scholarly journals Detecting internal resonances during model reduction

2021 ◽  
Vol 477 (2250) ◽  
pp. 20210215
Author(s):  
Evangelia Nicolaidou ◽  
Thomas L. Hill ◽  
Simon A. Neild
Keyword(s):  
Model Reduction ◽  
Selection Process ◽  
A Priori ◽  
Order Reduction ◽  
Element Model ◽  
Thin Plates ◽  
Modal Interactions ◽  
Internal Resonances ◽  
Static Condensation ◽  
Slender Beams

Model order reduction of geometrically nonlinear dynamic structures is often achieved via a static condensation procedure, whereby high-frequency modes are assumed to be quasi-statically coupled to a small set of lower frequency modes, which form the reduction basis. This approach is mathematically justifiable for structures characterized by slow/fast dynamics, such as thin plates and slender beams, and has been shown to provide highly accurate results. Nevertheless, selecting the reduction basis without a priori knowledge of the full-order dynamics is a challenging task; retaining redundant modes will lead to computationally suboptimal reduced-order models (ROMs), while omitting dynamically significant modes will lead to inaccurate results, and important features such as internal resonances may not be captured. In this study, we demonstrate how the error associated with static condensation can be efficiently approximated during model reduction. This approximate error can then be used as the basis of a method for predicting when dynamic modal interactions will occur, which will guide the reduction basis selection process. Equivalently, this may serve as a tool for verifying the accuracy of ROMs without the need for full-order simulations. The proposed method is demonstrated using a simple oscillator and a finite element model of a clamped–clamped beam.

scholarly journals Tuning nonlinear damping in graphene nanoresonators by parametric–direct internal resonance

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Ata Keşkekler ◽  
Oriel Shoshani ◽  
Martin Lee ◽  
Herre S. J. van der Zant ◽  
Peter G. Steeneken ◽  
...  
Keyword(s):  
Parametric Resonance ◽  
Internal Resonance ◽  
Microscopic Theory ◽  
Fold Increase ◽  
Nonlinear Damping ◽  
Supporting Evidence ◽  
Nonlinear Dissipation ◽  
Modal Interactions ◽  
Solid State Physics ◽  
Internal Resonances

AbstractMechanical sources of nonlinear damping play a central role in modern physics, from solid-state physics to thermodynamics. The microscopic theory of mechanical dissipation suggests that nonlinear damping of a resonant mode can be strongly enhanced when it is coupled to a vibration mode that is close to twice its resonance frequency. To date, no experimental evidence of this enhancement has been realized. In this letter, we experimentally show that nanoresonators driven into parametric-direct internal resonance provide supporting evidence for the microscopic theory of nonlinear dissipation. By regulating the drive level, we tune the parametric resonance of a graphene nanodrum over a range of 40–70 MHz to reach successive two-to-one internal resonances, leading to a nearly two-fold increase of the nonlinear damping. Our study opens up a route towards utilizing modal interactions and parametric resonance to realize resonators with engineered nonlinear dissipation over wide frequency range.

Energy-Based Model Reduction Methodology for Automated Modeling

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Loucas S. Louca ◽  
Jeffrey L. Stein ◽  
Gregory M. Hulbert
Keyword(s):  
Model Reduction ◽  
Order Reduction ◽  
Process Models ◽  
Model Parameters ◽  
Automated Modeling ◽  
Reduced Models ◽  
System Models ◽  
Quarter Car Model ◽  
Reduction Techniques ◽  
Physical Phenomena

In recent years, algorithms have been developed to help automate the production of dynamic system models. Part of this effort has been the development of algorithms that use modeling metrics for generating minimum complexity models with realization preserving structure and parameters. Existing algorithms, add or remove ideal compliant elements from a model, and consequently do not equally emphasize the contribution of the other fundamental physical phenomena, i.e., ideal inertial or resistive elements, to the overall system behavior. Furthermore, these algorithms have only been developed for linear or linearized models, leaving the automated production of models of nonlinear systems unresolved. Other model reduction techniques suffer from similar limitations due to linearity or the requirement that the reduced models be realization preserving. This paper presents a new modeling metric, activity, which is based on energy. This metric is used to order the importance of all energy elements in a system model. The ranking of the energy elements provides the relative importance of the model parameters and this information is used as a basis to reduce the size of the model and as a type of parameter sensitivity information for system design. The metric is implemented in an automated modeling algorithm called model order reduction algorithm (MORA) that can automatically generate a hierarchical series of reduced models that are realization preserving based on choosing the energy threshold below which energy elements are not included in the model. Finally, MORA is applied to a nonlinear quarter car model to illustrate that energy elements with low activity can be eliminated from the model resulting in a reduced order model, with physically meaningful parameters, which also accurately predicts the behavior of the full model. The activity metric appears to be a valuable metric for automating the reduction of nonlinear system models—providing in the process models that provide better insight and may be more numerically efficient.

