系物弦在温度场中受简谐激励的亚谐共振研究  

STUDY ON SUBHARMONIC RESONANT OF MASS-LOADED STRING IN TEMPERATURE FIELD

作　　者：杨志安[1] 齐家璋[2] 

机构地区：[1]唐山学院唐山市结构与振动工程重点实验室,唐山063000 [2]河北理工大学机械工程学院,唐山063009

出　　处：《机械强度》2009年第2期334-338,共5页Journal of Mechanical Strength

摘　　要：建立温度场中系物弦受简谐激励的数学模型,研究其亚谐共振规律。用伽辽金法得到系统的非线性振动方程。采用非线性振动的多尺度法求得系统亚谐共振的近似解,并进行数值分析。分析温度、阻尼、调谐值、激励幅值等参数对响应曲线的影响。给出1/3次亚谐共振存在非零解的条件。指出随着温度差的升高,系统的固有频率增加;随着阻尼的增加,幅频响应曲线向开口方向移动;随着调谐值的减小,响应曲线的振幅减小。力幅响应曲线的形状区别于经典的1/3次亚谐共振,是封闭的曲线。A mathematical model of mass-loaded string subjected to a harmonic excitation in temperature field is established. The nonlinear vibration equation of the system is derived by Galerkin＇ s principle. By means of the method of multiple scales for nonlinear analysis, the approximation solution of sub-harmonic resonance of the system is obtained. The existence condition for nonzero 1/3 subharmonic resonant solution of the system is obtained. Results of numerical analyses on the influence of temperature, damping, detuning, and excitation on response curves of the system are as follows. With the increasing of temperature difference, the nature frequency of the system increases. With the increasing of damping, amplitude frequency response curves move towards their opening mouth. With the decreasing of detuning, amplitudes of response curve decrease. Amplitude excitation response curves are closed curves, different from the conventional shape.

关 键 词：系物弦 温度场 非线性振动 亚谐共振 

分 类 号：O321[理学—一般力学与力学基础]