Vibration Mode Analysis of Frames by the Method of Reverberation Ray Matrix
Vibration Mode Analysis of Frames by the Method of Reverberation Ray Matrix
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DOI：
10.1115/1.3147127
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发表时间：
2009-10
期刊：
影响因子：
--
通讯作者：
F. Miao;Guojun Sun;Y. Pao
中科院分区：
文献类型：
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作者：
F. Miao;Guojun Sun;Y. Pao
混响射线矩阵（MRRM）方法是（Pao et al. 1999，“平面桁架和框架的动力响应和波传播”，AIAA J. 37(5), pp. 594-603）最近基于波传播理论发展起来的，用于桁架或框架结构的瞬态分析。在本研究中，采用MRRM来获得框架在单位冲击荷载作用下位移的频响函数（FRF）。框架的固有频率由频响函数确定，因为频响函数曲线在接近谐振频率时出现峰值。从MRRM控制方程的系数矩阵的伴随矩阵中提取振动模态。MRRM比数值方法，如有限元法（FEM）有优势，因为在MRRM中，框架被视为多连接梁的组合，并且采用梁微分方程的精确解来得到框架的系统矩阵。因此得到的振动模态是精确的。对由17根铝棒组成的平面框架进行了分析。在前几个模态上，MRRM计算得到的振动模态和固有频率与ANSYS有限元计算结果吻合较好；然而，当检测高阶模态时，两种方法之间的频率差异变得有点明显。
The method of reverberation ray matrix (MRRM) has been developed by (Pao et al. 1999, "Dynamic Response and Wave Propagation in Plane Trusses and Frames, " AIAA J., 37(5), pp. 594-603) recently based on the theory of wave propagation for transient analysis of truss or frame structures. In this study, the MRRM is employed to obtain the frequency response function (FRF) of displacement of a frame under the action of a unit impulse load. The natural frequencies of the frame are determined from the FRF, since the curve of FRF has peak when a resonant frequency is approached. The vibration mode is retrieved from the adjoint matrix of the coefficient matrix of the governing equations of MRRM. The MRRM has advantage over numerical methods, such as finite element method (FEM), since in MRRM the frame is treated as an assembly of multiconnected beams, and exact solutions to the beam differential equations are employed to yield the system matrix of the frame. The vibration mode obtained is therefore exact. A planar frame made of 17 aluminum bars is analyzed. The vibration modes, as well as natural frequencies obtained from MRRM, coincide accurately with those obtained from FEM of ANSYS for the first a few modes; however, the difference of the frequencies between the two methods becomes a bit obvious when high order modes are examined.