A Discrete Model for Transverse Vibration of a Cantilever Beam Carrying Multi Lumped Masses: Analogy with the Continuous Model

The purpose of the present paper is to make the analogy between a physically discrete model and a continuous model for non-constrained linear transverse vibrations of cantilever beams carrying multi lumped masses. The discrete model is an N-degree of freedom system made of N masses placed at the ends of solid bars connected with spiral springs. Calculations are made based on the classical vibration model involving the mass matrix [

m

ij

] and the linear rigidity matrix [

k

ij

]. The boundary conditions at the free ends are taken into account using the fact that no flexural rigidity is present at the bar located at the free end. The clamped end condition is taken into account using a spiral spring with a very high rigidity. The numerical results show a good convergence of the first and second linear frequencies obtained by the discrete model and those obtained via the Dunkerley second formula.