Equivalent rigidity method for estimating the natural frequency of telescopic cantilever beams

Telescopic cantilever beams have several applications in industry. When a cantilever with self–weight and tip mass is subjected to free vibrations the natural frequency of the system can be quantified with two methods of Finite Element Analyses and experiments. This paper builds on the state–of–the–art to establish an alternative analytical method. Abraham, Sivaloganathan and Rees have established that a telescopic cantilever exhibits Hookean behaviour within the elastic limits. Based on this finding a simple equivalent cantilever with equivalent rigidity derived from the load–deflection behaviour is established. The equivalent beam is then considered for estimating the natural frequency of the telescopic cantilever. A telescopic cantilever with two sections was considered. Using the concept of equivalent rigidity, the natural frequencies were calculated and the results compared with those obtained from Finite Element Analysis using Abaqus software. The close agreement between formulation and FEA verified the adequacy of the suggested method.