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# Free and forced vibration of a kinked cantilever beam

Reddy, BS and Simha, KRY and Ghosal, A (1999) Free and forced vibration of a kinked cantilever beam. In: ASME 1999 Design Engineering Technical Conferences, DETC 1999, 12-16 Sep 1999, Las Vegas; United States, pp. 169-177.

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Official URL: https://doi.org/10.1115/DETC99/VIB-8251

## Abstract

In this paper we use the assumed modes method to derive an analytical model of a kinked cantilever beam of unit mass carrying a kink mass (mk) and a tip mass(mt). The model is used to study the free and forced vibration of such a beam. For the free vibration, we obtain the mode shape of the complete beam by solving an eight order polynomial whose coefficients are functions of the kink mass, kink angle and tip mass. A relationship of the form f+(mk, mt, Î´)= mk + mt, (4+10/3 cosÎ´ cosd + 2/3 cos2 Î´)= constant appears to give the same fundamental frequency for a given kink angle, 5, and different combinations of kink mass and tip mass. To derive the dynamic equations of motion, the complete kinked beam mode shape is used in a Lagrangian formulation. The equations of motion are numerically integrated with a torque applied at the base and the tip response for various kink angles are presented. The results match those obtained from a traditional finite element formulation. Copyright Â© 1999 by ASME

Item Type: Conference Paper Proceedings of the ASME Design Engineering Technical Conference American Society of Mechanical Engineers (ASME) The copyright of this article belongs to American Society of Mechanical Engineers (ASME) Cantilever beams; Equations of motion; Nanocantilevers, Assumed modes method; Dynamic equations of motion; Finite element formulations; Free and forced vibrations; Free vibration; Fundamental frequencies; Lagrangian formulations; Order polynomials, Vibrations (mechanical) Division of Mechanical Sciences > Mechanical Engineering 12 Mar 2021 16:04 12 Mar 2021 16:04 http://eprints.iisc.ac.in/id/eprint/68263

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