On the vibration and stability of spinning axially loaded pre-twisted Timoshenko beams

Parametric instability of twisted Timoshenko beams with localized damage

“…The transformation relationships [34] between the inertial and twist coordinates are used to derive Eqs. (2) to (4).…”

“…Following the procedure, previously introduced by the first author [34] for the undamaged twisted beam, the system equations for a twisted Timoshenko beam with localized damage under a time-dependent axial load in the twist frame throughout the domain and the associated boundary conditions (at Z = 0, L) are obtained as follows:…”

“…The explicit form for M and equivalent form for (t) K i can be found in the appendix B of [34]. By replacing E,…”

“…In the next, a finite element method [34] is used to reduce the governing partial differential equations into a set of ordinary differential equations by using the Mindlin-type linear beam element with eight degrees of freedom. The displacement function of the beam element assumes the following form…”

“…The effects of rotational speed, twisted angle and aspect ratio on the natural frequencies and dynamic stability of axially spinning twisted Euler-Bernoulli beams were studied by Tekinalp and Ulsoy [29], and Lee [30], respectively. The vibration and stability behaviors of a spinning twisted Timoshenko beam were analyzed by Liao and Dang [31], Chen and Keer [32] and Chen [33][34] by a finite element method. The influences of twist angles and spinning speed on the natural frequencies and buckling loads were discussed.…”