A time-domain finite element model reduction method for viscoelastic linear and nonlinear systems

Abstract

Many authors have shown that the effective design of viscoelastic systems can be conveniently carried out by using modern mathematical models to represent the frequency-and temperaturedependent behavior of viscoelastic materials. However, in the quest for design procedures of real-word engineering structures, the large number of exact evaluations of the dynamic responses during iterative procedures, combined with the typically high dimensions of large finite element models, makes the numerical analysis very costly, sometimes unfeasible. It is especially true when the viscoelastic materials are used to reduce vibrations of nonlinear systems. As a matter of fact, which the resolution of the resulting nonlinear equations of motion with frequency-and temperature-dependent viscoelastic damping forces is an interesting, but hard-to-solve problem. Those difficulties motivate the present study, in which a time-domain condensation strategy of viscoelastic systems is addressed, where the viscoelastic behavior is modeled by using a four parameter fractional derivative model. After the discussion of various theoretical aspects, the exact and reduced time responses are calculated for a three-layer sandwich plate by considering nonlinear boundary conditions.

Kelvin Viscoelasticity and Lagrange Multipliers Applied to the Simulation of Nonlinear Structural Vibration Control

“…This strategy is originally described here for nonlinear strain measure, but was inspired in Mesquita and Coda (2002), Mesquita and Coda (2003) and Mesquita and Coda (2007) where linear viscoelastic models are proposed. As far as the authors knowledge goes it is different from all nonlinear viscoelastic formulations present in literature, see for example, Lemaitre and Chaboche (1990), Lemaitre (2001), Lima et al (2015), Holzapfel (1996), Simo (1987), Huber and Tsakmakis (2000), Petiteau et al (2013), Marko et al (2006) and Clough and Penzien (1985).…”

“…Moreover, the dampers used in such devices can be represented by viscous constitutive models that, associated with their stiffness, result in viscoelastic models similar to the Kelvin/Voigt one. The treatment of these linear and nonlinear viscoelastic formulations is usually done by more or less complicated traditional convolution techniques or decaying functions as explained by Lemaitre and Chaboche (1990), Lemaitre (2001), Lima et al (2015), Holzapfel (1996), Simo (1987), Huber and Tsakmakis (2000) and Petiteau et al (2013) used or not in vibration control (Marko et al (2006) and Clough and Penzien (1985)). There are no significant differences regarding the traditional rheological viscoelastic approach of materials in all consulted bibliography.…”

A Study of the Thermal Runaway Phase Generated During Cyclic Loading of Viscoelastic Materials Accounting for the Prestress

“…The temperatures at points A and C of the specimen were measured by using thermocouples and its signal was acquired and processed by a signal analyzer Agilent  34970. Also, in all tests, a vertical displacement,     To compare the simulations obtained previously with the acquired experimental results, the static displacement of the viscoelastic material was computed based on the tangent stiffness matrix concept (de Lima et al, 2015a). Also, it is assumed that only the viscoelastic cores are deformed during the application of the static displacements by the screws.…”

Sliding Mode Control of Vibration in Single-Degree-of-Freedom Fractional Oscillators

“…In the quest for analyzing and synthesizing viscoelastically damped structures, one of the primary tasks is to model the rheological behavior of viscoelastic materials. However, this is also a challenge work due to the high dependency on viscoelastic materials of operational and environmental factors such as vibration frequency, external temperature, pre-loads, etc [2].…”