
Stability analyses 243
the DQ weighting coefcients for the rst-order derivative. The discretised
beam equation at the virtual node
(, )
by the RDQ method is given as
+
ρ
×
=
++
+
+
−−
++
−
−
+
+
bb b
v
v
v
EI
A
www
ww
v
v
v
v
v
{}{( )( )( )
()()}0
jj jj jj
i
j
i
j
i
j
ii ii ii
ii ii
i
j
i
j
i
j
i
j
i
j
,,1,2
1
2
,2
4
,1
4
,
4
,1
4
,2
4
2
1
1
2
(5.64)
The values of the fourth order DQ weighting coefcients in Equation (5.64)
are computed by recursively applying Equation (5.63) with m = 4. The nal
equation of transverse beam deection in the discretised form is given as
−
+
ρ
−−
=
+
+
−
−
+
+
v
v
v
EI k
Ah
v
v
v
v
v
{1 21}{14641} 0
i
j
i
j
i
j
i
j
i
j
i