction (combined with micro-slip and macro-slip). To demonstrate the proposed approach, a simplified hula seal is placed between two very rigid plates (which relate to the transition piece and the liner). For validation, contact elements are used to model the interface between the plates and the hula seal. Transient dynamic analysis (TDA) in ANSYS is applied to the full order model. The model is shown to exhibit softening nonlinearity and micro-slip at all levels of pre-stress. To show that ROMs for this system are possible (i.e., they exist), we use proper orthogonal decomposition to show that the dynamics is dominated by a low number of spatial coherences. For a variety of frequency ranges and pre-stress levels, we show that a single such coherence is dominant. Next, low order models are proposed and their parameters are identified. A systematic method to identify these parameters is developed. Particular attention is paid to the amount of calculations needed for obtaining these parameters. Finally, the ROMs are validated by comparing their predictions with results from TDA for the full-order model. We show that these ROMs can accurately predict the nonlinear response of the system.

scholarly journals Fully Parameterized Reduced Order Models Using Hyper-Dual Numbers and Component Mode Synthesis

2015 ◽  
Author(s):  
Matthew S. Bonney ◽  
Daniel C. Kammer ◽  
Matthew R. W. Brake
Keyword(s):  
Truncation Error ◽  
Sampling Methods ◽  
Latin Hypercube Sampling ◽  
Component Mode Synthesis ◽  
Reduced Order Models ◽  
Dual Numbers ◽  
Order Model ◽  
Full System ◽  
Reduced Order ◽  
Computational Burden

The uncertainty of a system is usually quantified with the use of sampling methods such as Monte-Carlo or Latin hypercube sampling. These sampling methods require many computations of the model and may include re-meshing. The re-solving and re-meshing of the model is a very large computational burden. One way to greatly reduce this computational burden is to use a parameterized reduced order model. This is a model that contains the sensitivities of the desired results with respect to changing parameters such as Young’s modulus. The typical method of computing these sensitivities is the use of finite difference technique that gives an approximation that is subject to truncation error and subtractive cancellation due to the precision of the computer. One way of eliminating this error is to use hyperdual numbers, which are able to generate exact sensitivities that are not subject to the precision of the computer. This paper uses the concept of hyper-dual numbers to parameterize a system that is composed of two substructures in the form of Craig-Bampton substructure representations, and combine them using component mode synthesis. The synthesis transformations using other techniques require the use of a nominal transformation while this approach allows for exact transformations when a perturbation is applied. This paper presents this technique for a planar motion frame and compares the use and accuracy of the approach against the true full system. This work lays the groundwork for performing component mode synthesis using hyper-dual numbers.

Dynamic Analysis of a Protein-Ligand Molecular Chain Attached to an Atomic Force Microscope

2004 ◽  
Vol 126 (4) ◽  
pp. 496-513 ◽  
Author(s):  
Deman Tang ◽  
Earl H. Dowell
Keyword(s):  
Nonlinear Systems ◽  
Atomic Force Microscope ◽  
Reduced Order Model ◽  
Molecular Chain ◽  
Static Equilibrium ◽  
Reduced Order Models ◽  
Base Excitation ◽  
Order Model ◽  
Reduced Order ◽  
Atomic Force

Dynamic numerical simulation of a protein-ligand molecular chain connected to a moving atomic force microscope (AFM) has been studied. A sinusoidal base excitation of the cantilevered beam of the AFM is considered in some detail. A comparison between results for a single molecule and those for multiple molecules has been made. For a small number of molecules, multiple stable static equilibrium positions are observed and chaotic behavior may be generated via a period-doubling cascade for harmonic base excitation of the AFM. For many molecules in the chain, only a single static equilibrium position exists. To enable these calculations, reduced-order (dynamic) models are constructed for fully linear, combined linear/nonlinear and fully nonlinear systems. Several distinct reduced-order models have been developed that offer the option of increased computational efficiency at the price of greater effort to construct the particular reduced-order model. The agreement between the original and reduced-order models (ROM) is very good even when only one mode is included in the ROM for either the fully linear or combined linear/nonlinear systems provided the excitation frequency is lower than the fundamental natural frequency of the linear system. The computational advantage of the reduced-order model is clear from the results presented.

scholarly journals A Reduced Order Model of Mistuning Using a Subset of Nominal System Modes

