A Minimal Order Model From Zero to High Frequencies for Finite-Element Based Analysis of General 3-D Electromagnetic Problems

2013 ◽  
Author(s):  
Feng Sheng ◽  
Dan Jiao
Keyword(s):  
Finite Element ◽  
Low Frequency ◽  
Electromagnetic Analysis ◽  
Reduced Order Models ◽  
Minimal Order ◽  
Order Model ◽  
Package Design ◽  
High Frequencies ◽  
Reduced Order ◽  
Right Hand

Modern integrated circuits (IC) and package design has scaled into the deep submicron regime and the nanometer regime. Fast and broadband frequency-domain electromagnetic analysis has become increasingly important. The large problem size encountered in the analysis of ICs and packages is a major challenge especially for a finite element method (FEM) based electromagnetic analysis. To reduce the computational cost for large-scale electromagnetic analysis, model order reduction (MOR) methods have been developed to preprocess the huge linear system into reduced order models. However, in order to meet the modeling and simulation challenges arising from the IC and package design, existing MOR methods still have to overcome the following shortcomings. First, many existing MOR methods lack a closed-form error bound. Given an accuracy requirement, the model generated from existing methods may not be compact enough. Second, most of the existing reduced order models depend on frequency and right hand side. They lose efficiency when analyzing frequency-dependent problems with a large number of right hand sides. Last but not least, many existing MOR methods suffer from low frequency breakdown problem. Additional models have to be built if low frequency solutions, including DC solution, are required. This paper proposes a minimal order model for any prescribed accuracy for the finite element based solution of general 3-D problems having arbitrary lossless/lossy structures and inhomogeneous materials. This model entails no theoretical approximations. It is frequency and right hand side independent, and hence can be employed for both fast frequency and right hand side sweep. Moreover, the model does not suffer from low-frequency breakdown and is accurate from zero to high frequencies. To facilitate the application of such a minimal order model, we have also developed an efficient algorithm to generate this model. Numerical experiments have demonstrated the accuracy and efficiency of the proposed method. In addition to frequency-domain analysis, the proposed model can also be used for fast time-domain analysis.

scholarly journals Non-Linear Modeling of Centrifugal Stiffening Effects for Accurate Bladed Component Reduced-Order Models

2017 ◽  
Author(s):  
Elias Khalifeh ◽  
Elsa Piollet ◽  
Antoine Millecamps ◽  
Alain Batailly
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Angular Speed ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
Linear Finite Element ◽  
Centrifugal Stiffening ◽  
Blade Tip

The modeling of centrifugal stiffening effects on bladed components is of primary importance in order to accurately capture their dynamics depending on the rotor angular speed. Centrifugal effects impact both the stiffness of the component and its geometry. In the context of the small perturbation framework, when considering a linear finite element model of the component, an assumption typically made in the scientific literature involves a fourth-order polynomial development of the stiffness matrix in terms of the angular speed. This polynomial development may fail to provide an accurate representation of the geometry evolution of a blade. Indeed, the error on the blade-tip displacement associated to the use of a linear finite element model quickly reaches the same order of magnitude as the blade-tip/casing clearance itself thus yielding a 100 % error on the blade-tip/casing clearance configuration. This article focuses on the presentation of a methodology that allows for creating accurate reduced order models of a 3D finite element model accounting for centrifugal stiffening with a very precise description of the blade-tip/casing clearance configuration throughout a given angular speed range. The quality of the obtained reduced order model is underlined before its numerical behaviour in the context of non-linear dynamic simulations be investigated. It is evidenced that the new reduced order model features specific interactions that could not be predicted with a linear model. In addition, results highlight the limitations of numerical predictions made for high angular speeds with a linear model. Finally, a particular attention is paid to the numerical sensitivity of the proposed model. As a downside of its increased accuracy, it is underlined that its computation must be done carefully in order to avoid numerical instabilities.

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.

Intentional Mistuning With Predominant Aerodynamic Effects

2018 ◽  
Author(s):  
Carlos Martel ◽  
José J. Sánchez
Keyword(s):  
Finite Element ◽  
Traveling Waves ◽  
Element Model ◽  
Simple Expression ◽  
Reduced Order Model ◽  
Action Mechanism ◽  
Aerodynamic Forces ◽  
Order Model ◽  
Reduced Order ◽  
Random Mistuning

Intentional mistuning is a well known procedure to decrease the uncontrolled vibration amplification effects of the inherent random mistuning and to reduce the sensitivity to it. The idea is to introduce an intentional mistuning pattern that is small but much larger that the existing random mistuning. The frequency of adjacent blades is moved apart by the intentional mistuning, reducing the effect of the blade-to-blade coupling and thus the effect of the random mistuning. The situation considered in this work is more complicated because the main source for the blade damping is the effect of the aerodynamic forces (as it happens in a blisk for a family of blade dominated modes with very similar frequencies). In this case the damping is clearly defined for the tuned traveling waves but not for each blade. The problem is analyzed using the Asymptotic Mistuning Model methodology. A reduced order model is derived that allows us to understand the action mechanism of the intentional mistuning, and gives a simple expression for the estimation of its beneficial effect. The results from the reduced model are compared with those from a finite element model of a more realistic rotor under different forcing conditions.

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.

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