粘弹性框架瞬态响应的回传波射矩阵法研究

文章将应用于弹性杆系结构动态响应的回传波射矩阵法扩展应用于粘弹性框架的瞬态问题的求解。回传波射矩阵法在应用于弹性结构时,为了避免频域里矩阵求逆的奇异性,求解时对矩阵(I-R)-1采用牛曼级数展开;对于粘弹性结构,由于有粘性阻尼,所以不存在奇异性问题,不需用级数展开。文中用单根悬臂梁的例题和9根杆的框架的例题验证了回传波射矩阵法解粘弹性结构的精确性和计算效率。

Transient response of viscoelastic frames with the method of reverberation ray matrix

The reverberation ray matrix method for analyzing dynamic response of elastic trusses or frames is extended and used to solve the transient response of frames made of viscoelastic bars.Originally for the solution of elastic structure the matrix(I-R)-1 is expanded into Neumann series to circumvent the difficulty of singularity in reversing the matrix in the frequency domain.However,it is not necessary to expand this matrix since there is no singularity problem for viscoelastic frames due to visco-damping.The accuracy and effectiveness of applying the reverberation ray matrix method is verified by two examples:a cantilever bar subjected to the step-like axial load and a viscoelastic frame made of nine members,which is also subjected to the step-like load.