Author : Nitesh Bandewar and Sanjay Deshpande

Cantilever structures are found in almost all engineering branches and in practise. A tall chimney, a dead end of a piping system, aircraft wing, heat exchanger fins or a tall multi-storeyed building in civil engineering and several components in mobile system and aerospace system can also be treated at a first hand as one end fixed and other free kind of configurations. We also find that recently in nanotechnology typically the new technologies such as photostrictive materials are usually tested on standard configurations so as to know the effect on the original structure. FEA plays a very important role in the overall mechanical design process. It has been applied successfully to almost all kinds of problems, which range from statics to dynamics. Although we find lot of literature on static analysis with respect to verification and validation of result, this is not always the case with respect to dynamic problems in frequency and time domain due to complexity of physics and numeric. The man motive in this work is to consider a cantilever structure model such that the frequencies vary from few Hz to MHz range and analyse the natural frequency calculation accuracy on a given mesh. We show that the FEA results deviates much from exact solution for natural frequency calculations. This means if a user is to consider a selected frequency of interest and if that is not captured by FEA then suitable element and mesh has to be considered rather than a blind use of FEA software. It is expected that the users will benefit from the understanding we had from this work.

Keywords: FEA, Jacobian, Beam model,natural frequency,BEM,CAE,TRAI3,TETRA,PENTA, photostrictive, etc.