Large amplitude free vibrations of a uniform cantilever beam carrying an intermediate lumped mass and rotary inertia

This work is concerned with the non-linear period, for each of the first four modes, of planar, flexural large amplitude free vibrations of a slender, inextensible cantilever beam carrying a lumped mass with rotary inertia at an intermediate position along its span. Following the analysis carried out in reference [1] on a similar class of beam system, the shear deformation and rotary inertia are assumed to be negligible, while account is taken of axial inertia, non-linear curvature and the inextensibility condition, and an assumed single-mode Lagrangian method is used to form directly the third order non-linear unimodal temporal problem. Because of the strong non-linear terms in the temporal problem, the two-term harmonic balance (27HB) method is used to obtain an approximate solution to the period of oscillation. The 2THB results are compared, for some selected values of sytem parameters, to those obtained by using single term harmonic balance (STHB) and to those obtained by numerical integration of the temporal problem. Results in non-dimensional forms are presented graphically, for each of the first four modes, for the effect of position and magnitude of the mass and rotary inertia of the attached element on the variation of period of oscillation with amplitude. (C) 1997 Academic Press Limited.