6533b7d7fe1ef96bd12685ba
RESEARCH PRODUCT
On the dynamics of non-local fractional viscoelastic beams under stochastic agencies
Mario Di PaolaGioacchino AlottaGiuseppe FaillaFrancesco Paolo Pinnolasubject
Materials scienceDiscretization02 engineering and technologyWhite noiseIndustrial and Manufacturing Engineering0203 mechanical engineeringFractional viscoelasticityComposite materialImpulse responseNon local Timoshenko beamMechanical EngineeringMathematical analysisEquations of motionWhite noise021001 nanoscience & nanotechnologyPhysics::History of PhysicsNon local Timoshenko beam; Fractional viscoelasticity; White noise; State variable expansionFractional calculusNumerical integration020303 mechanical engineering & transportsMechanics of MaterialsStress resultantsFrequency domainCeramics and CompositesState variable expansionSettore ICAR/08 - Scienza Delle CostruzioniFractional viscoelasticity Non local Timoshenko beam State variable expansion White noise0210 nano-technologyNon local Timoshenko beam Fractional viscoelasticity White noise State variable expansiondescription
Abstract Non-local viscoelasticity is a subject of great interest in the context of non-local theories. In a recent study, the authors have proposed a non-local fractional beam model where non-local effects are represented as viscoelastic long-range volume forces and moments, exchanged by non-adjacent beam segments depending on their relative motion, while local effects are modelled by elastic classical stress resultants. Long-range interactions have been given a fractional constitutive law, involving the Caputo's fractional derivative. This paper introduces a comprehensive numerical approach to calculate the stochastic response of the non-local fractional beam model under Gaussian white noise. The approach combines a finite-element discretization with a fractional-order state-variable expansion and a complex modal transformation to decouple the discretized equations of motion. While closed-form expressions are derived for the finite-element matrices associated with elastic and fractional terms, fractional calculus is used to solve the decoupled equations of motion, in both time and frequency domain. Remarkably, closed-form expressions are obtained for the power spectral density, cross power spectral density, variance and covariance of the beam response along the whole axis. Time-domain solutions are obtained by time-step numerical integration methods involving analytical expressions of impulse response functions. Numerical examples show versatility of the non-local fractional beam model as well as computational advantages of the proposed solution procedure.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-01-01 | Composites Part B: Engineering |