Nonintrusive Structural Dynamic Reduced Order Modeling for Large Deformations: Enhancements for Complex Structures

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Ricardo Perez ◽  
X. Q. Wang ◽  
Marc P. Mignolet
Keyword(s):  
Degrees Of Freedom ◽  
Large Deformations ◽  
Nonlinear Behavior ◽  
Reduced Order Modeling ◽  
Model Parameters ◽  
Complex Structures ◽  
Plate Structures ◽  
Structural Dynamic ◽  
Reduced Order ◽  
Selection Of

This paper focuses on the development of nonlinear reduced order modeling techniques for the prediction of the response of complex structures exhibiting “large” deformations, i.e., a geometrically nonlinear behavior, which are nonintrusive, i.e., the structure is originally modeled within a commercial finite element code. The present investigation builds on a general methodology successfully validated in recent years on simpler beam and plate structures by: (i) developing a novel identification strategy of the reduced order model parameters that enables the consideration of the large number of modes (>50 say) that would be needed for complex structures, and (ii) extending a step-by-step strategy for the selection of the basis functions used to represent accurately the displacement field. The above novel developments are successfully validated on the nonlinear static response of a nine-bay panel structure modeled with 96,000 degrees of freedom within Nastran.

Reduced Order Model for the Geometric Nonlinear Response of Complex Structures

2012 ◽  
Author(s):  
Ricardo Perez ◽  
X. Q. Wang ◽  
Andrew Matney ◽  
Marc P. Mignolet
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Behavior ◽  
Reduced Order Model ◽  
Model Parameters ◽  
Complex Structures ◽  
Order Model ◽  
Plate Structures ◽  
Reduced Order ◽  
Nonlinear Static ◽  
Selection Of

This paper focuses on the development of nonlinear reduced order modeling techniques for the prediction of the response of complex structures exhibiting “large” deformations, i.e. a geometrically nonlinear behavior, and modeled within a commercial finite element code. The present investigation builds on a general methodology successfully validated in recent years on simpler beam and plate structures by: (i) developing a novel identification strategy of the reduced order model parameters that enables the consideration of the large number of modes (> 50 say) that would be needed for complex structures, and (ii) extending an automatic strategy for the selection of the basis functions used to represent accurately the displacement field. The above novel developments are successfully validated on the nonlinear static response of a 9-bay panel structure modeled with 96,000 degrees of freedom within Nastran.

Simulation of Singly and Doubly Clamped Nanotube Based NEMS Devices

2009 ◽  
Author(s):  
P. Chen ◽  
B. Peng ◽  
L. Ding ◽  
W. H. Xu ◽  
Y. Q. Wang ◽  
...  
Keyword(s):  
Nonlinear Deformation ◽  
Large Deformations ◽  
Nonlinear Behavior ◽  
Reduced Order Modeling ◽  
Multiphysics Simulation ◽  
Reduced Order ◽  
Theoretical Predictions ◽  
Simulation Results ◽  
Novel Devices ◽  
Insight Into

In this paper a multiphysics simulation of nanotube based nano-electromechanical systems is reported. Assuming continuum mechanics, the nonlinear deformation of the nanotube is simulated using reduced order modeling method. In particular, we study singly and doubly clamped nanotubes under electrostatic actuation. The simulation emphasizes the prediction of the pull-in voltage of the device, a key design parameter. Moreover, the nonlinear behavior associated with finite kinematics (i.e., large deformations), neglected in previous studies, are investigated in detail. The multiphysics simulation results agree well with the theoretical predictions verifying that the numerical model is valid. The results show that nonlinear kinematics results in an important increase in the pull-in voltage of doubly clamped nanotube devices, but that it is negligible in the case of singly clamped devices. These models provide a guide on the effect of the various geometrical variables and insight into the design of novel devices.

