采用解析方法,研究了带损伤平面桁架结构的静力问题。对于含有n个子结构的平面桁架结构,建立一个与理想桁架结构等价的循环周期结构体系,对其中一个子结构建立控制方程,将杆件损伤处理为方程的荷载项,运用U 变换法对静力学方程组进行解耦,推导出各个节点位移的解析表达式。应用解析表达式分析带一个杆件损伤桁架结构的节点位移,并与无损伤时结构的解相比较,结果显示,有损伤时相关节点位移较无损伤时有所增大,且其位移变化合理,验证了解析表达式的可行性。
This paper presents an analytical static study of the plane truss with rigidity damage. Firstly, an equivalent structure with cyclic periodicity is built. The rigidity damage of the bar can be expressed as an additional loading in the governing equations of a substructure. Then, by using the U-transformation technique, the equations may be uncoupled into independent equations. The nodal displacements are solved in the analytical form. Lastly, a calculation example is taken, and the obtained nodal displacements are compared to the those of a perfect structure. It is shown that the variations of the displacements are reasonable. This paper provides a means for analyzing the influence of the rigidity damage on the plane truss structure.
[1] Nakahira N, Ozawa K, Naruoka M. Vibration of plane trusses by the Newmark method[J]. Computers & Structures, 1990, 37(4): 515-520.
[2] Beskos D E. Dynamics and stability of plane trusses with gusset plates[J]. Computers & Structures, 1979, 10(5): 785-795.
[3] 刘福寿, 金栋平, 陈辉. 环形桁架结构动力分析的等效力学模型[J]. 振动工程学报, 2013, 26(4): 516-521. Liu Fushou, Jin Dongping, Chen Hui. An equivalent mechanics model for the dynamic analysis of hoop truss structures[J]. Journal of Vibration Engineering, 2013, 26(4): 516-521.
[4] 陈建军, 车建文, 陈勇, 等. 基于概率的桁架结构动力分析[J]. 振动与冲击, 2000, 19(1): 64-67. Chen Jianjun, Che Jianwen, Chen Yong, et al. Dynamic characteristic analysis of truss structures based on probability[J]. Vibration and Shock, 2000, 19(1): 64-67.
[5] 马娟, 陈建军, 高伟, 等. 基于模糊因子法的模糊桁架结构动力特性分析[J]. 振动与冲击, 2005, 24(1): 64-67. Ma Juan, Chen Jianjun, Gao Wei, et al. Dynamic characteristic analysis of fuzzy truss structure based on fuzzy factor method [J]. Journal of Vibration and Shock, 2005, 24(1): 64-67.
[6] 林立广, 陈建军, 马娟, 等. 基于区间因子法的不确定性桁架结构动力响应分析[J]. 应用力学学报, 2008, 25(4): 612-615. Lin Liguang, Chen Jianjun, Ma Juan, et al. Dynamic response analysis for uncertainty truss structures with interval factor method[J]. Chinese Journal of Applied Mechanics, 2008, 25(4): 612-615.
[7] 方辉. 基于子结构能量的点阵结构损伤诊断方法研究[J]. 振动与冲击, 2011, 30(8): 12-18. Fanghui. Substructure energy based nondestructive evaluation approach for lattice structures [J]. Journal of Vibration and Shock, 2011, 30(8): 12-18.
[8] 史涌泉. 大型桥梁结构的损伤识别方法研究[D]. 江西: 南昌大学, 2012. Shi Yongquan. Damage identification research for large- scale bridge structures [D]. Jiangxi: Nanchang University, 2012.
[9] 邵云飞. 桁架结构损伤识别方法研究[D]. 兰州: 兰州理工大学, 2007. Shao Yunfei. The research on truss structure damage identification[D]. lanzhou: Lanzhou University of Technology, 2007.
[10] Chan H C, Cai C W, Cheung Y K. Exact analysis of structures with periodicity using U- transformation[M]. Singapore: World Scientific, 1998.
[11] 蔡承武. 旋转周期结构的分析解[J]. 中山大学学报: 自然科学版, 1986, 25(2): 64-72. Cai Chengwu. On analytical solution of rotationally periodic structures[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 1986, 25 (2): 64-72.
[12] Cai C W, Cheung Y K, Chan H C. Transverse vibration analysis of plane trusses by analytical method[J]. Journal of Sound and Vibration, 1989, 133(1): 139-150.
[13] Cheung Y K, Chan H C, Cai C W. Natural vibration analysis of rectangular networks[J]. International Journal of Space Structures, 1988, 3(3): 139-152.
[14] Cai W S, Li Y, Chan H C. Natural vibration analysis of diagonal networks[J]. Structural Engineering and Mechanics, 1998, 6(5): 517-527.
