510
13 Finite Difference Method for the Vibration Analysis …
Table 13.6 Values of cross-segmental integrations of standard B 3 -spline and its second
φ
(1) φ
(2) dy.
φ (1)
S i j
φ
(2)
Section
L1
Section
L2
Section
L3
Section
L4
×
1
10 ×
1
36h
Section
L4
3
66
99
12
Section
L3
6
33
132
21
Section
L2
21
132
33
6
Section
L1
12
99
66
3
Table 13.7 Values of cross-segmental integrations of the second derivatives of standard B 3 -splines,
φ
(1) φ
(2) dy
φ
(1)
S i j
φ
(2)
Section
L 1
Section
L 2
Section
L 3
Section
L 4
×
1
36h 3
Section
L 4
6
0
18
12
Section
L 3
0
18
36
18
Section
L 2
18
36
18
0
Section
L 1
12
18
0
6
[N mw ] is defined by Eq. (13.45)–(13.47).
The acceleration components of this point is given by
{ ¨
f } = { ¨
w} = [N mw ]{ ¨
X } e
(13.57)
The components of the inertia force of a small elements of volume dV at that
point are given by
{ f I } = ρdV { ¨
w} = ρdV [N mw ] { ¨
X } e
(13.58)
where ρ is the mass density of the plate material.