摘要
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.
The reverberation-ray matrix method is suitable for solving complex boundary value problems re presented 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.
出处
《浙江大学学报（工学版）》
EI
CAS
CSCD
北大核心
2009年第6期1065-1070,共6页
Journal of Zhejiang University：Engineering Science
基金
国家自然科学基金资助项目(1047213010725210)
新世纪优秀人才支持计划资助项目(NCET)
