自复位结构是一种震后不需修复或仅需少量修复即可继续投入使用的新型抗震结构。目前有关自复位结构地震响应的研究多是在确定性激励下进行，鲜有涉及随机激励环境。本文假定地震动加速度过程为金井清过滤白噪声模型，研究了随机地震激励下单自由度自复位体系的平稳响应。应用广义谐波平衡技术分解旗帜形的恢复力，建立与原系统的等效非线性随机系统。通过 Stratonovich-Khasminskii极限定理作随机平均,得到关于幅值的近似一维扩散过程。建立并求解对应的FPK方程，得到关于幅值的稳态概率密度函数并进行参数分析。数值结果表明，能量耗散系数与屈服位移的减小能降低系统响应，同时，随着这两个参数的变化，系统会出现随机P分岔现象。最后，通s过蒙特卡罗数值模拟法验证了解析解的有效性。
Abstract
Self centering structure is a new type of aseismic structure which can be put into use without repair or with only a small amount of repair after earthquake. At present, most of studies on seismic response of self-centering structure are performed under deterministic excitation, and few involve random excitation environment. Here, the stationary response of a single-DOF self-centering system under random seismic excitation was studied, and the acceleration process of the ground motion was assumed to be Kanai-Tajimi filtered white noise model. The generalized harmonic balance technique was used to decompose restoring force of flag shape, and the equivalent nonlinear stochastic system to the original system was established. By means of Stratonovich-Khasminskii limit theorem and stochastic averaging, an approximate one-dimensional diffusion process for amplitude was obtained. The corresponding FPK equation was established and solved, the analytical solution to the steady-state probability density function for amplitude was obtained and this function’s parametric analysis was done. Numerical results showed that decrease in energy dissipation coefficient and yield displacement can reduce response of the system; with variation of these two parameters, the system can have random P-bifurcation phenomenon. Finally, the effectiveness of the analytical solution was verified with Monte Carlo numerical simulation method.
关键词
自复位结构 /
随机振动 /
金井清过滤白噪声激励 /
随机平均法 /
稳态概率密度函数
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Key words
self-centering structure /
random vibration /
Kanai-Tajimi filtered white noise excitation /
stochastic averaging method /
steady state probability density function
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参考文献
[1] 吕西林, 陈云, 毛苑君. 结构抗震设计的新概念——可恢复功能结构 [J]. 同济大学学报, 2011, 39(7):941-948.
Lv X L, Chen Y, Mao Y J. New concept of structural seismic design: earthquake resilient structures [J]. Journal of Tongji University, 2011, 39(7):941-948.
[2] 吕西林, 周颖, 陈聪. 可恢复功能抗震结构新体系研究进展 [J]. 地震工程与工程振动, 2014, 34(4): 130-139.
Lv X L, Zhou Y, Chen C. Research progress on innovative earthquake-resilient structural systems [J]. Earthquake Engineering and Engineering Vibration, 2014, 34(4): 130-139.
[3] 孙玉康, 李启才, 张萍, 等. 自复位钢框架—蝴蝶形钢板剪力墙体系两层结构抗震试验研究 [J]. 振动与冲击, 2020, 39(14):
214-241.
Sun Y K, Li Q C, Zhang P, et al. Experimental aseismic investigation on a two-story self-centering structure equipped with
Butterfly-shaped steel plate shear walls [J]. Journal of vibration and shock, 2020, 39(14): 214-241.
[4] 毕仲君, 胡志强, 王琪, 等. 基于新型自复位摩擦耗能支撑的RC框架结构地震残余变形控制 [J]. 振动与冲击, 2020,
39(15): 95-102.
Bi Z J, Hu Z Q, Wang Q, et al. Seismic residual deformation control for RC frame structures based on a novel self-centering friction damping brace [J]. Journal of vibration and shock, 2020, 39(15): 95-102.
[5] 张艳霞, 黄威振, 刘安然, 等. 自复位免修复摩擦耗能支撑性能研究 [J]. 振动与冲击, 2018, 37(4): 136-176.
Zhang Y X, Huang W Z, Liu A R, et al. A study on the behavior of self-centering and free-repair braces with friction dampers [J].
Journal of vibration and shock, 2018, 37(4): 136-176.
[6] Guo T, Wang J S, Song Y S, et al. Self-centering cable brace with friction devices for enhancing seismic performance of RC frame
structures [J]. Engineering Structures, 2020, 207, 110187.
[7] Li J L, Wang W, Qu B. Seismic design of low-rise steel building frames with self-centering panels and steel strip braces [J].
Engineering Structures, 2020, 216.
[8] Christopoulos C. Frequency response of flag-shaped single degree-of-freedom hysteretic systems [J]. Journal of Engineering
Mechanics, 2004, 130(8): 894-903.
[9] Liu M, Zhou P, Li H. Novel self-centering negative stiffness damper based on combination of shape memory alloy and prepressed
springs [J]. Journal of aerospace engineering, 2018, 31(6): 1-106.
[10] 胡晓斌，江卫波. 自复位单自由度体系随机地震响应分析 [J]. 振动与冲击, 2016, 35: 152-157.
Hu X B, Jiang W B. A random seismic response analysis of self-centering SDOF systems [J]. Journal of vibration and shock, 2016, 35: 152-157.
[11] Wu Y, Zhu W Q. Stationary response of multi-degree-of-freedom vibro-impact systems to Poisson white noises [J]. Physics Letter
A, 2008, 372(5): 623-630.
[12] Roberts J B, Spanos P D. Stochastic averaging an approximate method of solving random vibration problems [J]. International Journal of Non-linear Mechanics, 1986, 21(2): 111-134.
[13] Zhu W Q. Recent developments and applications of the stochastic averaging method in random vibration [J]. Applied Mechanics Reviews, 1996, 49(10S), 1169.
[14] Zhu W Q, Ying Z G. Stochastic averaging of quasi non-integrable Hamiltonian systems [J]. Journal of Applied Mechanics, 1997, 64(1):157-164.
[15] 杜修力, 陈厚群. 地震动随机模拟及其参数确定方法 [J]. 地震工程与工程振动, 1994, 14(4):1-5.
Du X L. Chen H Q. Random simulation and its parameter determination method of earthquake ground motion [J]. Earthquake
Engineering and Engineering Vibration, 1994, 14(4):1-5.
[16] 欧进萍, 朱荻涛. 设计用随机地震动的模型及其参数确定 [J]. 地震工程与工程振动, 1991, 11(3):45-54.
Ou J P. Zhu D T. Random earthquake ground motion model and its parameter determination in aseismic design [J]. Earthquake
Engineering and Engineering Vibration, 1991, 11(3):45-54.
[17] Kanai K. An Empirical Formula for the spectrum of strong Earthquake Motions [J]. Bull. Earthquake Res. Int., Univ. Tokyo, 1961, 39(1): 85-95.
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