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Structural Engineering and Mechanics Volume 69, Number 3, February10 2019 , pages 283-291 DOI: https://doi.org/10.12989/sem.2019.69.3.283 |
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Analytical solution for free vibration of multi-span continuous anisotropic plates by the perturbation method |
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Jiepeng Liu, Liang Cao and Y. Frank Chen
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| Abstract | ||
| Accurately determining the natural frequencies and mode shapes of a structural floor is an essential step to assess the floor\'s human-induced vibration serviceability. In the theoretical analysis, the prestressed concrete floor can be idealized as a multi-span continuous anisotropic plate. This paper presents a new analytical approach to determine the natural frequencies and mode shapes of a multi-span continuous orthotropic plate. The suggested approach is based on the combined modal and perturbation method, which differs from other approaches as it decomposes the admissible functions defining the mode shapes by considering the intermodal coupling. The implementation of this technique is simple, requiring no tedious mathematical calculations. The perturbation solution is validated with the numerical results. | ||
| Key Words | ||
| perturbation method; multi-span continuous anisotropic plate; intermodal coupling; natural frequencies | ||
| Address | ||
| Jiepeng Liu and Y. Frank Chen: 1) School of Civil Engineering, Chongqing University, Chongqing, China 2) Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China Liang Cao: 1) School of Civil Engineering, Chongqing University, Chongqing, China 2) Postdoctoral Research Station, School of Civil Engineering, Chongqing University, Chongqing 400045, China 3) Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China | ||