Free vibration analysis of Euler-Bernoulli beams under non-classical boundary conditions

João Fernandes da Silva¹; Lucas Allende Dias do Nascimento¹; Simone dos Santos Hoefel¹

¹ Universidade Federal do Piauí

doi:10.20906/CPS/CON-2016-1053

Resumo

The flexible beams carrying attachments often appear in engineering structures, modal analysis of those structures is important and necessary in structural design. The analysis of vibrating beams with ends elastically restrained against rotation and translation or with ends carrying concentrated masses or rotational inertias is of great interest in a variety of practical cases. In this analysis, the governing differential equations of the beam, which is a partial differential equation with variable coefficients, and that of the mass-spring system, which is an ordinary differential equation, are found. The exact solution of the problem is then obtained using non-classical boundary conditions and the eigenvalues and eigenfunctions are obtanied. Finally, some cases with available results in the literature are presented and analyzed.

Palavras-chave: Euler-Bernoulli beam; Non-classical boundary conditions; Natural frequencies