General response of viscoelastic systems modelled by fractional operators

DOI10.1016/0016-0032(88)90086-5zbMath0648.73018OpenAlexW1995185918MaRDI QIDQ1105402

Joseph Padovan, Yue Hua Guo

Publication date: 1988

Published in: Journal of the Franklin Institute (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0016-0032(88)90086-5

zbMATH Keywords

hypergeometric functionsexponential functionsgeneralized inverseasymptotic characteristicsarbitrary operator ordercombined responseseigenvalue characteristicserror-complementary errorfractionalized Maxwell- Kelvin-Voigt type viscoelastic system responsesgeneralized harmonic- type spectral excitationsimpulse-transient behaviorimpulse-transient-mixed solution propertiesincomplete gamma-functionsLaplace transfommixed order formulationsnonlinear characteristics of fractional operatorsRiemann-Liouville differential formulationsteady responses

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) (74D99) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70) Integral, integro-differential, and pseudodifferential operators (47Gxx)

Related Items (7)

Dynamic Optimization for Vibration Systems Including Hydraulic Engine Mounts ⋮ Application of numerical inverse Laplace transform algorithms in fractional calculus ⋮ A general result on non-existence of finite-time stable equilibria in fractional-order systems ⋮ A generalised fractional derivative approach to viscoelastic material properties measurement ⋮ Physical and geometrical interpretation of fractional operators ⋮ Multi-objective optimization of distributed-order fractional damping ⋮ HEREDITARY EFFECTS OF EXPONENTIALLY DAMPED OSCILLATORS WITH PAST HISTORIES

Cites Work

• Asymptotic steady state behavior of fractionally damped systems
• Numerical analysis of discrete fractional integrodifferential structural dampers
• Computational algorithms for FE formulations involving fractional operators
• L'intégrale de Riemann-Liouville et le problème de Cauchy
• Harmonic Dispersion Analysis of Incremental Waves in Uniaxially Prestressed Plastic and Viscoplastic Bars, Plates, and Unbounded Media
• What is the Laplace Transform?
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