振动筛非线性谐波共振研究  

Nonlinear harmonic resonance analysis of vibrating screen

作　　者：逄锦飞 杜东源 刘航 刘小蛮[1] 杜国君[1] Pang Jinfei;Du Dongyuan;Liu Hang;Liu Xiaoman;Du Guojun(Yanshan University,Hebei Key Laboratory of Heavy Equipment and Large Structural Mechanics Reliability,066004,Qinhangdao,China;Qinhuangdao Honghe Machinery Co.,Ltd.,066000,Qinhuangdao,China;Qinhuangdao Tobacco Machinery Co.,Ltd.,066000,Qinhuangdao,China)

机构地区：[1]燕山大学河北省重型装备与大型结构力学可靠性重点实验室,秦皇岛066004 [2]秦皇岛弘和机械有限责任公司,秦皇岛066000 [3]秦皇岛烟草机械有限责任公司,秦皇岛066000

出　　处：《应用力学学报》2020年第6期2657-2663,I0023,I0024,共9页Chinese Journal of Applied Mechanics

摘　　要：对受简谐激励作用下振动筛的非线性谐波共振问题进行研究。在系统非线性振动方程的基础上,给出系统的位移表达式。设定位移函数,应用伽辽金积分得到了具有位移和惯性混合边界条件的系统时间域的非线性振动方程。利用多尺度法对该系统的非线性谐波共振特性进行分析求解,推导出系统稳态运动的亚谐波共振和超谐波共振幅频响应的特征方程。通过数值计算,给出了超、亚谐波共振的幅频特性曲线和亚谐波共振稳定性判定条件。得到超、亚谐波共振情况下共振幅值随激励幅值或弹片长度的增大而增大,弹片数和末端质量对共振区幅频特性的影响较小;以及随协调参数增大,亚谐波共振幅值突然出现,呈多值现象且幅值变化逐渐趋于平缓等结论。In this paper, the nonlinear harmonic resonance of the vibrating screen under simple harmonic excitation is studied. Based on the nonlinear vibration equation of the system, the displacement expression of the system is given. The displacement function is set and the Galerkin integral is used to obtain the nonlinear vibration equation in the time domain of the system with mixed displacement and inertia boundary conditions. The multi-scale method is used to analyze and solve the nonlinear harmonic resonance characteristics of the system, and the characteristic equations of the subharmonic resonance and superharmonic common amplitude frequency response of the system in steady state motion are derived. Through numerical calculation, the amplitude-frequency characteristic curves of super-harmonic resonance and sub-harmonic resonance and the judgment conditions of sub-harmonic resonance stability are given. In the case of super-harmonic resonance and sub-harmonic resonance, the common amplitude value increases with the increase of excitation amplitude or rod length. The number of spring pieces and the end mass have little effect on the amplitude-frequency characteristics of the resonance zone, and with the increase ofcoordination parameters, the sub-harmonic common amplitude value suddenly appears, showing a multi-value phenomenon and the amplitude changing gradually tends to be flat.

关 键 词：振动筛 非线性振动 谐波共振 稳定性 伽辽金法 多尺度法 惯性边界条件 

分 类 号：O322[理学—一般力学与力学基础]