Stochastic Description of a Slender Cantilever Beam Carrying a Lumped Mass Axially Excited by a Shaker

A detailed theoretical investigation into the single-mode approximate response of a slender cantilever beam carrying a lumped mass axially excited by a shaker, where, the narrow-band random excitation characters to feature the very weak fluctuation in frequency of the excitation are taken into consideration, is presented. The method of multiple scales is used and the stochastic jump has been investigated for the principal parametric resonance of the system by using the stationary joint probability by using finite difference method. For the force-response domain, there is a region of excitation acceleration within which the joint probability density has two peaks: an outer flabellate peak and a central volcano peak. Results show that the outer flabellate peak decreases while the central volcano peak increases as the value of the excitation acceleration decreases.