scholarly journals Complex Eigenvalue Analysis for Structures With Viscoelastic Behavior

2011 ◽  
Author(s):  
G. Chevallier ◽  
F. Renaud ◽  
J.-L. Dion ◽  
S. Thouviot
Keyword(s):  
State Space ◽  
Viscoelastic Behavior ◽  
Maxwell Model ◽  
Accurate Method ◽  
Eigenvalue Analysis ◽  
Theoretical Development ◽  
Complex Eigenvalue ◽  
Viscoelastic Materials ◽  
Space Problem ◽  
Internal States

This document deals with a method for eigenvalue extraction for the analysis of structures with viscoelastic materials. A generalized Maxwell model is used to model linear viscoelasticity. Such kind of model necessitates a state-space formulation to perform eigenvalue analysis with standard solvers. This formulation is very close to ADF formulation. The use of several materials on the same structure and during the same analysis may lead to a large number of internal states. This article purpose is to identify simultaneously all the viscoelastic materials and to constrain them to have the same time-constants. As it is usually possible, the size of the state-space problem is therefore widely reduced. Moreover, an accurate method for reducing mass and stiffness operators is proposed; The enhancement of the modal basis allows to obtain good results with large reduction. As the length of the paper is limited, only theoretical development are presented in the present paper while numerical results will be presented in the conference.

scholarly journals Bayesian Joint Input-State Estimation for Nonlinear Systems

Vibration ◽  
2020 ◽  
Vol 3 (3) ◽  
pp. 281-303
Author(s):  
Timothy J. Rogers ◽  
Keith Worden ◽  
Elizabeth J. Cross
Keyword(s):  
Nonlinear Systems ◽  
Gaussian Process ◽  
State Estimation ◽  
State Space ◽  
Mean Squared Error ◽  
Duffing Oscillator ◽  
State Space Model ◽  
Input State ◽  
Force Model ◽  
Internal States

This work suggests a solution for joint input-state estimation for nonlinear systems. The task is to recover the internal states of a nonlinear oscillator, the displacement and velocity of the system, and the unmeasured external forces applied. To do this, a Gaussian process latent force model is developed for nonlinear systems. The model places a Gaussian process prior over the unknown input forces for the system, converts this into a state-space form and then augments the nonlinear system with these additional hidden states. To perform inference over this nonlinear state-space model a particle Gibbs approach is used combining a “Particle Gibbs with Ancestor Sampling” Markov kernel for the states and a Metropolis-Hastings update for the hyperparameters of the Gaussian process. This approach is shown to be effective in a numerical case study on a Duffing oscillator where the internal states and the unknown forcing are recovered, each with a normalised mean-squared error less than 0.5%. It is also shown how this Bayesian approach allows uncertainty quantification of the estimates of the states and inputs which can be invaluable in further engineering analyses.

Linking Internal Dissipation Mechanisms to the Effective Complex Viscoelastic Moduli of Ferroelectrics

2016 ◽  
Vol 84 (2) ◽  
Author(s):  
Charles S. Wojnar ◽  
Dennis M. Kochmann
Keyword(s):  
Microstructure Evolution ◽  
Domain Switching ◽  
Constitutive Models ◽  
Viscoelastic Behavior ◽  
Maxwell Model ◽  
Hysteretic Behavior ◽  
Ferroelectric Ceramics ◽  
Internal Variables ◽  
Viscoelastic Parameters ◽  
Generalized Maxwell Model

Microstructural mechanisms such as domain switching in ferroelectric ceramics dissipate energy, the nature, and extent of which are of significant interest for two reasons. First, dissipative internal processes lead to hysteretic behavior at the macroscale (e.g., the hysteresis of polarization versus electric field in ferroelectrics). Second, mechanisms of internal friction determine the viscoelastic behavior of the material under small-amplitude vibrations. Although experimental techniques and constitutive models exist for both phenomena, there is a strong disconnect and, in particular, no advantageous strategy to link both for improved physics-based kinetic models for multifunctional rheological materials. Here, we present a theoretical approach that relates inelastic constitutive models to frequency-dependent viscoelastic parameters by linearizing the kinetic relations for the internal variables. This enables us to gain qualitative and quantitative experimental validation of the kinetics of internal processes for both quasistatic microstructure evolution and high-frequency damping. We first present the simple example of the generalized Maxwell model and then proceed to the case of ferroelectric ceramics for which we predict the viscoelastic response during domain switching and compare to experimental data. This strategy identifies the relations between microstructural kinetics and viscoelastic properties. The approach is general in that it can be applied to other rheological materials with microstructure evolution.

scholarly journals Investigation on viscoelastic behavior of virgin EPDM/ reclaimed rubber blends using Generalized Maxwell Model (GMM)

2021 ◽  
Vol 93 ◽  
pp. 106989
Author(s):  
Atefeh Salimi ◽  
Foroud Abbassi-Sourki ◽  
Mohammad Karrabi ◽  
Mir Hamid Reza Ghoreishy
Keyword(s):  
Viscoelastic Behavior ◽  
Maxwell Model ◽  
Rubber Blends ◽  
Generalized Maxwell Model

Nonlinear Dynamic Viscoelastic Model for Osteoarthritic Cartilage Indentation Force

2011 ◽  
Author(s):  
A. Vidal-Lesso ◽  
E. Ledesma-Orozco ◽  
R. Lesso-Arroyo ◽  
L. Daza-Benitez
Keyword(s):  
Mechanical Properties ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Indentation Test ◽  
Maxwell Model ◽  
Relaxation Curve ◽  
Geometrical Parameters ◽  
Osteoarthritic Cartilage

Biomechanical properties and dynamic response of soft tissues as articular cartilage remains issues for attention. Currently, linear isotropic models are still used for cartilage analysis in spite of its viscoelastic nature. Therefore, the aim of this study was to propose a nonlinear viscoelastic model for cartilage indentation that combines the geometrical parameters and velocity of the indentation test with the thickness of the sample as well as the mechanical properties of the tissue changing over time due to its viscoelastic behavior. Parameters of the indentation test and mechanical properties as a function of time were performed in Laplace space where the constitutive equation for viscoelasticity and the convolution theorem was applied in addition with the Maxwell model and Hayes et al. model for instantaneous elastic modulus. Results of the models were compared with experimental data of indentation tests on osteoarthritic cartilage of a unicompartmental osteoarthritis cases. The models showed a strong fit for the axial indentation nonlinear force in the loading curve (R2 = 0.992) and a good fit for unloading (R2 = 0.987), while an acceptable fit was observed in the relaxation curve (R2 = 0.967). These models may be used to study the mechanical response of osteoarthritic cartilage to several dynamical and geometrical test conditions.

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