Selection of Degrees of Freedom for Dynamic Analysis

1987 ◽  
Vol 109 (1) ◽  
pp. 65-69 ◽  
Author(s):  
K. W. Matta
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
General Purpose ◽  
Component Mode Synthesis ◽  
Complex Structures ◽  
Large Complex ◽  
Static Condensation ◽  
Basis Vectors ◽  
Selection Of

A technique for the selection of dynamic degrees of freedom (DDOF) of large, complex structures for dynamic analysis is described and the formulation of Ritz basis vectors for static condensation and component mode synthesis is presented. Generally, the selection of DDOF is left to the judgment of engineers. For large, complex structures, however, a danger of poor or improper selection of DDOF exists. An improper selection may result in singularity of the eigenvalue problem, or in missing some of the lower frequencies. This technique can be used to select the DDOF to reduce the size of large eigenproblems and to select the DDOF to eliminate the singularities of the assembled eigenproblem of component mode synthesis. The execution of this technique is discussed in this paper. Examples are given for using this technique in conjunction with a general purpose finite element computer program GENSAM[1].

A Component-Based Parametric Reduced-Order Modeling Technique and Its Application to Probabilistic Vibration Analysis and Design Optimization

2006 ◽  
Author(s):  
Keychun Park ◽  
Geng Zhang ◽  
Matthew P. Castanier ◽  
Christophe Pierre
Keyword(s):  
Design Optimization ◽  
Probabilistic Analysis ◽  
Structural Design ◽  
Vibration Analysis ◽  
Reduced Order Modeling ◽  
Design Parameters ◽  
Model Parameters ◽  
Reduced Order ◽  
Analysis And Design ◽  
Structural Design Optimization

In this paper, a component-based parametric reduced-order modeling (PROM) technique for vibration analysis of complex structures is presented, and applications to both structural design optimization and uncertainty analysis are shown. In structural design optimization, design parameters are allowed to vary in the feasible design space. In probabilistic analysis, selected model parameters are assumed to have predefined probability distributions. For both cases, each realization corresponding to a specific set of parameter values could be evaluated accurately based on the exact modes for the system with those parametric values. However, as the number of realizations increases, this approach becomes prohibitively expensive, especially for largescale finite element models. Recently, a PROM method that employs a fixed projection basis was introduced to avoid the eigenanalysis for each variation while retaining good accuracy. The fixed basis is comprised of a combination of selected mode sets of the full model calculated at only a few sampling points in the parameter space. However, the preparation for the basis may still be cumbersome, and the simulation cost and the model size increase rapidly as the number of parameters increases. In this work, a component-based approach is taken to improve the efficiency and effectiveness of the PROM technique. In particular, a component mode synthesis method is employed so that the parameter changes are captured at the substructure level and the analysis procedure is accelerated. Numerical results are presented for two example problems, a design optimization of a pickup truck and a probabilistic analysis of a simple L-shaped plate. It is shown that the new component-based approach significantly improves the efficiency of the PROM technique.

scholarly journals A Reduced Order Modeling Technique for Mistuned Bladed Disks

1997 ◽  
Vol 119 (3) ◽  
pp. 439-447 ◽  
Author(s):  
M. P. Castanier ◽  
G. O´ttarsson ◽  
C. Pierre
Keyword(s):  
Monte Carlo ◽  
Degrees Of Freedom ◽  
Order Reduction ◽  
Reduced Order Modeling ◽  
Modeling Technique ◽  
Mode Analysis ◽  
Bladed Disks ◽  
Engineering Structures ◽  
Element Analysis ◽  
Reduced Order

The analysis of the response statistics of mistuned turbomachinery rotors requires an expensive Monte Carlo simulation approach. Simple lumped parameter models capture basic localization effects but do not represent well actual engineering structures without a difficult parameter identification. Current component mode analysis techniques generally require a minimum number of degrees of freedom which is too large for running Monte Carlo simulations at a reasonable cost. In the present work, an order reduction method is introduced which is capable of generating reasonably accurate, very low order models of tuned or mistuned bladed disks. This technique is based on component modes of vibration found from a finite element analysis of a single disk-blade sector. It is shown that the phenomenon of mode localization is well captured by the reduced order modeling technique.

scholarly journals A Bifurcation Analysis and Sensitivity Study of Brake Creep Groan

2021 ◽  
Vol 31 (16) ◽  
Author(s):  
Shaun Smith ◽  
James Knowles ◽  
Byron Mason ◽  
Sean Biggs
Keyword(s):  
Periodic Orbits ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Period Doubling ◽  
Nonlinear Behavior ◽  
Sensitivity Study ◽  
Friction Model ◽  
Model Parameters ◽  
Period Doubling Bifurcations ◽  
Simple Models

