FORCED VIBRATIONS AND STABIITY OF AN ELASTICALLY RESTRAINED TAPERED BEAM

The objective of this paper is to present results for the nonlinear forced vibrations of an elastically restrained tapered beam due to a periodic excitation. The restrained end of the beam is modelled by a torsional spring and a translational spring. Also, the excitation force will be applied to the tapered beam by two methods; concentrated load and a distributed load with a given excitation frequency at which the latter case simulate an interesting application when a gust wind applied on a high rise building. The method of harmonic balance will be used to study the steady state frequency response of the beam under the two excitation methods and for different values of physical parameters such as the root translational and rotational stiffness and the beam taper ratio. Results for the forced vibrations will be presented for the first three modes of vibration as well as the dynamic behaviour of the beam system, i.e. the softening or hardening behaviour.