Stability and Dynamics of a Slightly Curved Viscoelastic Pipe Resting on Linear and Nonlinear Viscoelastic Foundation: Fid-Bau Portal

Stability and Dynamics of a Slightly Curved Viscoelastic Pipe Resting on Linear and Nonlinear Viscoelastic Foundation

Oyelade, Akintoye O. / Ikhile, Osamudiamen G. / Oyediran, Ayo A.

Stability and nonlinear dynamics of slightly curved viscoelastic pipe conveying fluid resting on linear and nonlinear viscoelastic foundations is investigated. The dissipation of the pipe material is modelled using the Kelvin–Voigt scheme. The equation of motion was derived using Hamilton’s principle. Three different trigonometry initial curvatures were considered corresponding to simply supported, clamped simply supported and clamped–clamped boundary conditions. Eigenfunction expansion method was employed to change the partial differential equation of motion to modal ordinary differential equations. The first four modes were considered and solved for natural frequency. The linear natural frequency analysis shows that an increase in viscoelasticity coefficient reduces the natural frequency for all the boundary conditions considered. An increase in viscoelasticity coefficient eliminates coupled mode flutter especially for the third and fourth mode and has no effect on first critical velocity. An increase in initial curvature increases the natural frequency, and the increase is more pronounced for the clamped simply supported boundary condition. The linear stiffness increases the critical velocity and natural frequency of the pipe. Bifurcation diagrams and phase plane plots are presented for various boundary conditions. Chaotic motions are observed without viscoelasticity but are dampened out as increase in viscoelasticity coefficient.