MDTM is applied for the first time to this problem Verification with finite element model Studying the influence of some parameters on the natural frequencies This research concerns a non-uniform beam with a three dimensional rigid tip mass whose center of gravity is not coincided with the attachment point of the beam and subjected to both torsional and flexural deformations in two orthogonal planes. A semi-numerical method called Multi-Step Differential Transform Method (MDTM) is employed to obtain natural frequencies and mode shapes of the system for two different boundary conditions, i.e. the left end clamped or free. The influence of tip mass dimensions, beam length and taper ratio on the natural frequencies are studied, and the finite element software (ANSYS) is employed to compare the results and confirm the accuracy of the model.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.