Determine expressionsfor q ( m − 1 , n ) → ( m , n ) , q ( m + 1 , n ) → ( m , n ) , q ( m , n + 1 ) → ( m , n ) and q ( m , n − 1 ) → ( m , n ) for conduction associated with a control volume that spans two different materials. There is no contact resistance at the interface between the materials. The control volumes are L units long into the page. Write the finite difference equation under steady-state conditions for node ( m , n ) .
Determine expressionsfor q ( m − 1 , n ) → ( m , n ) , q ( m + 1 , n ) → ( m , n ) , q ( m , n + 1 ) → ( m , n ) and q ( m , n − 1 ) → ( m , n ) for conduction associated with a control volume that spans two different materials. There is no contact resistance at the interface between the materials. The control volumes are L units long into the page. Write the finite difference equation under steady-state conditions for node ( m , n ) .
Solution Summary: The author explains how to find the expressions for q_(m-1,n), & the finite difference equation.
Determine expressionsfor
q
(
m
−
1
,
n
)
→
(
m
,
n
)
,
q
(
m
+
1
,
n
)
→
(
m
,
n
)
,
q
(
m
,
n
+
1
)
→
(
m
,
n
)
and
q
(
m
,
n
−
1
)
→
(
m
,
n
)
for conduction associated with a control volume that spans two different materials. There is no contact resistance at the interface between the materials. The control volumes are L units long into the page. Write the finite difference equation under steady-state conditions for node
(
m
,
n
)
.
Q1 A three-level offshore platform located in the Helang Oilfield area has a 1500 kg floor
steel grating supported at each level. The structure sometimes is subjected to a vertical
ocillation movement during rough sea waves given by function of y(t) = Y sin ot
If the steel grating only moves in the vertical direction and is supported by one
equivalent spring and damper at each steel grating pole level with stiffness, k, = (300
xT) Nim, k= (200 x T) Nm and k = (100 × T) Ním while damping, c: = (15 x U)
Nsm, c: = (10 x U) Ns'm and c; = (5 x U) Nsim, respectively, as simplified in Figure
Q1. Neglect the effect of gravitational force.
Use
T=4 and U = 6
Table 1
5th digit of
matric number
6th digit of
matrix number
T
4
1
4
1
4
2
3
3
6
4
4
6.
5
3
6.
6.
2
6
7
2
7
1
6.
1
(a) Sketch a free body diagram for each steel grating that includes the mass's action
and reaction forces.
(b) Determine the equation of motion in a matrix form using Newton's second law,
[m]ÿ + [clý + [k]y = F.
(c) By omitting…
evaluate the expression, f(x+h)-F(x)/h , f(x)=\sqrt(2x)
7
d°y]6
dy
dy
dy
32 +7=0
dz
Q-1. Find the order differential equation of
+7
+ 6-
dr5
dz
dz?
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