146
4 Numerical Methods in Structural Dynamics …
Table 4.2
Numerical integration of Duhamel’s integral
Evaluation of A
τ s
F(τ)
sin pτ
sin pτ
(2)
× (4)
Multiplier
(5)
× (6)
A∗
A
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
0.00
0
0
1.0
0
1
⎪
⎭
⎪
⎬
⎫
⎪
⎭
⎪
⎬
⎫
4
6 . 4
2
8
2
3 . 2
9
2
7 . 9
6
8
6
1 . 4
2
0
0
0.01
44
0.295
0.956
42.06
4
0.0006
0.02
88
0.564
0.826
72.69
1
0.0006
0.03
132
0.782
0.623
82.23
4
0.0012
0.04
176
0.931
0.365
64.24
1
0.00018
Evaluation of B
(2)
× (3)
Multiplier
(10)
× (11)
B∗
B
(9)
× (3)
(14)
× (4)
(15)
− (16)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
0
1
⎪
⎭
⎪
⎬
⎫
⎪
⎭
⎪
⎬
⎫
3
6
1 . 6
8
2
1
4 . 8
8
9
4 . 3
6
1
5 . 2
9
0
0
0
0
0
12.98
4
0.0002
49.63
1
0.0002
0.00034
0.00016
0.00018
103.22
4
0.0016
163.86
1
0.0018
0.00168
0.00066
0.00102
*
and
have been calculated by summing up the three consecutive values of the previous column as given in bracket and multiplying it by
3mp