黏滑摩擦的光滑化互补模型及其在摩擦摆隔震支座中的应用

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振动与冲击 ›› 2025, Vol. 44 ›› Issue (1) : 272-280.

土木工程

黏滑摩擦的光滑化互补模型及其在摩擦摆隔震支座中的应用

吴阳，张楠，张欣刚*，张树翠，毕皓皓，姚文莉

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Smoothing NLCP model of stick-slip friction and its application in FPBs

WU Yang, ZHANG Nan, ZHANG Xingang*, ZHANG Shucui, BI Haohao, YAO Wenli

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摘要

为研究摩擦摆隔震支座在地震作用下的黏滑摩擦响应问题，提出一种处理非光滑黏滑摩擦问题的光滑化模型。首先，基于线性互补理论构建摩擦力余量和相对滑移速度的互补方程。其次，在短时区间内对相对滑移速度进行时间平均，利用时均滑移速度代替时变滑移速度重构互补变量，并将其转化为一组非线性互补方程，从而将非光滑的黏滑摩擦问题进行光滑化处理。随后，将摩擦摆隔震支座等效为一种考虑恢复力效应的2维摩擦耦合模型，结合所提光滑化模型进行地震响应分析，并与经典的Coulomb摩擦模型和LuGre摩擦模型进行了对比验证。研究结果表明，所提模型既能够在宏观上反映黏滑摩擦的stick-slip切换，同时还能实现非光滑问题的光滑化分析，避免在非光滑事件中频繁切换动力学模型。采用不同摩擦模型对摩擦摆隔震支座的地震响应进行计算，验证了所提模型的准确性和有效性。

Abstract

To investigate the stick-slip friction response of friction pendulum bearings (FPB) under seismic actions, a smoothing model is proposed to address the non-smooth stick-slip friction problem. Firstly, complementary equations for friction saturation and relative slip velocity are formulated based on linear complementarity theory. Secondly, the relative slip velocity is averaged over short time intervals, and the complementary variable is reconstructed using the time-averaged slip velocity instead of the time-varying slip velocity, transforming it into a set of nonlinear complementary equations, thereby smoothing the non-smooth stick-slip friction problem. Subsequently, the FPB is equivalently modeled as a 2D friction-coupling model considering the effect of restitution force. Seismic response analysis is conducted using the proposed smoothing model and compared with classical Coulomb and LuGre friction models for validation. Results demonstrate that the proposed model can effectively capture the macroscopic stick-slip transition of stick-slip friction while smoothing non-smooth problems and avoiding frequent dynamic model switching in such events. Seismic responses of the FPB are computed using different friction models, verifying the accuracy and effectiveness of the proposed model.

导出引用

吴阳, 张楠, 张欣刚, 张树翠, 毕皓皓, 姚文莉. 黏滑摩擦的光滑化互补模型及其在摩擦摆隔震支座中的应用[J]. 振动与冲击, 2025, 44(1): 272-280

WU Yang, ZHANG Nan, ZHANG Xingang, ZHANG Shucui, BI Haohao, YAO Wenli. Smoothing NLCP model of stick-slip friction and its application in FPBs[J]. Journal of Vibration and Shock, 2025, 44(1): 272-280

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