Free vibration analysis of elastically connected multiple-beams with general boundary conditions using improved Fourier series method

摘要

Lots of dynamic systems in science and engineering can be simplified as the elastically connected multiple-beams, such as carbon nano tubes and pipes. However, in the majority of current study, just translational spring is considered on beam coupling interfaces. As we know that, not only the translation but also the rotational deformation will occur during beam bending problem. In this work, general beam vibration model is established, in which both two types of translational and rotational springs are taken into account for the coupling interface and both ends. An improved Fourier series is employed for the vibration displacement description for each beam, in which the additional terms are introduced to meet the continuity requirement when the constructed expression is used as the admissible functions. Modal parameters can be determined through the application of Rayleigh-Ritz procedure to the system energy formulation. The current model is then validated through the comparison with those from other analytical approach in open literature. The results show that the current model can made efficient and accurate prediction on the modal property of such complex beam system. The effect of rotational spring on the modal characteristics is also emphasized.