Free vibration of heated Euler-Bernoulli beams with thermal postbuckling deformations

Abstract

Based on the accurate geometrical nonlinear theory for Euler-Bernoulli beams, considering the coupling of the longitudinal and transverse motions, the harmonic responses of small vibration of uniformly heated beams with and without static thermal postbuckling deformations are presented by employing the numerical shooting technique. Characteristic curves of the lower order frequencies versus the temperature parameter are illustrated for pinned-pinned, fixed-fixed, and also pinned-fixed boundary constraints. The numerical results show that all the frequencies of unbuckled beams decrease continuously with the increment of the temperatures rise. However, when the beam is in a postbuckled state, all the lower frequencies increase along with the increment of temperature, except for the third- and the fourth-order frequencies of the pinned-pinned beam.