Winkler地基上柱式桥墩受双频激励双重亚谐共振

杨志安; 聂志凌

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Winkler地基上柱式桥墩受双频激励双重亚谐共振

应用基础研究 | 更新时间：2026-09-14

- Winkler地基上柱式桥墩受双频激励双重亚谐共振
- Double Subharmonic Resonances of the Column Bridge Pier Subjected to Double Frequency Excitations on Winkler Foundation
- 中北大学学报（自然科学版） 2011年32卷第4期页码：419-425
- 作者机构：
  
  1. 唐山市结构与振动工程重点实验室
  2. 西南交通大学土木工程学院
- 作者简介：
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- 纸质出版：2011
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杨志安, 聂志凌. Winkler地基上柱式桥墩受双频激励双重亚谐共振[J]. 中北大学学报（自然科学版）, 2011,32(4):419-425.

杨志安, 聂志凌. Double Subharmonic Resonances of the Column Bridge Pier Subjected to Double Frequency Excitations on Winkler Foundation[J]. 2011, 32(4): 419-425.
杨志安, 聂志凌. Winkler地基上柱式桥墩受双频激励双重亚谐共振[J]. 中北大学学报（自然科学版）, 2011,32(4):419-425. DOI：

杨志安, 聂志凌. Double Subharmonic Resonances of the Column Bridge Pier Subjected to Double Frequency Excitations on Winkler Foundation[J]. 2011, 32(4): 419-425. DOI：

摘要

为了研究W ink ler地基上柱式桥墩的非线性响应

由拉格朗日运动方程导出W ink ler地基上柱式桥墩受双频激励的耦合动力学方程

应用非线性振动的多尺度法

求得了简化系统满足双重亚谐共振近似解

并对其进行了数值计算.应用奇异性理论对幅频响应方程进行了奇异性分析

得到了开折参数平面的转迁集与分岔图.分析了小参数和阻尼等对系统双重亚谐共振幅频响应曲线的影响.增大阻尼可以使幅频响应曲线向开口方向偏移

减小小参数取值时可以使幅频响应曲线向左下方偏移.

Abstract

In order to deal with the nonlinear response of the column bridge pier subjected to double frequency excitations on Winkler foundation

the coupling dynamic equations of the system was derived according to Lagrange equation.By using the multiple scales method

the approximate solutions for the double subharmonic resonances of the reduced system were obtained and numerical calculations were carried out.With the aid of singularities theory

transition sets and bifurcation diagrams of unfolding parameter plane were obtained.The influences of small parameters and dumping coefficients on the amplitude frequency response curves were numerically analyzed.With the increase of damping coefficient

the amplitude frequency response curves moved to the opening mouth.With the decrease of small parameter

the amplitude frequency response curves moved to the left below.

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Keywords

references

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