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.

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.

scholarly journals A COMPARISON OF ONE- AND TWO-SIDED KRYLOV–ARNOLDI PROJECTION METHODS FOR FULLY COUPLED, DAMPED STRUCTURAL-ACOUSTIC ANALYSIS

2013 ◽  
Vol 21 (02) ◽  
pp. 1350004 ◽  
Author(s):  
R. SRINIVASAN PURI ◽  
DENISE MORREY
Keyword(s):  
Coupled System ◽  
Dimensional Subspace ◽  
Second Order ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Frequency Moments ◽  
Arnoldi Algorithm ◽  
Higher Dimensional ◽  
Fully Coupled

The two-sided second-order Arnoldi algorithm is used to generate a reduced order model of two test cases of fully coupled, acoustic interior cavities, backed by flexible structural systems with damping. The reduced order model is obtained by applying a Galerkin–Petrov projection of the coupled system matrices, from a higher dimensional subspace to a lower dimensional subspace, whilst preserving the low frequency moments of the coupled system. The basis vectors for projection are computed efficiently using a two-sided second-order Arnoldi algorithm, which generates an orthogonal basis for the second-order Krylov subspace containing moments of the original higher dimensional system. The first model is an ABAQUS benchmark problem: a 2D, point loaded, water filled cavity. The second model is a cylindrical air-filled cavity, with clamped ends and a load normal to its curved surface. The computational efficiency, error and convergence are analyzed, and the two-sided second-order Arnoldi method shows better efficiency and performance than the one-sided Arnoldi technique, whilst also preserving the second-order structure of the original problem.

scholarly journals Geometrically nonlinear autonomous reduced order model for rotating structures

2018 ◽  
Author(s):  
Mikel Balmaseda ◽  
Georges Jacquet-Richardet ◽  
Antoine Placzek ◽  
Duc-Minh Tran
Keyword(s):  
Normal Modes ◽  
Harmonic Balance Method ◽  
Reduced Order Model ◽  
Static Equilibrium ◽  
Evaluation Procedure ◽  
Element Formulation ◽  
Geometrically Nonlinear ◽  
Reduced Basis ◽  
Order Model ◽  
Reduced Order

In the present work, as an extension to [2], an autonomous geometrically nonlinear reduced order model for the study of dynamic solutions of complex rotating structures is developed. In opposition to the classical finite element formulation for geometrically nonlinear rotating structures that considers small linear vibrations around the static equilibrium, nonlinear vibrations around the pre-stressed equilibrium are now considered. For that purpose, the linear normal modes are used as a reduced basis for the construction of the reduced order model. The stiffness evaluation procedure method (STEP) [4] is applied to compute the nonlinear forces induced by the displacements around the static equilibrium. This approach enhances the classical linearised small perturbations hypothesis to the cases of large displacements around the static pre-stressed equilibrium. Furthermore, a comparison between the steady solution given by HHT-α [1] and the Harmonic Balance Method (HBM) [3] is carried out. The proposed reduced order models are evaluated for a rotating beam case study.

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