Mathematical modeling of flexible beam- A comparative study

In this paper, the complete development and analysis of two approaches on mathematical modeling of flexible beam are presented. The mathematical modeling of flexible beam is done using Euler Newton method combined with Assumed Mode Method (AMM) as well as Lagrangian technique in conjunction with AMM. The first model is derived based on Timoschenko beam theory whereas second model is based on Euler Bernoulli beam theory. A bang-bang torque is applied as an input and the dynamic response of the system is investigated. A comparative assessment is presented for validation of the models characterizing the manipulator system, in both time and frequency domain. Performances of the models were evaluated with the manipulator theoretical natural frequencies obtained analytically. The proposed study can be used for the design and development of model based controllers in future.