.. , . , , 1/2

.

: m [tn] = [kN*s2/m], c [kN*s/m], k [kN/m], E [kN/m2], I[m4] : / 3EI/h3, 12EI/h3 : sin(AB) = sinAcosB cosAsinB, cos(AB) = cosAcosB sinAsinB

II.

m + c + ku(t) = P(t) u(t) = uc(t) + up(t) )t(u (t)u() uc(t)

= k / m , =cr

cc

=

c2m

, d = 21- uc(t) = e-0t ( cos dt + sin dt ), uc(t) e-0t R0, R0 = 2 2A +B , , u0, u0 up(t), :

= u0 up(0), B = 0 0 0 p 0 pd

(u u ) [u (0) u (0)]

+ - +

( n ) = ln(Rj/Rj+n) = n* 2-12 n*2

() ( ) P(t) = 0 up(t) = 0. P(t) = P0 *sin t up(t) = (S1 sin t + S2 cos t), S1 = ust*(1-2)*D2, S2 = ust*(-2)* D2, = 2 22 = ust*D =1S +S

D =

2 2 2

1(1- ) (2*) .

: Pga, P0 = -m*Pga

( ) mu + cu + ku = P(t) t

Duhamel u(t) = =0

h(t-) P( ) dd m

1

0

t P() e-(t-) sin[d(t-)]d ( , uc(t) )

.. , . , , 2/2 () d() = PSa(T) [m/sec2 %g] - PSv = 0* Sd, PSa = 02* Sd Vb = k*Sd = m*PSa, Mb = h*Vb, (h = ) Vs = (3EI/h3)*Sd () Vs = (12EI/h3)*Sd () Ms = Vs*h () Ms = Vs*h/2 ()

II.

M + C + K U = F(t) U U 2 = [0] j2 = , j=1,2,,n {K j2 } j = [0] [j] = ., ( j=1,2,,n) [] = [[1], [2],, [n]]

[u] = [] [q] = j , [qj] = n

jj 1

[ ][q ] TjT

j j

[ ][m][u][ ][m][ ]

( ) M + C + K Q = F(t) * + C* + K* Q = F*(t) Q Q Q Q

( j=1,2,,n) + + qj = + 2jj + j2 qj = *jm q j *jc q j *jk *jf (t) jq jq*j

*j

f (t)m

= jf (t)

ag(t) Fg(t) = - [1] ag(t), F*(t) = Fg(t) = - [1] ag(t), = -ag(t) j = -Lj ag(t) *jf (t)

k kk 1

m

jq jq+ 2jj + j2 qj = *f (t)j

*jm

= -ag(t)

k kjk 1

2k kj

k 1

m

m

= - j ag(t)

: Sd(T,), Sv(T,), Sa(T,) ag(t), j Sd,j = j Sd(Tj,j), Sv,j = j Sv(Tj,j), Sa,j = j Sa(Tj,j) k (.. ) j jku = j,k k Sd(Tk,k), jku = j,k k Sv(Tk,k), jku = j,k k Sa(Tk,k)

j ( SRSS) ju =

2jk

k 1

u = 2 2 2 , ( ) j1 j2 ju u ... u

Vb = j jj

m u

m + c+ ku(t) = P(t) ( u(t) = uc(t) + up(t) ( ) ( mu + cu + ku = P(t) ( Duhamel ( u(t) ==P() e-(t-) sin[d(t-)]d( , uc(t) )