Dynamics of an array formed by three neutrally buoyant cylindrical cantilevers subjected to tensile follower forces

The flexural-rotational coupled motion of three identical flexible cylindrical cantilevers joined symmetrically to a central head is investigated. Effects of the tensile follower forces and inertia parameters on the natural frequencies of the system are studied. The analysis suggests two types of inplane motion: one corresponding to the oscillation of the cantilevers without any rotation of the central body, while the other involves coupled motion of the array. The former corresponds to the repeated eigenvalues which are identical to those of a single cantilever having the same axial tension parameter, P. Three sets of eigenvalues govern the out-of-plane motion: (a) the central head remaining stationary with no rolling motion of the array; (b) vertical motion of the central body without any rolling motion of the array; and (c) rigid body rolling motion without any vertical motion of the central head. There is a possibility of dynamic instability for small inertia parameters and large axial tension.