Pipeline Dent Management Program

2002 ◽  
Author(s):  
Scott D. Ironside ◽  
L. Blair Carroll
Keyword(s):  
Finite Element ◽  
Oil And Gas ◽  
Selection Process ◽  
Element Model ◽  
Field Trials ◽  
Management Program ◽  
Operating Conditions ◽  
Published Data ◽  
Element Analysis ◽  
The Past

Enbridge Pipelines Inc. operates the world’s longest and most complex liquids pipeline network. As part of Enbridge’s Integrity Management Program In-Line Inspections have been and will continue to be conducted on more than 15,000 km of pipeline. The Inspection Programs have included using the most technologically advanced geometry tools in the world to detect geometrical discontinuities such as ovality, dents, and buckles. During the past number of years, Enbridge Pipelines Inc. has been involved in developing a method of evaluating the suitability of dents in pipelines for continued service. The majority of the work involved the development of a method of modeling the stresses within a dent using Finite Element Analysis (FEA). The development and validation of this model was completed by Fleet Technology Limited (FTL) through several projects sponsored by Enbridge, which included field trials and comparisons to previously published data. This model combined with proven fracture mechanics theory provides a method of determining a predicted life of a dent based on either the past or future operating conditions of the pipeline. CSA Standard Z662 – Oil and Gas Pipeline Systems provides criteria for the acceptability of dents for continued service. There have been occurrences, however, where dents that meet the CSA acceptability criteria have experienced failure. The dent model is being used to help define shape characteristics in addition to dent depth, the only shape factor considered by CSA, which contribute to dent failure. The dent model has also been utilized to validate the accuracy of current In-Line Inspection techniques. Typically a dent will lose some of its shape as the overburden is lifted from the pipeline and after the indentor is removed. Often there can be a dramatic “re-rounding” that will occur. The work included comparing the re-rounded dent shapes from a Finite Element model simulating the removal of the constraint on the pipe to the measured dent profile from a mold of the dent taken in the field after it has been excavated. This provided a measure of the accuracy of the tool. This paper will provide an overview of Enbridge’s dent management program, a description of the dent selection process for the excavation program, and a detailed review of the ILI validation work.

LIFESPAN ESTIMATES FOR SOLUTIONS OF POLYHARMONIC KIRCHHOFF SYSTEMS

2012 ◽  
Vol 22 (02) ◽  
pp. 1150009 ◽  
Author(s):  
GIUSEPPINA AUTUORI ◽  
FRANCESCA COLASUONNO ◽  
PATRIZIA PUCCI
Keyword(s):  
A Priori Estimates ◽  
Driving Forces ◽  
A Priori ◽  
Thin Plates ◽  
Existence Of A Solution ◽  
Dissipative Term ◽  
Maximal Solutions ◽  
Elastic Bodies ◽  
Priori Estimates ◽  
Deformation Processes

In mathematical physics we increasingly encounter PDEs models connected with vibration problems for elastic bodies and deformation processes, as it happens in the Kirchhoff–Love theory for thin plates subjected to forces and moments. Recently Monneanu proved in Refs. 26 and 27 the existence of a solution of the nonlinear Kirchhoff–Love plate model. In this paper we treat several questions about non-continuation for maximal solutions of polyharmonic Kirchhoff systems, governed by time-dependent nonlinear dissipative and driving forces. In particular, we are interested in the strongly damped Kirchhoff–Love model, containing also an intrinsic dissipative term of Kelvin–Voigt type. Global non-existence and a priori estimates for the lifespan of maximal solutions are proved. Several applications are also presented in special subcases of the source term f and the nonlinear external damping Q.

