1 Introduction
2 Equations of motion and variational statement for a nonlocal TBT
2.1 Hamilton’s principle
2.2 Equations of motion
2.3 Variational statement
3 Free vibration WQEM formulation
4 Forced vibration WQEM formulation
4.1 WQEM formulation using a mode shape interpolation basis
4.1.1 Switching the interpolation basis
4.1.2 Time discretization
4.1.3 Frequency response curve
4.2 WQEM formulation using Galerkin technique
5 Numerical results and discussion
Material | Young modulus | Poisson’s ratio | Density | |
---|---|---|---|---|
(GPa) | (kg/\(\hbox {m}^{3}\)) | |||
Metal: | Aluminum | 70 | 0.24 | 2700 |
Ceramic: | Silicon | 210 | 0.3 | 2370 |
5.1 Performance of WQEM
WQEM frequencies | WQEM Error to the finest grid (\(n_{x}=15\)) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\({\hat{k}}_{L}\) | \({\hat{k}}_{NL}\) | \({\hat{k}}_{S}\) | \(n_{x}\qquad \)5 | 7 | 9 | 11 | 13 | 15 | 5 | 7 | 9 | 11 | 13 |
CC boundary condition | |||||||||||||
0 | 10 | 0 | 18.9494 | 18.8515 | 18.8457 | 18.8460 | 18.8459 | 18.8460 | 0.55% | 0.03% | 0.00% | 0.00% | 0.00% |
50 | 39.1014 | 38.2234 | 38.3300 | 38.3410 | 38.3300 | 38.3349 | 2.00% | 0.29% | 0.01% | 0.02% | 0.01% | ||
50 | 0 | 19.9220 | 19.6928 | 19.6725 | 19.6747 | 19.6744 | 19.6745 | 1.26% | 0.09% | 0.01% | 0.00% | 0.00% | |
50 | 39.5717 | 38.6928 | 38.6940 | 38.7806 | 38.7275 | 38.7479 | 2.13% | 0.14% | 0.14% | 0.08% | 0.05% | ||
100 | 0 | 21.0748 | 20.7009 | 20.6692 | 20.6742 | 20.6739 | 20.6739 | 1.94% | 0.13% | 0.02% | 0.00% | 0.00% | |
50 | 40.1518 | 39.2720 | 39.1479 | 39.3220 | 39.2238 | 39.2559 | 2.28% | 0.04% | 0.28% | 0.17% | 0.08% | ||
50 | 10 | 0 | 20.2043 | 20.1123 | 20.1069 | 20.1072 | 20.1071 | 20.1071 | 0.48% | 0.03% | 0.00% | 0.00% | 0.00% |
50 | 39.7251 | 38.8613 | 38.9661 | 38.9769 | 38.9661 | 38.9709 | 1.94% | 0.28% | 0.01% | 0.02% | 0.01% | ||
50 | 0 | 21.1192 | 20.9029 | 20.8838 | 20.8859 | 20.8856 | 20.8857 | 1.12% | 0.08% | 0.01% | 0.00% | 0.00% | |
50 | 40.1882 | 39.3230 | 39.3242 | 39.4094 | 39.3571 | 39.3773 | 2.06% | 0.14% | 0.13% | 0.08% | 0.05% | ||
100 | 0 | 22.2099 | 21.8553 | 21.8253 | 21.8300 | 21.8297 | 21.8297 | 1.74% | 0.12% | 0.02% | 0.00% | 0.00% | |
50 | 40.7595 | 39.8931 | 39.7710 | 39.9422 | 39.8457 | 39.8772 | 2.21% | 0.04% | 0.27% | 0.16% | 0.08% | ||
HH boundary condition | |||||||||||||
0 | 10 | 0 | 9.8477 | 9.8282 | 9.8283 | 9.8283 | 9.8283 | 9.8283 | 0.20% | 0.00% | 0.00% | 0.00% | 0.00% |
50 | 24.2162 | 24.2082 | 24.2080 | 24.2081 | 24.2081 | 24.2081 | 0.03% | 0.00% | 0.00% | 0.00% | 0.00% | ||
50 | 0 | 11.3241 | 11.2678 | 11.2698 | 11.2699 | 11.2699 | 11.2699 | 0.48% | 0.02% | 0.00% | 0.00% | 0.00% | |
50 | 24.8499 | 24.8191 | 24.8185 | 24.8187 | 24.8187 | 24.8187 | 0.13% | 0.00% | 0.00% | 0.00% | 0.00% | ||
100 | 0 | 12.9362 | 12.8625 | 12.8692 | 12.8694 | 12.8693 | 12.8693 | 0.52% | 0.05% | 0.00% | 0.00% | 0.00% | |
50 | 25.6200 | 25.5649 | 25.5642 | 25.5645 | 25.5645 | 25.5645 | 0.22% | 0.00% | 0.00% | 0.00% | 0.00% | ||
10 | 0 | 12.1068 | 12.0910 | 12.0910 | 12.0911 | 12.0911 | 12.0911 | 0.13% | 0.00% | 0.00% | 0.00% | 0.00% | |
50 | 25.2195 | 25.2118 | 25.2116 | 25.2117 | 25.2117 | 25.2117 | 0.03% | 0.00% | 0.00% | 0.00% | 0.00% | ||
50 | 0 | 13.3354 | 13.2876 | 13.2894 | 13.2895 | 13.2895 | 13.2895 | 0.35% | 0.01% | 0.00% | 0.00% | 0.00% | |
50 | 25.8285 | 25.7990 | 25.7984 | 25.7985 | 25.7985 | 25.7985 | 0.12% | 0.00% | 0.00% | 0.00% | 0.00% | ||
