TD 3 Calcul des Structures et Vibrations : Vibration forcée de poutre

⃗
F=Fcos(Ωt)⃗e3
L
h x3b x2
E ρ
ωi
ϕi(x1)
m(ϕi, ϕi)=1
¯u3(x1, t) = P∞
i=1 ϕi(x1)qi(t)
qi(t)
¯u3(x1, t)

¯u3
¯u3(x1, t) = N1(x1)φ1(t) + N2(x1)φ2(t)
N1(x1)N2(x1)
1
L2x1(x1−L),1 L2x2
1,1
L2(x1−L)2,1 L3x1(x1−L)(x1−L 2).
δ¯u3(x1) = N1(x1)δφ1+N2(x1)δφ2
[U(t)] = [φ1(t)φ2(t)]T
R µ
ρ
C⃗e1t= 0
θ01(x1)C⃗e1
t≥0
m(ϕi, ϕi) = 1
θ1(x1, t)t≥0
ZL
0
x2
1(x1−L)2x1=L5
30 ,ZL
0
x2
1(x1−L)2(x1−L
2)x1= 0,ZL
0
x2
1(x1−L)2(x1−L
2)2x1=L7 840