摘要
基本解是边界元法、格林函数法、基本解法等数值方法必备的理论基础之一.大多问题的基本解已经被推导出来,但杆件结构强迫振动分析的时域基本解未见相关报道.现有方法在求解强迫振动问题时通常采用一定技巧将问题等效为静力问题,并利用静力基本解进行求解,这就增加了列式过程的复杂程度和方法的计算工作量.论文通过振型分解、杜哈梅积分等步骤推导出杆件结构强迫振动分析的时域基本解,该基本解可以直接用于结构的动力响应分析,提高运算效率.论文工作可以为边界元法等数值方法在进行杆系结构强迫振动分析时提供新的思路.
The fundamental solution is one of the basic theories of many numerical analysis methods,such as the boundary element method,the Green's function method,the fundamental solution method,et al.The fundamental solution to most problems has been derived,but the fundamental solutions for forced vibration problem of beam structure in time domain has not been reported.When solving the forced vibration problems,The dynamic problem is converted into a static problem using some techniques in existing methods,and the static problem fundamental solutions will be adopted.These converted techniques will increases the computational complexity and calculation workload.In this paper,the modal decomposition,and the DuHamel's integral be adopted in derived the fundamental solutions for forced vibration of beam structure in time domain.This work can provide a new idea for the numerical method such as boundary element method in forced vibration analysis of the beam structures.
出处
《固体力学学报》
CSCD
北大核心
2014年第S1期9-17,共9页
Chinese Journal of Solid Mechanics
基金
高等学校博士学科点专项科研基金项目(20110172120038)
中央高校基本科研业务费专项资金(2012ZM0090)资助
关键词
时域基本解
杆件结构
强迫振动分析
the fundamental solutions,beam structure,forced vibration
