非平稳激励下绝对位移直接求解非线性结构的时频分析

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (9) : 168-176.

论文

李喜梅1,2，陶铖1,2，王建成3

作者信息 +

Time-frequency analysis of nonlinear structure excitation input directly solved with absolute displacement under non-stationary excitation

LI Ximei1,2, TAO Cheng1,2, WANG Jiancheng3

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文章历史 +

摘要

强震作用下地震动能量的时-频演变特性对迟滞非线性的结构有着极大影响，然而通用有限元软件现有的计算模块进行频域分析时不能对非线性结构输入解耦的EPSD矩阵，限制了随机振动理论对大型复杂结构的仿真计算。将绝对位移直接求解的虚拟激励法引入多维多点的非线性动力方程，通过APDL的外部程序调用接口对非平稳地震动EPSD矩阵进行解耦与降维处理，并转化为独立于时间变量的四维均匀调制激励矩阵，实现对非线性结构精确高效的非平稳激励动态输入与随机动力响应的计算求解。最后以一座中承式三跨钢管混凝土系杆拱桥为例，计算拱肋、拱脚和桥面系响应的时变功率谱及方差。结果表明，绝对位移直接求解的激励输入方式很好地模拟了非线性结构体系所带来的时滞现象，为通用有限元软件实现非线性结构多维多点非平稳激励随机响应的求解与分析提供了可行性依据。

Abstract

The time-frequency evolution characteristics of ground motion energy under strong earthquakes have a great impact on hysteretic nonlinear structures. However, the existing calculation modules of general finite element software cannot input the decoupled EPSD matrix for nonlinear structures when performing frequency domain analysis, which thus limits the simulation of large complex structures by random vibration theory. The pseudo excitation method of absolute displacement direct solution was introduced into the multi-dimensional and multi-point nonlinear dynamic equation, and the non-stationary ground motion EPSD matrix was decoupled and dimension-reduced through the APDL external program call interface, and transformed into a four-dimensional uniformly modulated excitation matrix which is independent of the variable of time. The matrix can achieve accurate and efficient calculation and solution of non-stationary excitation dynamic input and random dynamic response of nonlinear structures. Finally, taking a half-through three-span CFST tied arch bridge as an example, the time-varying power spectrum and variance of the system responses of arch rib, arch foot and bridge deck were calculated. The results show that the excitation input method of absolute displacement direct solution can simulate the time-delay phenomenon caused by nonlinear structural system very well, which can provide a feasible basis for the solution and analysis of multi-dimensional and multi-point non-stationary excitation random response of nonlinear structure by the general finite element software.

导出引用

李喜梅1,2，陶铖1,2，王建成3. 非平稳激励下绝对位移直接求解非线性结构的时频分析[J]. 振动与冲击, 2023, 42(9): 168-176

LI Ximei1,2, TAO Cheng1,2, WANG Jiancheng3. Time-frequency analysis of nonlinear structure excitation input directly solved with absolute displacement under non-stationary excitation[J]. Journal of Vibration and Shock, 2023, 42(9): 168-176

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