Stability of an extensible rotating rod

Biointerface dynamics – Multi scale modeling considerations

“…These changes have been expressed by applying the internal variable theory [37][38][39]. The internal variable theory is a useful tool for considering the system irreversible structural changes.…”

“…The short time free energy changes for the corresponding fractional Kelvin-Voigt model Eqs. (25) and (26) based on modified Atanackovic approach [37] is expressed as: …”

Bifurcation analysis of the rotating axially compressed nano‐rod with imperfections

“…System of equations (7), subject to (8), can be reduced to a single equation, represented by the action of a non-linear operator on deflection y equated with zero. The operator is obtained either as the integro-differential operator of the second order, or as the differential operator of the fourth order.…”

“…The buckling problem of a rotating compressed rod, described by the elastic moment-curvature constitutive equation, is considered in [3,10,17,20], while in [5,7] the rod is allowed to have variable cross section and extensible axis, and in [19] there are additional rigid bodies attached to the rod. Static stability problem of a non-local rotating compressed rod, described by the Eringen stress gradient constitutive model, is studied in [8,9] for the clamped-clamped and clamped-free rod, while in [1] a non-local clamped-free rod rotating about the axis perpendicular to rod's axis is considered.…”