Vibration and instability analysis of fluid-conveying nanotubes resting on viscoelastic foundation
Based on Hamiltons principle and nonlocal elastic theory,the vibration differential equation of the system was established for investigating the vibration instability of clamped-clamped carbon nanotubes(CNTs)conveying fluid under longitudinal magnetic field resting on viscoelastic foundation.The Kelvin-Voigt and Maxwell linear solid types of viscoelastic foundations were utilized to model the interaction be-tween CNTs and surrounding viscoelastic medium.The resulting equations of motion were transformed to a general eigenvalue problem by applying the differential quadrature method(DQM).Results show the longi-tudinal magnetic field effects increase the natural frequency,thus makes the system more stable.However nonlocal parameter reduce system stiffness,making the system more prone to divergent instability.Specifically,this study showed different foundation models are used for viscoelastic foundations,and there are differences interaction between nanotubes and surrounding viscoelastic medium.For Kelvin-Voigt model increasing in damping coefficients reduces system stability,while the increase in elastic coeffi-cient enhances system stability.For Maxwell model exhibits a"first up then down"effect on system stabili-ty with the increase of damping and elastic parameters.
carbon nanotubedivergence instabilityKelvin-Voigt modelMaxwell modellongitudinal magnetic field
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