Size-dependent vibrational behavior of embedded spinning tubes under gravitational load in hygro-thermo-magnetic fields

Abstract

In the present investigation, with the aim of performance improvement of size-dependent bi-gyroscopic structures, the vibrational behavior of spinning small-scale tunes conveying fluid embedded in various foundations subjected to distributed tangential load and hygro-thermo-magnetic environments by including gravitational effect is investigated. The modified couple stress theory is used to study the microscale tube, and the modified nonlocal theory is utilized to model the nanoscale tubes. A parametric investigation is also conducted to highlight the impacts of various key factors such as gravity, flow profile modification factor, fluid velocity, spinning speed, substrate coefficients, boundary conditions, size-dependent parameters, and environmental attacks on divergence and flutter thresholds of the structure. The dynamical equations are solved using Laplace transformation as well as Galerkin discretization techniques, and forward and backward frequencies are identified accordingly. Meanwhile, the instability borders of the system are obtained analytically. Campbell and stability diagrams, and the time history of the system, are acquired. The results revealed that contrary to influences of gravity, magnetization, and size-dependent parameters, the compressive tangential load and humidity have decreasing effects on the vibrational frequencies and make the system prone to experience static and dynamical instabilities. Moreover, it is determined that applying the viscous foundation eliminates the re-stabilization zone in the system stability evolution, and after the occurrence of the divergence phenomenon, the system immediately undergoes the flutter instability.

The effects of the elastic foundations on the frequency of the viscoelastic FG porous doubly-curved macro/nanosize shell subjected to hygro-thermo-magnetic fields using a novel quasi-3D shell theory

“…where a mn and v mn are the damping parameters and the damped vibration frequency, respectively. By inserting equation (25) into equations (23a)-(23f), the governing equations of motion of the viscoelastic FG porous doubly-curved panel rested on the foundation are obtained as below:…”

“…Zhu et al 24 analyzed the vibration behavior of rotating FG nanotubes conveying fluid in the magnetic fields. Lingling et al 25 investigated the size-dependent vibration of nanotubes with spin motion in magneto-hygro-thermal environments. Dindarloo and Zenkour 26 studied the dynamics of FG nanoshells in thermal fields based on the nonlocal strain gradient theory.…”