scholarly journals Stochastic Reduced-Order Model in Low-Frequency Dynamics in Presence of Numerous Local Elastic Modes

2011 ◽  
Vol 78 (6) ◽  
Author(s):  
C. Soize ◽  
A. Batou
Keyword(s):  
Structural Dynamics ◽  
Complex Structure ◽  
Probabilistic Approach ◽  
Low Frequency ◽  
Reduced Order Model ◽  
Frequency Range ◽  
Order Model ◽  
Reduced Order ◽  
Global Modes ◽  
Elastic Modes

This paper deals with the nonusual case in structural dynamics for which a complex structure exhibits both the usual global elastic modes and numerous local elastic modes in the low-frequency range. Despite the presence of these local elastic modes, we are interested in constructing a stochastic reduced-order model using only the global modes and in taking into account the local elastic modes with a probabilistic approach. In the first part, a formulation and an algorithm, which allow the “global elastic modes” and the “local elastic modes” to be calculated, are presented. The second part is devoted to the construction of the stochastic reduced-order model with the global elastic modes and in taking into account the uncertainties on the effects of the local elastic modes by the nonparametric probabilistic approach. Finally, an application, which validates the proposed theory is presented.

Piezoelectric Shunt Vibration Damping of Structural-Acoustic Systems: Finite Element Formulation and Reduced-Order Model

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Jean-François Deü ◽  
Walid Larbi ◽  
Roger Ohayon ◽  
Rubens Sampaio
Keyword(s):  
Low Frequency ◽  
Coupled System ◽  
Vibration Damping ◽  
Reduced Order Model ◽  
Element Formulation ◽  
Inviscid Fluid ◽  
Frequency Range ◽  
Order Model ◽  
Reduced Order ◽  
Projection Techniques

For noise and vibration attenuation, various approaches can be employed depending on the frequency range to attenuate. Generally, active or passive piezoelectric techniques are effective in the low-frequency range, while dissipative materials, such as viscoelastic or porous treatments, are efficient for higher-frequency domain. In this work, a reduced-order model is developed for the approximation of a fully coupled electromechanical-acoustic system using modal projection techniques. The problem consists of an elastic structure with surface-mounted piezoelectric patches coupled with a compressible inviscid fluid. The piezoelectric elements, connected with resonant shunt circuits, are used for the vibration damping of the coupled system. Numerical examples are presented in order to illustrate the accuracy and the versatility of the proposed reduced-order model, especially in terms of prediction of attenuation.

Reduced Order Model Analysis for Two Dimensional Molecular Dynamic Chain Structure Attached to an Atomic Force Microscope

2003 ◽  
Author(s):  
Deman Tang ◽  
Earl H. Dowell
Keyword(s):  
Atomic Force Microscope ◽  
Excitation Frequency ◽  
Chain Structure ◽  
Reduced Order Model ◽  
Two Dimensional ◽  
Order Model ◽  
Global Mode ◽  
Reduced Order ◽  
Atomic Force ◽  
Global Modes

Dynamic analysis and numerical simulation of a protein-ligand chain structure connected to a moving atomic force microscope (AFM) has been conducted. The elements of the chain are free to extend and rotate relative to each other in a two-dimensional plane. Sinusoidal base excitation of the cantilevered beam of the AFM is considered in some detail. Reduced order (dynamic) models are constructed using global modes for both linear and nonlinear dynamic systems with and without the “nearest neighbor assumption”. The agreement between the original and reduced order models (ROM) is very good even when only one global mode is included in the ROM for either the linear case or for the nonlinear case, provided the excitation frequency is lower than the fundamental natural frequency of the linear system. For higher excitation frequencies, more global modes are required. The computational advantage of the reduced order model is clear from the results presented.

Reduced Order Model Analysis for Two-Dimensional Molecular Dynamic Chain Structure Attached to an Atomic Force Microscope

2004 ◽  
Vol 126 (3) ◽  
pp. 531-546 ◽  
Author(s):  
Deman Tang ◽  
Earl H. Dowell
Keyword(s):  
Atomic Force Microscope ◽  
Excitation Frequency ◽  
Chain Structure ◽  
Reduced Order Model ◽  
Two Dimensional ◽  
Order Model ◽  
Global Mode ◽  
Reduced Order ◽  
Atomic Force ◽  
Global Modes

Dynamic analysis and numerical simulation of a protein-ligand chain structure connected to a moving atomic force microscope (AFM) has been conducted. The elements of the chain are free to extend and rotate relative to each other in a two-dimensional plane. Sinusoidal base excitation of the cantilevered beam of the AFM is considered in some detail. Reduced order (dynamic) models are constructed using global modes for both linear and nonlinear dynamic systems with and without the “nearest neighbor assumption.” The agreement between the original and reduced order models (ROM) is very good even when only one global mode is included in the ROM for either the linear case or for the nonlinear case, provided the excitation frequency is lower than the fundamental natural frequency of the linear system. For higher excitation frequencies, more global modes are required. The computational advantage of the reduced order model is clear from the results presented.

scholarly journals Simulation-Free Hyper-Reduction for Geometrically Nonlinear Structural Dynamics: A Quadratic Manifold Lifting Approach

2018 ◽  
Vol 13 (7) ◽  
Author(s):  
Shobhit Jain ◽  
Paolo Tiso
Keyword(s):  
Structural Dynamics ◽  
Direct Methods ◽  
Cost Effective ◽  
Reduced Order Model ◽  
Geometrically Nonlinear ◽  
Order Model ◽  
Reduced Order ◽  
Manual Selection ◽  
Modal Derivatives ◽  
Dynamics Problems

We present an efficient method to significantly reduce the offline cost associated with the construction of training sets for hyper-reduction of geometrically nonlinear, finite element (FE)-discretized structural dynamics problems. The reduced-order model is obtained by projecting the governing equation onto a basis formed by vibration modes (VMs) and corresponding modal derivatives (MDs), thus avoiding cumbersome manual selection of high-frequency modes to represent nonlinear coupling effects. Cost-effective hyper-reduction is then achieved by lifting inexpensive linear modal transient analysis to a quadratic manifold (QM), constructed with dominant modes and related MDs. The training forces are then computed from the thus-obtained representative displacement sets. In this manner, the need of full simulations required by traditional, proper orthogonal decomposition (POD)-based projection and training is completely avoided. In addition to significantly reducing the offline cost, this technique selects a smaller hyper-reduced mesh as compared to POD-based training and therefore leads to larger online speedups, as well. The proposed method constitutes a solid alternative to direct methods for the construction of the reduced-order model, which suffer from either high intrusiveness into the FE code or expensive offline nonlinear evaluations for the determination of the nonlinear coefficients.

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