Search results for "Euler–Bernoulli beam"

showing 3 items of 3 documents

Fractional visco-elastic Euler–Bernoulli beam

2013

Abstract Aim of this paper is the response evaluation of fractional visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads. Starting from the local fractional visco-elastic relationship between axial stress and axial strain, it is shown that bending moment, curvature, shear, and the gradient of curvature involve fractional operators. Solution of particular example problems are studied in detail providing a correct position of mechanical boundary conditions. Moreover, it is shown that, for homogeneous beam both correspondence principles also hold in the case of Euler–Bernoulli beam with fractional constitutive law. Virtual work principle is also derived and applied to some c…

Constitutive equationVirtual work principleCurvatureFractional calculuViscoelasticityQuasi-static problemsVisco-elastic beamMaterials Science(all)Euler-Bernoulli beamModelling and SimulationGeneral Materials ScienceVirtual workBoundary value problemMathematicsApplied MathematicsMechanical EngineeringMathematical analysisFractional calculusCondensed Matter PhysicsFractional calculusClassical mechanicsMechanics of MaterialsQuasi-static problemModeling and SimulationEuler–Bernoulli beamBending momentCylinder stressSettore ICAR/08 - Scienza Delle CostruzioniInternational Journal of Solids and Structures
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Stochastic Response Of Fractionally Damped Beams

2014

Abstract This paper aims at introducing the governing equation of motion of a continuous fractionally damped system under generic input loads, no matter the order of the fractional derivative. Moreover, particularizing the excitation as a random noise, the evaluation of the power spectral density performed in frequency domain highlights relevant features of such a system. Numerical results have been carried out considering a cantilever beam under stochastic loads. The influence of the fractional derivative order on the power spectral density response has been investigated, underscoring the damping effect in reducing the power spectral density amplitude for higher values of the fractional de…

PhysicsCantileverEuler-Bernoulli beam Fractional constitutive law Power spectral densityMechanical EngineeringMathematical analysisAerospace EngineeringSpectral densityOcean EngineeringStatistical and Nonlinear PhysicsCondensed Matter PhysicsEuler–Bernoulli beam fractional constitutive law power spectral densityFractional calculusSystem dynamicsTerm (time)AmplitudeNuclear Energy and EngineeringControl theoryFrequency domainSettore ICAR/08 - Scienza Delle CostruzioniExcitationCivil and Structural Engineering
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On the moving load problem in beam structures equipped with tuned mass dampers

2017

This paper proposes an original and efficient approach to the moving load problem on Euler–Bernoulli beams, with Kelvin–Voigt viscoelastic translational supports and rotational joints, and in addition, equipped with Kelvin–Voigt viscoelastic tuned mass dampers (TMDs). While supports are taken as representative of external devices such as grounded dampers or in-span supports with flexibility and damping, the rotational joints may model rotational dampers or connections with flexibility and damping arising from imperfections or damage. The theory of generalised functions is used to treat the discontinuities of the response variables, which involves deriving exact complex eigenvalues and eigen…

Rotational joint02 engineering and technologyMoving load01 natural sciencesViscoelasticityDamper0203 mechanical engineeringDeflection (engineering)Control theoryTuned mass damper0103 physical sciencesTime domain010301 acousticsPhysicsbusiness.industryMechanical EngineeringCharacteristic equationMoving loadStructural engineeringCondensed Matter PhysicsTuned mass damper020303 mechanical engineering & transportsMechanics of MaterialsEuler–Bernoulli beamTranslational supportbusinessBeam (structure)Meccanica
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