Stochastic Modeling of Surface Viscoelastic Treatments Combined with Model Condensation Procedures

Abstract

Abstract. Engineering structures incorporating viscoelastic materials are characterized by inherent uncertainties affecting the parameters that control the efficiency of the viscoelastic dampers. In this context, the handling of variability in viscoelastic systems is a natural and necessary extension of the modeling capability of the present techniques of deterministic analysis. Among the various methods devised for uncertainty modeling, the stochastic finite element method has received major attention, as it is well adapted for applications to complex engineering systems. In this paper, the stochastic finite element method applied to a structural three-layer sandwich plate finite element containing a viscoelastic layer, with random parameters modelled as random fields, is presented. Accounting for the dependence of the behaviour of the viscoelastic materials with respect to frequency and temperature, using the concepts of complex modulus and shift factor, the uncertainties are modelled as homogeneous Gaussian stochastic fields and are discretized according to the spectral method, using Karhunen-Loève expansions. The modeling procedure is confined to the frequency domain, and the dynamic responses are characterized by frequency response functions (FRF's). Monte Carlo Simulation (MCS) combined with Latin Hypercube Sampling is used as the stochastic solver. The typically high dimensions of finite element models of viscoelastic systems combined with the large number of Monte Carlo samples to be computed make the evaluation of the FRF's variability computer intensive. Those difficulties motivate the use of condensation methods specially adapted for viscoelastic systems, in order to alleviate the computational cost. After the presentation of the underlying formulation, numerical applications of moderate complexity are presented and discussed aiming at demonstrating the main features and, particularly, the computation cost savings provided by the association of MCS with the suggested condensation procedure.

Preface

“…Numerical implementation was based on the development made by Khatua and Cheung (1973) and Lima et al (2010). The structure is a clamped-clamped-free-free rectangular plate made of aluminum, fully treated with a layer of 3M ISD112 TM between base-plate and constrained-layer.…”

Stochastic modeling of flexible rotors

“…In this paper, the well-known Karhunen-Loève (KL) decomposition, which is a continuous representation for random fields expressed as the superposition of orthogonal random variables weighted by deterministic spatial functions (Ghanem and Spanos, 1991), is used. According to this technique, a random field can be viewed as a spatial extension of a random variable that describes the spatial correlation of a structural parameter that fluctuates randomly (de Lima et al, 2010). A one-dimensional random field ( ) (Nieuwenhof and Coyette, 2003).…”

Fatigue damage investigation and optimization of a viscoelastically damped system with uncertainties

“…To develop more representative systems, the inclusion of uncertainties in the models has been studied for the past few years [1]. However, this kind of analysis has become more broadly applied due to the development of model condensation strategies and computers with robust processing and storage capacities, making it possible to solve large finite element (FE) models of industrial interest that require considerable computational resources [2][3][4]. The design of structures subjected to dynamic loads should consider comfort, durability, safety and reliability in the presence of mechanical vibrations.…”