Civil Engineering |
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Free vibration analysis of concrete beams with corrugated steel webs based on Zig-zag theory |
Lin-yuan HU1( ),Wei-qiu CHEN1,Zhi-cheng ZHANG2,Rong-qiao XU2,*( ) |
1. School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China 2. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China |
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Abstract Concrete beams with CSWs were idealized as sandwich beams with an orthotropic core, according to the characteristics of the corrugated steel web (CSW). The assumptions of a zig-zag displacement and a layer-wise parabolic distribution of the transverse shear stress were introduced to derive the governing equations for the free vibration of concrete beams with CSWs based on the variational principle of mixed energy. The transverse shear stress in the developed theory satisfied the traction-free condition at both top and bottom surfaces of the beam, as well as the continuity condition at the interfaces between adjacent layers. The shear correction factor is therefore not necessary. The frequency equation of the beam with CSWs was derived and solved analytically for the frequencies and corresponding mode shapes under various boundary conditions. Comparisons with other methods indicate that the present theory can accurately predict the dynamic behavior of such beams.
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Received: 07 January 2018
Published: 04 March 2019
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Corresponding Authors:
Rong-qiao XU
E-mail: hulinyuan@zju.edu.cn;xurongqiao@zju.edu.cn
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基于Zig-zag理论的波形钢腹板梁自由振动分析
根据波形钢腹板梁的特点,将波形钢腹板梁模拟为具有正交各向异性层的夹芯梁,并引入层间连续的Zig-zag位移假设和分层抛物线分布的横向切应力假设,基于混合能变分原理,建立波形钢腹板梁自由振动的Zig-zag理论. 该理论的横向切应力满足上、下表面为0以及层间连续条件,因此无需引入剪切修正系数. 导出波形钢腹板梁的频率方程,得到不同边界条件下的频率和振型. 与其他方法的对比表明该理论能够精确地预测波形钢腹板梁的动力学特性.
关键词:
波形钢腹板,
Zig-zag理论,
混合能变分原理,
自由振动,
频率,
振型
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