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

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.

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.