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浙江大学学报(工学版)
J4  2009, Vol. 43 Issue (6): 1065-1070    DOI: 10.3785/j.issn.1008-973X.2009.
    
Extension and application of reverberation-ray matrix method to dynamic responses of structures
JIANG Ji-qing1, BAO Yi-xing1,2, CHEN Wei-qiu1
（1. Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China; 2. Key Laboratory of
Soft Soils and Geoenvironmental Engineering of Ministry of Education, Zhejiang University, Hangzhou 310027, China）
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Abstract  

The  reverberation-ray matrix method is suitable for solving complex boundary value problems represented by linear partial differential equations with respect to spatial and temporal variables. However, the formulation is so far confined to the case of external concentrated loads applied at the junctions only. In order to develop the method further, a non-uniform Timoshenko beam subjected to arbitrary distributive loads was considered and the piece-wise uniform model was employed. The formulation within the framework of  reverberation-ray matrix analysis was established based on the general solution of inhomogeneous governing equations obtained by Fourier transform. Numerical results were given and good convergence of the dynamic responses was observed by the increasing number of piece-wise sub-beams. The steady state responses and the early time transient responses were also calculated and compared with other predictions, and good agreement was observed．

Published: 01 June 2009
CLC:  TU311.3  
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Cite this article:

JIANG Ji-Qing, BAO Yi-Xin, CHEN Wei-Qiu. Extension and application of reverberation-ray matrix method to dynamic responses of structures. J4, 2009, 43(6): 1065-1070.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2009.     OR     http://www.zjujournals.com/eng/Y2009/V43/I6/1065


结构动力分析中回传射线矩阵法的扩展与应用

回传射线矩阵法适用于求解包含空间与时间变量的线性偏微分方程组及复杂边界条件问题,但迄今为止回传射线矩阵法仅局限于处理节点处作用集中力情形,对实际结构中常见的分布荷载情况没有涉及.为拓展回传射线矩阵法的应用范围,以非均匀Timoshenko梁为分析对象,结合分段均匀梁模型,利用Fourier变换得到任意分布荷载作用下方程的通解,并基于回传射线矩阵法的基本原理构造了计算列式.给出了算例,分析了不同划分段数下非均匀梁的动力响应,结果表明收敛良好.计算了非均匀梁的稳态响应和早期瞬态响应,与其他方法进行了比较,吻合良好.

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