Vibrational characteristics of a multi-span beam with elastic transverse supports of different shaped sections

Abstract

Objectives In order to overcome the difficulties caused by boundary and elastic transverse supports in studying the vibrational characteristics of a continuous multi-span beam, this paper establishes an analytical model of the free vibration of a multi-span beam based on the Euler-Bernoulli beam theory.Methods First, a new improved Fourier series form is constructed to represent the lateral displacement function of the multi-span beam over the entire segment. Second, the series expression of the displacement function is substituted into the Lagrangian function and combined with the Rayleigh-Ritz method, and the problem of free vibration is transformed into the form of eigenvalues of a standard matrix. The natural frequencies of an elastically supported multi-span beam can be solved.Results In selected numerical examples, by changing the value of the translational elastic stiffness at the elastic support, the vibrational characteristics of the multi-span beam with any elastic support can be obtained. The feasibility and accuracy of the proposed method are fully verified by a comparison with existing results in the literature.Conclusions Through the numerical simulation of the vibrational characteristics of a multi-span beam based on an Improved Fourier Series Method（IFSM）, this paper provides effective preliminary assessment for the dynamic performance of a multi-span beam.

Keywords

• multi-span beam
• elastic support
• natural frequency
• improved fourier series method (ifsm)