Question

Q

in n D.O.F system’s equations of motion,

Write sequence of forced vibration analysis

M=mass matrix

K=stifeness matrix

C=proportional damping matrix

f(t)= external vector

x= state vector

문제4) 임의의 입력을 가지는 n D.0.F system의 운동방정식은 다음과 같이 기술 된다. madal analysis에 의한 강제진동 해 석 순서를 기술하여라. 이 때 M은 지량행 렬, K는 강성 행렬, C는 비례 댐핑행렬, 는 상태 벡터, f(t)는 외력 벡터이다. Mx+ Ca+ Kx = f(t) 여기서 비례댐핑(proportional C는 damping)의 경우에 제한한다.

Answer 1

I have taken s as stiffness element instead of k.
P VIBRAT fORce DAMPED TION Fo cos Gt C. dempingee Sxtumdi Ineeitar fes eelLe fo Ceos t haai mo 2 Оuce Sx i - cos Gt -o S cos Cut V + 8x men emeous nov ubo te's Jolu -Fm

tus ecols zt B e A eat - C m 2. 2- -C dampre whe hence 2 Sm Sm C -an CJn 2- - L Oveudanped ym Ceutreatly dempelk 1

tus ecols zt B e A eat - C m 2. 2- -C dampre whe hence 2 Sm Sm C -an CJn 2- - L Oveudanped ym Ceutreatly dempelk 1

e opadis 6porntutiol noluge Hene vbuiation occude . -1 + - -n -wnt / A +Bt) e onea Exponent Both t undeudamped sutim a, = damped fau Fron-1ag)p +8 e wd)t A - -ant A e +Be n,e o. e + 8 e A e A nt 4u Rucos + (A-B)in wst) A+B =A-B R cos Wyt+ tb J Fant A Re Ji peruedei. ces (wdt )

Date: X nalueat DECREEMENT RATIO SUccesive e consecutive ocilanon . RyRlem constaut un LagaRITme DECREEMENT It decerorment ato dinoid natvaial -Wnt ln whu an27

nt R e cos (adt +p). dies CF CF as cos wt 3 m m cas Gut PS - Reptaee D -(Fo/m casGut) (Folm) cos C>t Fo/m Cas t - estat R cos tp R2 Fo Rcosd cosaE cos(wt-d scullation m folm Cos t-D folm cos ( wt - 6) - 2a^wr + Polm cos (t -b } Gn n

Date: fols Pg WE 2. Indpendiut me eonst final Solu will be as tpooceds No CF vib

A соs wt - ф) A m Aw Cas wt-p) (at - ф) A 2 cos ces Ct 11 Kuь m cx Cues Ct cos wt-p) СAW COS cos wt Cut-) lwt- SA Cos = O max Epaiy max A ut