Creep groan is the undesirable vibration observed in the brake pad and disc as brakes are applied during low-speed driving. The presence of friction leads to nonlinear behavior even in simple models of this phenomenon. This paper uses tools from bifurcation theory to investigate creep groan behavior in a nonlinear 3-degrees-of-freedom mathematical model. Three areas of operational interest are identified, replicating results from previous studies: region 1 contains repelling equilibria and attracting periodic orbits (creep groan); region 2 contains both attracting equilibria and periodic orbits (creep groan and no creep groan, depending on initial conditions); region 3 contains attracting equilibria (no creep groan). The influence of several friction model parameters on these regions is presented, which identify that the transition between static and dynamic friction regimes has a large influence on the existence of creep groan. Additional investigations discover the presence of several bifurcations previously unknown to exist in this model, including Hopf, torus and period-doubling bifurcations. This insight provides valuable novel information about the nature of creep groan and indicates that complex behavior can be discovered and explored in relatively simple models.

scholarly journals Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks—Part II: Application

2000 ◽  
Vol 123 (1) ◽  
pp. 100-108 ◽  
Author(s):  
R. Bladh ◽  
M. P. Castanier ◽  
C. Pierre
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Theoretical Models ◽  
Companion Paper ◽  
Reduced Order Modeling ◽  
Bladed Disks ◽  
Reduced Order ◽  
Component Interface ◽  
Forced Responses

In this paper, the component-mode-based methods formulated in the companion paper (Part I: Theoretical Models) are applied to the dynamic analysis of two example finite element models of bladed disks. Free and forced responses for both tuned and mistuned rotors are considered. Comprehensive comparisons are made among the techniques using full system finite element solutions as a benchmark. The accurate capture of eigenfrequency veering regions is of critical importance for obtaining high-fidelity predictions of the rotor’s sensitivity to mistuning. Therefore, particular attention is devoted to this subject. It is shown that the Craig–Bampton component mode synthesis (CMS) technique is robust and yields highly reliable results. However, this is achieved at considerable computational cost due to the retained component interface degrees of freedom. It is demonstrated that this problem is alleviated by a secondary modal analysis reduction technique (SMART). In addition, a non-CMS mistuning projection method is considered. Although this method is elegant and accurate, it is seen that it lacks the versatility and efficiency of the CMS-based SMART. Overall, this work shows that significant improvements on the accuracy and efficiency of current reduced order modeling methods are possible.

Reduced Order Modeling and Vibration Analysis of Mistuned Bladed Disk Assemblies With Shrouds

1999 ◽  
Vol 121 (3) ◽  
pp. 515-522 ◽  
Author(s):  
R. Bladh ◽  
M. P. Castanier ◽  
C. Pierre
Keyword(s):  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Reduced Order Modeling ◽  
Forced Response ◽  
Modeling Technique ◽  
Computationally Efficient ◽  
Bladed Disks ◽  
Reduced Order ◽  
Synthesis Approach

This paper presents important improvements and extensions to a computationally efficient reduced order modeling technique for the vibration analysis of mistuned bladed disks. In particular, this work shows how the existing modeling technique is readily extended to turbomachinery rotors with shrouded blades. The modeling technique employs a component mode synthesis approach to systematically generate a reduced order model (ROM) using component modes calculated from a finite element model (FEM) of the rotor. Based on the total number of degrees of freedom, the ROM is typically two or three orders of magnitude smaller than the FEM. This makes it feasible to predict the forced response statistics of mistuned bladed disks using Monte Carlo simulations. In this work, particular attention is devoted to the introduction of mistuning into the ROM of a shrouded assembly. Mistuning is modeled by projecting the mistuned natural frequencies of a single, cantilever blade with free shrouds onto the harmonic modes of the shrouded blade assembly. Thus, the necessary mistuning information may be measured by testing individual blades.

scholarly journals Subspace-Based Reduced-Order Modeling Methods for Structural Dynamic Systems

PAMM ◽  
2016 ◽  
Vol 16 (1) ◽  
pp. 245-246
Author(s):  
Stefanie Tegtmeyer ◽  
Udo Nackenhorst
Keyword(s):  
Dynamic Systems ◽  
Reduced Order Modeling ◽  
Structural Dynamic ◽  
Reduced Order ◽  
Modeling Methods
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