1999 ◽  
Author(s):  
M.-T. Yang ◽  
J. H. Griffin
Keyword(s):  
Degrees Of Freedom ◽  
Reduced Order Model ◽  
Reduced Order Models ◽  
Order Model ◽  
Disk System ◽  
Element Analysis ◽  
Reduced Order ◽  
Nominal System ◽  
Harmonic Response ◽  
Bladed Disk

Reduced order models have been reported in the literature that can be used to predict the harmonic response of mistuned bladed disks. It has been shown that in many cases they exhibit structural fidelity comparable to a finite element analysis of the full bladed disk system while offering a significant improvement in computational efficiency. In these models the blades and disk are treated as distinct substructures. This paper presents a new, simpler approach for developing reduced order models in which the modes of the mistuned system are represented in terms of a sub-set of nominal system modes. It has the following attributes: the input requirements are relatively easy to generate; it accurately predicts mistuning effects in regions where frequency veering occurs; as the number of degrees of freedom increases it converges to the exact solution; it accurately predicts stresses as well as displacements; and it accurately models the deformation and stresses at the blades’ bases.

scholarly journals Construction of reduced-order models for fluid flows using deep feedforward neural networks

2019 ◽  
Vol 872 ◽  
pp. 963-994 ◽  
Author(s):  
Hugo F. S. Lui ◽  
William R. Wolf
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Fluid Flows ◽  
Leading Edge ◽  
Feedforward Neural Networks ◽  
Orthogonal Decomposition ◽  
Reduced Order Models ◽  
Order Model ◽  
Sparse Regression ◽  
Reduced Order ◽  
Proper Orthogonal

We present a numerical methodology for construction of reduced-order models (ROMs) of fluid flows through the combination of flow modal decomposition and regression analysis. Spectral proper orthogonal decomposition is applied to reduce the dimensionality of the model and, at the same time, filter the proper orthogonal decomposition temporal modes. The regression step is performed by a deep feedforward neural network (DNN), and the current framework is implemented in a context similar to the sparse identification of nonlinear dynamics algorithm. A discussion on the optimization of the DNN hyperparameters is provided for obtaining the best ROMs and an assessment of these models is presented for a canonical nonlinear oscillator and the compressible flow past a cylinder. Then the method is tested on the reconstruction of a turbulent flow computed by a large eddy simulation of a plunging airfoil under dynamic stall. The reduced-order model is able to capture the dynamics of the leading edge stall vortex and the subsequent trailing edge vortex. For the cases analysed, the numerical framework allows the prediction of the flow field beyond the training window using larger time increments than those employed by the full-order model. We also demonstrate the robustness of the current ROMs constructed via DNNs through a comparison with sparse regression. The DNN approach is able to learn transient features of the flow and presents more accurate and stable long-term predictions compared to sparse regression.

Forced Response Analysis of a Mistuned Compressor Blisk Comparing Three Different Reduced Order Model Approaches

2016 ◽  
Author(s):  
Mauricio Gutierrez Salas ◽  
Ronnie Bladh ◽  
Hans Mårtensson ◽  
Paul Petrie-Repar ◽  
Torsten Fransson ◽  
...  
Keyword(s):  
Structural Modeling ◽  
Forced Response ◽  
Response Analysis ◽  
Reduced Order Models ◽  
Energy Localization ◽  
Order Model ◽  
Foreign Object Damage ◽  
Reduced Order ◽  
Manufacturing Tolerances ◽  
Blade Failure

Accurate structural modeling of blisk mistuning is critical for the analysis of forced response in turbomachinery. Apart from intentional mistuning, mistuning can be due to the manufacturing tolerances, corrosion, foreign object damage and in-service wear in general. It has been shown in past studies that mistuning can increase the risk of blade failure due to energy localization. For weak blade to blade coupling, this localization has been shown to be critical and higher amplitudes of vibration are expected in few blades. This paper presents a comparison of three reduced order models for the structural modeling of blisks. Two of the models assume cyclic symmetry while the third model is free of this assumption. The performance of the reduced order models for cases with small and large amount of mistuning will be examined. The benefits and drawbacks of each reduction method will be discussed.

Accuracies of Reduced Order Models of a Bladed Rotor With Geometric Mistuning

2013 ◽  
Vol 136 (7) ◽  
Author(s):  
Yasharth Bhartiya ◽  
Alok Sinha
Keyword(s):  
Natural Frequencies ◽  
Domain Analysis ◽  
Forced Response ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
Model Based ◽  
Bladed Rotor

The results from a reduced order model based on frequency mistuning are compared with those from recently developed modified modal domain analysis (MMDA). For the academic bladed rotor considered in this paper, the frequency mistuning analysis is unable to capture the effects of geometric mistuning, whereas MMDA provides accurate estimates of natural frequencies, mode shapes, and forced response.

