Mathcad Professional - C4. Newm - Civil Engineering Beta... · Mathcad Professional - C4. Newm...
4
Force Function kip 1000lb := m 0.2533 := k 10 := x 0 5 8.6602 10 8.6602 5 0 0 0 0 0 0 ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ := c 0.1592 := i 0 10 .. := ∆t 0.1 := 0 0.2 0.4 0.6 0.8 1 0 2 4 6 8 10 x i i ∆t ⋅
Transcript of Mathcad Professional - C4. Newm - Civil Engineering Beta... · Mathcad Professional - C4. Newm...
Force Functionkip 1000lb:=
m 0.2533:=
k 10:= x
0
5
8.6602
10
8.6602
5
0
0
0
0
0
0
⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝
⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟
⎠
:=
c 0.1592:=
i 0 10..:=
∆t 0.1:=
0 0.2 0.4 0.6 0.8 10
2
4
6
8
10
xi
i ∆t⋅
Newmark's Beta Method:Linear Systems:
uuu β γ, m, c, k, ∆t, x,( ) kbar kγ
β ∆t⋅c⋅+
1
β ∆t2
⋅
m⋅+←
a1
β ∆t⋅m⋅
γ
βc⋅+←
b1
2 β⋅m⋅ ∆t
γ
2 β⋅1−⎛
⎜⎝
⎞⎠
⋅⎡⎢⎣
⎤⎥⎦
c⋅+←
u0 0←
udot0 0←
udotdot0
x0 c udot0⋅− k u0⋅−
m←
∆Pi xi 1+ xi−( )←
∆Pbari ∆Pi a udoti⋅+ b udotdoti⋅+←
∆ui∆Pbarikbar
←
∆udotiγ
β ∆t⋅∆ui⋅
γ
βudoti⋅⎛
⎜⎝
⎞⎠
− ∆t 1γ
2 β⋅−⎛
⎜⎝
⎞⎠
⋅ udotdoti⋅+⎡⎢⎣
⎤⎥⎦
←
∆udotdoti1
β ∆t2
⋅
∆ui⋅1
β ∆t⋅udoti⋅−
12 β⋅
udotdoti⋅−←
ui 1+ ui ∆ui+←
udoti 1+ udoti ∆udoti+←
udotdoti 1+ udotdoti ∆udotdoti+←
i 0 10..∈for
umax u←
:=
β14
:= γ12
:=
disp uuu β γ, m, c, k, ∆t, x,( ):=
disp
001
2
3
4
5
6
7
8
9
10
11
00.044
0.233
0.612
1.083
1.431
1.423
0.962
0.191
-0.604
-1.144
-1.254
=
0 0.2 0.4 0.6 0.8 12
1
0
1
2
disp( )i
i ∆t⋅
