Abstract
Piezoelectric patches with adapted electrical circuits or viscoelastic dissipative materials are two solutions particularly adapted to reduce vibration of light structures. To accurately design these solutions, it is necessary to describe precisely the dynamical behaviour of the structure. It may quickly become computationally intensive to describe robustly this behaviour for a structure with nonlinear phenomena, such as contact or friction for bolted structures, and uncertain variations of its parameters. The aim of this work is to propose a non-intrusive reduced stochastic method to characterize robustly the vibrational response of a structure with random parameters. Our goal is to characterize the eigenspace of linear systems with dynamic properties considered as random variables. This method is based on a separation of random aspects from deterministic aspects and allows us to estimate the first central moments of each random eigenfrequency with a single deterministic finite elements computation. The method is applied to a frame with several Young's moduli modeled as random variables. This example could be expanded to a bolted structure including piezoelectric devices. The method needs to be enhanced when random eigenvalues are closely spaced. An indicator with no additional computational cost is proposed to characterize the ’’proximity” of two random eigenvalues.
Highlights
In order to accurately predict the vibrational response of a structure, uncertainty modeling and quantification in computational mechanics have received particular attention in recent years
The matrices of interest in the present paper are the result of a finite-dimensional approximation of an underlying continuous system and their randomness is tied to the uncertainty in the parameters of this system
We propose to use the polynomial chaos (PC) expansion only for the random eigenvalues for which the SMR2 accuracy is not sufficient
Summary
In order to accurately predict the vibrational response of a structure, uncertainty modeling and quantification in computational mechanics have received particular attention in recent years. The matrices of interest in the present paper are the result of a finite-dimensional approximation of an underlying continuous system and their randomness is tied to the uncertainty in the parameters of this system For such systems, closed-form expressions are generally not available for the solution of the random eigenvalue problem. Many papers are based on the perturbation method to estimate statistics of random eigenvalues and eigenvectors [5, 6, 7]. The aim of this paper is to propose an indicator to be able to discriminate which method is more adapted : perturbation method for most of the cases or SSFEM for some cases The estimate of this indicator is based on a reduced number of deterministic finite element computations.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
