Computation of eigenvalues in proportionally damped viscoelastic structures based on the fixed-point iteration

DOI10.1016/j.amc.2012.09.026zbMath1311.65138OpenAlexW2085274529MaRDI QIDQ2344640

Mario Lázaro, Marcelo Epstein, José L. Pérez-Aparicio

Publication date: 15 May 2015

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10251/57627

zbMATH Keywords

numerical methodfixed-point iterationcomplex eigenvaluesviscoelastic structuresproportional dampingreal eigenvalues

Mathematics Subject Classification ID

Linear constitutive equations for materials with memory (74D05) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (4)

Variational characterization of real eigenvalues in linear viscoelastic oscillators ⋮ A survey on variational characterizations for nonlinear eigenvalue problems ⋮ Critical damping in nonviscously damped linear systems ⋮ The polynomial pivots as initial values for a new root-finding iterative method

Cites Work

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• Uniform decay in viscoelasticity for kernels with small non-decreasingness zones
• On Haar wavelet operational matrix of general order and its application for the numerical solution of fractional Bagley Torvik equation
• A generalised fractional derivative approach to viscoelastic material properties measurement
• Analytical approximate solution of nonlinear dynamic system containing fractional derivative by modified decomposition method
• Sensitivity analysis of the largest dependent eigenvalue functions of eigensystems
• Iterative algorithms for nonlinear eigenvalue problems. Application to vibrations of viscoelastic shells
• An Arnoldi method for nonlinear eigenvalue problems
• Computational methods for complex eigenproblems in finite element analysis of structural systems with viscoelastic damping treatments
• Asymptotic behavior for a viscoelastic problem with not necessarily decreasing kernel
• Analytical solution of the Bagley-Torvik equation by Adomian decomposition method
• Eigenderivative analysis of asymmetric non‐conservative systems
• Higher order eigensensitivities-based numerical method for the harmonic analysis of viscoelastically damped structures
• ANALYSIS OF FOUR-PARAMETER FRACTIONAL DERIVATIVE MODEL OF REAL SOLID MATERIALS
• Vibration analysis of beams with non-local foundations using the finite element method
• Fractional calculus - A different approach to the analysis of viscoelastically damped structures
• A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
• A method for eigenvalues of sparse λ-matrices
• Dynamics of Viscoelastic Structures—A Time-Domain, Finite Element Formulation
• Reliable use of determinants to solve non-linear structural eigenvalue problems efficiently
• Dynamics of viscoelastic structures
• Uniform convexity of the hyperbolic metric and fixed points of holomorphic mappings in the Hilbert ball
• Finite element modeling of frequency-dependent material damping using augmenting thermodynamic fields
• Closed-Form Solutions and the Eigenvalue Problem for Vibration of Discrete Viscoelastic Systems
• LINEAR DAMPING MODELS FOR STRUCTURAL VIBRATION
• Qualitative dynamic characteristics of a non-viscously damped oscillator
• Mean Value Theorems for Vector Valued Functions
• Variational Principles in Irreversible Thermodynamics with Application to Viscoelasticity

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