Abstract:

This article presents large deflection data for prismatic (unvarying cross section across length) and non-prismatic (tapered, i.e. varying cross section across length) cantilever beams subjected to concentrated tip loads using the finite element method for different taper ratios. The approximate nonlinear solution is derived from the perspective of a polynomial function. The tapered beams that correlate to the nonprismatic cantilever beams have different widths, depths, and diameters. Using the aforementioned large displacement data that have been analysed, a very simple approach is used to evaluate the large amplitude first mode frequency for the cantilever beam with (nonprismatic) tapered and without (prismatic) tapered. The current approach can be used effectively to find accurate results with far less computer capacity as compared to other methods available in the literature. The difference between the current findings and the bibliographic data is shown. The major goal of this work is to contribute to the simple description of polynomial functions for large amplitude first mode free vibration frequency problems with and without tapered beams in terms load parameter(𝜆) versus tip slope (𝛼)and tip amplitude(𝑎/𝐿). Large amplitude first mode frequency (𝛺) increases with tip slope(𝛼). This indicates that the prismatic and non-prismatic cantilever beams exhibit hardening type nonlinearity. At a particular tip slope(𝛼), the diameter taper shows higher frequency than other tapered beams and uniform beams. According to current studies, it can be restricted to a lower range of tip slope(𝛼)or amplitude(𝑎/𝐿).

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