Vibration Analysis of Beams with Arbitrary Elastic Boundary Conditions
In this paper, one newly developed method named the Improved Fourier Series method is applied to the vibration analysis of a beam elastically supported at the both end. The flexural displacement of the beam is supposed to be one set of Fourier Series coupled with four appended terms. Based on the Rayleigh-Ritz procedure and and the vibration characteristics of the beam are also acquired by solving these two matrices. In the end, the frequencies calculated are also compared with those from references and Results ar the Hamilton’s equation, the mass matrices and the stiffness matrices of the beam are obtained e all proved excellent.
B. L. Lv et al., "Vibration Analysis of Beams with Arbitrary Elastic Boundary Conditions", Applied Mechanics and Materials, Vols. 66-68, pp. 1325-1329, 2011