《汽车理论》课程教学课件（英文讲稿）第6章 汽车平顺性 Ride Performance 6.3 Simplify of Automobile Vibration System and Vibration of Single Mass System（汽车振动系统的简化及单质量系统的振动）

2.FreeVibrationofSingleMassSystemsecond-order eguation with constant coefficients二阶常系数方程m2m,z+C(z-g)+K(z-g)=0K艺+ (z - g) = 0(2-) +一mm9

second-order equation with constant coefficients 二阶常系数方程 2. Free Vibration of Single Mass System 2 2 2 ( ) ( ) 0 ( ) ( ) 0 m z C z q K z q C K z z q z q m m          

K2n =assume :1m.m.の。:system natural circular frequency系统固有圆频率f。=2元2元LC：damping ratio阻尼比，=2/m,K

2 0 2 2 2 , C K n m m assume:    0 2 damping rati 2 o n C m K    ： 阻尼比，   0 0 0 2 : system natural circular frequency 1 2 2 K f m       系统固有圆频率

homogenous differential equation齐次方程z+2nz +のjz = 0 0.25, belong to small damp:. z = Ae-nt sin(Jo? -n?t + α)O, : system natural frequency with damp有阻尼固有频率,,=-n2ne-vibration scope attenuation according to振幅按e-nt衰减

2 2 0 0.25, belong to small damp sin( ) nt z Ae n t          2 2 0 : system natural frequency with damp vibration scope attenuation according to , r r nt nt n e e      有阻尼固有频率,   振幅按 衰减 2 0 homogenous differential equation 2 0 : z nz z     齐次方程

Z一nteA2t2Ot1-Ae-ntT1Attenuation vibration curve衰减振动曲线

Attenuation vibration curve 衰减振动曲线

Attenuation vibration inf luenced by E阻尼比对衰减振动的影响（1）-n2=の。Or =1a个=0,S=1= 0,=0big damp=no vibration大阻尼时系统不振动0 - 0r ~ 3% = 0, ~ 0o~0.25=0o有阻尼后振动频率变化不大

2 2 2 0 0 1 r       n ＝ － Attenuation vibration inf luenced by  0 0 0 0.25 3 r r             ％ 有阻尼后振动频率变化不大        r r 1 0  ＝ ＝ big damp no vibration 大阻尼时系统不振动