Free vibration analysis of a monosymmetric open section euler-bernoulli beam by means of two different methods

Abstract

In this paper, coupled flexural-torsional free vibration of a monosymmetric open section Euler-Bernoulli beam is studied by using two different methods, i.e. the dynamic transfer matrix method (DTMM) and the finite element method (FEM). The natural frequencies obtained from the FEM are observed to be closer to the exact values compared to the DTMM, since the beam deformation functions selected in the FEM have the same form as the real deflection curve of beam has. When the two methods are compared in terms of cpu time, the DTMM requires less computation time to yield reasonably accurate natural frequencies. This advantage of the DTMM is mainly due to the size of the transfer matrix, which remains unchanged independent of the number of elements while the size of coefficient matrix leading to the characteristic equation in the FEM increases with increasing element number. In addition, the mode shapes obtained from the DTMM are found to be satisfactorily accurate. Moreover, the DTMM requires less algebra to derive the transfer matrix. It is concluded that the DTMM, due to its advantages mentioned above, would be superior to the FEM especially in handling lattice type structures.