Quasi-static and dynamical analysis for viscoelastic Timoshenko beam with fractional derivative constitutive relation

DOI10.1007/BF02437724zbMath1141.74340OpenAlexW2061631421MaRDI QIDQ1611479

Genguo Li, Zheng-You Zhu, Chang-Jun Cheng

Publication date: 21 October 2002

Published in: Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02437724

zbMATH Keywords

dynamical responseweakly singular Volterra integro-differential equationfractional derivative constitutive relationviscoelastic Timoshenko beam

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics (74H10) Vibrations in dynamical problems in solid mechanics (74H45)

Related Items (12)

A contour method for time-fractional PDEs and an application to fractional viscoelastic beam equations ⋮ Two approaches for studying the impact response of viscoelastic engineering systems: an overview ⋮ Fractional visco-elastic Timoshenko beam deflection via single equation ⋮ A locking-free finite element formulation for a non-uniform linear viscoelastic Timoshenko beam ⋮ Quasi-static analysis for viscoelastic Timoshenko beams with damage ⋮ Some remarks on a new DQ-based method for solving a class of Volterra integro-differential equations ⋮ Positive solution of singular boundary value problem for a nonlinear fractional differential equation ⋮ Fractional viscoelastic beam under torsion ⋮ Positive solution of a nonlinear fractional differential equation involving Caputo derivative ⋮ Time depended deformation and buckling of viscoelastic thick plates by a fully discretized finite strip method using third order shear deformation theory ⋮ Dynamical behavior of nonlinear viscoelastic Timoshenko beams with damage on a viscoelastic foundation ⋮ Vibrations suppression of fractionally damped plates using multiple optimal dynamic vibration absorbers

Cites Work

• Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass systems
• Dynamical behavior of nonlinear viscoelastic beams
• Applications of Fractional Calculus to the Theory of Viscoelasticity
• The mixed finite element method for the quasi-static and dynamic analysis of viscoelastic timoshenko beams
• On the Fractional Calculus Model of Viscoelastic Behavior
• Numerical Inversion of a Laplace Transform
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