摘要
矿井提升机在提升重物的过程中,由于质量和刚度的变化引起的系统固有频率十分缓慢的变化,因此考虑钢绳质量的矿井提升机系统是一个慢变参数振动系统.本文首先应用KuzmakLuke的多尺度法得到有一般非线性弹性力的强非线性振动系统解的周期性条件及用Jacobi椭圆函数表示的平方非线性振动和立方非线性振动的首阶渐近解.其次,将得到的结果分别应用于有平方、立方非线性弹性力的质量慢变的矿井提升系统.最后,将理论结果应用于某个矿井提升系统,应用算例的渐近解和数值解的比较表明本方法是有效的.
When a mine hoist is lifting a heavy weight, the natural frequency of the system varies slowly with the changes of mass and stiffness. So the mine hoist system is an oscillatory system with slowly varying parameters if the mass of steel rope is taken into account. The multiple scales method of Kuzmak-Luke was firstly applied to obtain the periodicity condition of solutions of strongly nonlinear oscillators with generally nonlinear spring, and then Jacobian elliptic functions were used to express the leading order approximate solutions of quadratic and cubic nonlinear oscillators. Secondly, the obtained results were applied respectively to mine hoist systems with slowly varying mass and with quadratic or cubic nonlinear spring. Finally, the theoretical results were used to deal with certain mine hoist systems, and comparisons of asymptotic ,solutions with numerical solutions of two examples showed the efficiency of the proposed method.
出处
《动力学与控制学报》
2005年第4期30-33,共4页
Journal of Dynamics and Control
基金
国家自然科学基金(10272117)
中国博士后科学基金(2004036517)资助项目~~
关键词
非线性振动
矿井提升系统
多尺度法
慢变参数
nonlinear oscillation, mine hoist system, multiple scales method, slowly varying parameter