(Generalized) Bloch mode synthesis for the fast dispersion curve calculation of 3D periodic metamaterials

2021 ◽  
Vol 263 (4) ◽  
pp. 2102-2113
Author(s):  
Vanessa Cool ◽  
Lucas Van Belle ◽  
Claus Claeys ◽  
Elke Deckers ◽  
Wim Desmet
Keyword(s):  
Dispersion Curve ◽  
Periodic Structures ◽  
Cell Model ◽  
Stop Band ◽  
Computational Cost ◽  
Order Reduction ◽  
Element Model ◽  
Unit Cell ◽  
Reduction Techniques ◽  
Bloch Mode

Metamaterials, i.e. artificial structures with unconventional properties, have shown to be highly potential lightweight and compact solutions for the attenuation of noise and vibrations in targeted frequency ranges, called stop bands. In order to analyze the performance of these metamaterials, their stop band behavior is typically predicted by means of dispersion curves, which describe the wave propagation in the corresponding infinite periodic structure. The input for these calculations is usually a finite element model of the corresponding unit cell. Most common in literature are 2D plane metamaterials, which often consist of a plate host structure with periodically added masses or resonators. In recent literature, however, full 3D metamaterials are encountered which are periodic in all three directions and which enable complete, omnidirectional stop bands. Although these 3D metamaterials have favorable vibro-acoustic characteristics, the computational cost to analyze them quickly increases with unit cell model size. Model order reduction techniques are important enablers to overcome this problem. In this work, the Bloch Mode Synthesis (BMS) and generalized BMS (GBMS) reduction techniques are extended from 2D to 3D periodic structures. Through several verifications, it is demonstrated that dispersion curve calculation times can be strongly reduced, while accurate stop band predictions are maintained.

Explaining monotonic ranking functions

2020 ◽  
Vol 14 (4) ◽  
pp. 640-652
Author(s):  
Abraham Gale ◽  
Amélie Marian
Keyword(s):  
Decision Making ◽  
Selection Process ◽  
A Priori ◽  
Data Distribution ◽  
Synthetic Data ◽  
Decision Processes ◽  
Decision Makers ◽  
Ranking Functions ◽  
High School Admissions ◽  
Parameter Values

Ranking functions are commonly used to assist in decision-making in a wide variety of applications. As the general public realizes the significant societal impacts of the widespread use of algorithms in decision-making, there has been a push towards explainability and transparency in decision processes and results, as well as demands to justify the fairness of the processes. In this paper, we focus on providing metrics towards explainability and transparency of ranking functions, with a focus towards making the ranking process understandable, a priori , so that decision-makers can make informed choices when designing their ranking selection process. We propose transparent participation metrics to clarify the ranking process, by assessing the contribution of each parameter used in the ranking function in the creation of the final ranked outcome, using information about the ranking functions themselves, as well as observations of the underlying distributions of the parameter values involved in the ranking. To evaluate the outcome of the ranking process, we propose diversity and disparity metrics to measure how similar the selected objects are to each other, and to the underlying data distribution. We evaluate the behavior of our metrics on synthetic data, as well as on data and ranking functions on two real-world scenarios: high school admissions and decathlon scoring.

A new model order reduction method for the design of compensator by using moment matching algorithm

2019 ◽  
Vol 42 (3) ◽  
pp. 472-484 ◽  
Author(s):  
Arvind Kumar Prajapati ◽  
Rajendra Prasad
Keyword(s):  
Model Reduction ◽  
Lower Order ◽  
Large Scale ◽  
Order Reduction ◽  
Order System ◽  
Moment Matching ◽  
Matching Algorithm ◽  
New Model ◽  
Factor Division Algorithm ◽  
Lower Order System

The aim of this paper is the construction of a new model reduction technique for large scale stable linear dynamic systems. It is principally focused on the dominant modes and time moments retention. This reduction implicates the translation of the overall important features confined in the large scale complete order model into the lower order system, allowing the computation of approximant denominator by using generalized pole clustering method. The approximant numerator is obtained by means of the factor division algorithm. As a result, a lower order system is obtained. To demonstrate its effectiveness, to highlight some fundamental of its features, and to accomplish its accuracy, a comparative study is done. Two standard numerical examples are taken, where approximant model computed by the proposed method is compared with the reduced order models computed from the recently proposed methods as well as well-known model reduction schemes. The paper is also emphasized on the design of compensator by using moment matching algorithm with the help of the reduced model. The design of compensator is validated and illustrated with the help of a standard numerical example taken from the literature.

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