Generation of Equivalent Circuit Models From Simulation Data of a Thermal System

2002 ◽  
Author(s):  
M. Bikdash ◽  
Y. P. Pang ◽  
E. P. Scott
Keyword(s):  
Complete Solution ◽  
Electrical Circuit ◽  
Reduced Order Model ◽  
Thermal System ◽  
Reduced Order Models ◽  
Order Model ◽  
Simulation Data ◽  
Cooling Fluid ◽  
Reduced Order ◽  
High Level

To enable the design and analysis of Integrated Power Electronics Models (IPEMs), a high level of software integration is needed. The solvers needed range form electrical circuit simulators, like Saber, to thermal analysis and CFD solvers like I-DEAS. As an electrical design parameter is changed, its effect will, in principle, be felt all the way to the temperature distribution in the cooling fluid, and hence a complete solution of the temperature field may have to be recomputed. This is of course computationally prohibitive. Hence a reduced-order model of the thermal behavior of the heat sink is of great interest. In this paper, we will present an algorithm that can automatically generate these reduced-order models from finite-element simulations.

Order Reduction of Parametrically Excited Nonlinear Systems Subjected to External Periodic Excitations

2009 ◽  
Author(s):  
Sangram Redkar ◽  
S. C. Sinha
Keyword(s):  
Nonlinear Systems ◽  
Fundamental Solution ◽  
Invariant Manifold ◽  
Large Scale ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
And Control

In this work, some techniques for order reduction of nonlinear systems with periodic coefficients subjected to external periodic excitations are presented. The periodicity of the linear terms is assumed to be non-commensurate with the periodicity of forcing vector. The dynamical equations of motion are transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of the resulting equations become time-invariant while the forcing and/or nonlinearity takes the form of quasiperiodic functions. The techniques proposed here; construct a reduced order equivalent system by expressing the non-dominant states as time-varying functions of the dominant (master) states. This reduced order model preserves stability properties and is easier to analyze, simulate and control since it consists of relatively small number of states in comparison with the large scale system. Specifically, two methods are outlined to obtain the reduced order model. First approach is a straightforward application of linear method similar to the ‘Guyan reduction’, the second novel technique proposed here, utilizes the concept of ‘invariant manifolds’ for the forced problem to construct the fundamental solution. Order reduction approach based on invariant manifold technique yields unique ‘reducibility conditions’. If these ‘reducibility conditions’ are satisfied only then an accurate order reduction via ‘invariant manifold’ is possible. This approach not only yields accurate reduced order models using the fundamental solution but also explains the consequences of various ‘primary’ and ‘secondary resonances’ present in the system. One can also recover ‘resonance conditions’ associated with the fundamental solution which could be obtained via perturbation techniques by assuming weak parametric excitation. This technique is capable of handing systems with strong parametric excitations subjected to periodic and quasi-periodic forcing. These methodologies are applied to a typical problem and results for large-scale and reduced order models are compared. It is anticipated that these techniques will provide a useful tool in the analysis and control system design of large-scale parametrically excited nonlinear systems subjected to external periodic excitations.

Nonlinear Parametric Reduced-Order Model for the Structural Dynamics of Hybrid Electric Vehicle Batteries

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Jauching Lu ◽  
Kiran D'Souza ◽  
Matthew P. Castanier ◽  
Bogdan I. Epureanu
Keyword(s):  
Hybrid Electric Vehicle ◽  
Vibration Response ◽  
Point Of View ◽  
Reduced Order Models ◽  
Structural Variations ◽  
Order Model ◽  
Reduced Order ◽  
Modal Density ◽  
Battery Packs ◽  
High Modal Density

Battery packs used in electrified vehicles exhibit high modal density due to their repeated cell substructures. If the excitation contains frequencies in the region of high modal density, small commonly occurring structural variations can lead to drastic changes in the vibration response. The battery pack fatigue life depends strongly on their vibration response; thus, a statistical analysis of the vibration response with structural variations is important from a design point of view. In this work, parametric reduced-order models (PROMs) are created to efficiently and accurately predict the vibration response in Monte Carlo calculations, which account for stochastic structural variations. Additionally, an efficient iterative approach to handle material nonlinearities used in battery packs is proposed to augment the PROMs. The nonlinear structural behavior is explored, and numerical results are provided to validate the proposed models against full-order finite element approaches.

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