On the parametric excitation of a Timoshenko beam due to intermittent passage of moving masses: instability and resonance analysis

Abstract

A Timoshenko beam excited by a sequence of identical moving masses is studied as a time-varying problem. The effects of centripetal and Coriolis accelerations besides the vertical component of acceleration of the moving mass are considered. Using Galerkin procedure, the partial differential equations of motion which are derived by Hamilton’s principle are transformed to ordinary differential equations. The incremental harmonic balance method is implemented to determine the boundary curve of instability and other companion curves of resonance in the parameter plane. A new approach for identifying the conditions of resonance is investigated by presenting an intuitive definition of resonance for time-varying systems. The influence of employing different deformation theories on the critical parameter values of stability and resonance curves is studied. The validity of the instability and resonance curves is examined by numerical simulations and also ascertained through comparing with those reported in the literature. © 2014, Springer-Verlag Wien.