Analytical solution for free vibration of Timoshenko beam with different modulus
Received date: 2017-05-08
Online published: 2019-12-31
杨洋, 姚文娟 . 不同模量铁木辛柯梁的自由振动特性分析[J]. 上海大学学报(自然科学版), 2019 , 25(6) : 978 -989 . DOI: 10.12066/j.issn.1007-2861.1976
Free vibration of a beam with different modulus in tension and compression was studied. Unit body under a pure shear condition with different modulus in tension and compression was used to derivean expression of shear elasticity modulus with variational elasticity modulus. Based on elastic mechanics, structural mechanics, and the theory of different modulus, a vibration differential equation of Timoshenko Beam and Euler-Bernoulli beam is established, and the free vibration frequency of a simply supported Timoshenko Beam calculated. Considering different modulus, the position of neutral axis have a step change in the period of vibration, making the principle mode function piecewise. The results indicate that different modulus of a material has a great influence on the natural frequency of beam, which induces decrease in then at ural frequencies and therefore is worth consideration in structural vibration.
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