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31I15 IJAET0715576 v6 iss3 1299to1312.pdf


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International Journal of Advances in Engineering & Technology, July 2013.
©IJAET
ISSN: 22311963

III.

RESULTS AND DISCUSSION

Tables 1 and 2 and figures 1 and 2 give validation results for the FORTRAN programmes developed
for this study. Tables 1 and 2 refer. The corresponding displacement and velocity components lack
repetition with increasing number of completed excitation periods and across Runge-Kutta schemes
implemented. A comparison of the corresponding periodic displacement and velocity revealed
corresponding absolute deviation range of 0.0-6.2 and 0.0-3.5 respectively. However, the same
corresponding qualitative Poincare patterns were formed across the numerical schemes, see figures 1
and 2. It is to be noted that the Poincare patterns in figures 1 and 2 compare excellently well with
those reported by Gregory and Jerry (1990) for respective damp quality of 2 and 4, fixed excitation
amplitude of 1.5 and fixed drive frequency of
Table 1:
No of
excitation
periods
completed
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Table 2:
No of
excitation
periods
completed
1
2
3
4
5
6
7
8

1303

2
.
3

Sample steady simulated Poincare Solutions at fixed excitation amplitude and drive
frequency.
q=2

q=4

RK41

RK51

RK41

RK51

1

2

1

2

1

2

1

2

-2.241
-0.588
1.076
-2.450
2.521
-2.750
0.343
-0.011
-2.616
0.607
0.001
2.103
0.787
-2.644
0.619
0.001
2.064
0.074
-2.909
0.157

1.591
2.277
1.944
1.438
0.431
1.217
0.278
1.426
1.283
0.067
1.380
0.190
2.226
1.298
0.061
1.378
0.170
1.400
1.060
0.541

-2.241
-0.588
1.076
-2.450
2.521
-2.750
0.343
-0.011
-2.616
0.606
0.001
2.104
0.893
-2.961
0.149
-0.028
-2.086
-0.034
1.012
-2.382

1.591
2.277
1.944
1.438
0.431
1.217
0.278
1.426
1.283
0.068
1.380
0.191
2.171
1.054
0.559
1.443
1.664
2.176
2.020
1.494

2.194
1.715
1.324
-0.449
-1.280
-0.600
-2.898
1.722
-0.976
-0.658
-1.637
-0.617
0.655
2.717
-1.200
1.826
0.610
-2.912
1.872
-0.475

-0.062
2.365
2.221
2.804
2.058
0.760
0.982
1.850
2.130
0.861
2.229
0.709
-0.476
0.358
1.565
-0.032
-0.650
0.897
1.776
1.612

2.183
2.909
2.910
-0.825
-0.283
-0.487
0.698
1.870
-0.081
1.909
-0.076
1.934
-0.026
2.040
1.268
3.025
-0.170
1.479
1.696
0.279

-0.070
0.788
0.578
0.772
2.838
1.690
-0.278
-0.238
-0.363
-0.240
-0.374
-0.224
-0.414
-0.156
-0.585
0.621
-0.071
-0.470
-0.319
-0.501

Sample steady simulated Poincare Solutions at fixed excitation amplitude and drive frequency
continued
q=2

q=4

RK42

RK52

RK42

RK52

1

2

1

2

1

2

1

2

-2.241
-0.588
1.076
-2.450
2.521
-2.750
0.343
-0.011

1.591
2.277
1.944
1.438
0.431
1.217
0.278
1.426

-2.241
-0.588
1.076
-2.450
2.521
-2.750
0.343
-0.011

1.591
2.277
1.944
1.438
0.431
1.217
0.278
1.426

2.184
-2.381
1.192
1.398
1.913
-0.015
2.062
2.137

-0.069
1.643
-0.295
-0.470
-0.215
-0.421
-0.141
-0.163

2.183
-3.103
1.756
-1.282
-0.606
2.398
-0.239
2.187

-0.070
1.019
1.786
2.049
0.714
0.182
0.367
-0.115

Vol. 6, Issue 3, pp. 1299-1312