100 | 0 | 14.7290 | 14.6644 | 14.6703 | 14.6705 | 14.6704 | 14.6704 | 0.40% | 0.04% | 0.00% | 0.00% | 0.00% | |
50 | 26.5703 | 26.5172 | 26.5165 | 26.5168 | 26.5168 | 26.5168 | 0.20% | 0.00% | 0.00% | 0.00% | 0.00% |
5.2 Free vibration response
\(\frac{L}{h}\) | A | \({\hat{\mu }}_{0}^2\) | DQM [36] | WQEM | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(n_k\quad \)1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | |||
HH boundary condition | ||||||||||
10 | 0 | 0 | 13.9369 | 13.9348 | 13.9333 | 13.9324 | 13.9369 | 13.9348 | 13.9333 | 13.9324 |
1 | 13.6251 | 13.6231 | 13.6218 | 13.6209 | 13.6251 | 13.6231 | 13.6218 | 13.6209 | ||
3 | 13.1293 | 13.1277 | 13.1265 | 13.1258 | 13.1293 | 13.1277 | 13.1265 | 13.1258 | ||
0.5 | 0 | 14.4771 | 14.4596 | 14.4491 | 14.4435 | 14.4771 | 14.4596 | 14.4491 | 14.4435 | |
1 | 14.1774 | 14.1597 | 14.1491 | 14.1435 | 14.1774 | 14.1597 | 14.1491 | 14.1435 | ||
3 | 13.7021 | 13.6842 | 13.6734 | 13.6677 | 13.7021 | 13.6842 | 13.6734 | 13.6677 | ||
1 | 0 | 15.9917 | 15.9338 | 15.8994 | 15.8814 | 15.9917 | 15.9338 | 15.8994 | 15.8814 | |
1 | 15.7242 | 15.6653 | 15.6304 | 15.6121 | 15.7242 | 15.6653 | 15.6304 | 15.6121 | ||
3 | 15.3027 | 15.2424 | 15.2066 | 15.1878 | 15.3027 | 15.2424 | 15.2066 | 15.1878 | ||
100 | 0 | 0 | 14.0261 | 14.0261 | 14.0261 | 14.0260 | 14.0261 | 14.0261 | 14.0261 | 14.0260 |
1 | 13.7107 | 13.7107 | 13.7106 | 13.7106 | 13.7107 | 13.7107 | 13.7106 | 13.7106 | ||
3 | 13.2092 | 13.2092 | 13.2092 | 13.2091 | 13.2092 | 13.2092 | 13.2092 | 13.2091 | ||
0.5 | 0 | 14.5671 | 14.5516 | 14.5425 | 14.5377 | 14.5671 | 14.5516 | 14.5425 | 14.5377 | |
1 | 14.2639 | 14.2481 | 14.2387 | 14.2339 | 14.2639 | 14.2481 | 14.2387 | 14.2339 | ||
3 | 13.7830 | 13.7666 | 13.7569 | 13.7519 | 13.7830 | 13.7666 | 13.7569 | 13.7519 | ||
1 | 0 | 16.0844 | 16.0280 | 15.9948 | 15.9775 | 16.0844 | 16.0280 | 15.9948 | 15.9775 | |
1 | 15.8133 | 15.7559 | 15.7220 | 15.7043 | 15.8133 | 15.7559 | 15.7220 | 15.7043 | ||
3 | 15.3863 | 15.3271 | 15.2921 | 15.2739 | 15.3863 | 15.3271 | 15.2921 | 15.2739 | ||
CC boundary condition | ||||||||||
10 | 0 | 0 | 24.1208 | 24.0840 | 24.0594 | 24.0456 | 24.1208 | 24.0840 | 24.0594 | 24.0456 |
1 | 23.3367 | 23.3036 | 23.2814 | 23.2689 | 23.3367 | 23.3036 | 23.2814 | 23.2689 | ||
3 | 22.1324 | 22.1048 | 22.0863 | 22.0757 | 22.1324 | 22.1048 | 22.0863 | 22.0757 | ||
0.5 | 0 | 24.4560 | 24.4086 | 24.3778 | 24.3607 | 24.4560 | 24.4086 | 24.3778 | 24.3607 | |
1 | 23.7261 | 23.6791 | 23.6487 | 23.6320 | 23.7261 | 23.6791 | 23.6487 | 23.6320 | ||
3 | 22.6093 | 22.5626 | 22.5329 | 22.5165 | 22.6093 | 22.5626 | 22.5329 | 22.5165 | ||
1 | 0 | 25.4351 | 25.3575 | 25.3090 | 25.2827 | 25.4351 | 25.3575 | 25.3090 | 25.2827 | |
1 | 24.8580 | 24.7719 | 24.7185 | 24.6898 | 24.8581 | 24.7719 | 24.7185 | 24.6898 | ||
3 | 23.9850 | 23.8856 | 23.8247 | 23.7921 | 23.9850 | 23.8856 | 23.8247 | 23.7921 | ||
100 | 0 | 0 | 24.7300 | 24.7296 | 24.7293 | 24.7291 | 24.7300 | 24.7296 | 24.7293 | 24.7291 |
1 | 23.9267 | 23.9263 | 23.9261 | 23.9259 | 23.9267 | 23.9263 | 23.9261 | 23.9259 | ||
3 | 22.6875 | 22.6872 | 22.6870 | 22.6869 | 22.6875 | 22.6872 | 22.6870 | 22.6869 | ||
0.5 | 0 | 25.0640 | 25.0526 | 25.0459 | 25.0423 | 25.0640 | 25.0526 | 25.0459 | 25.0423 | |
1 | 24.3167 | 24.3020 | 24.2933 | 24.2888 | 24.3167 | 24.3020 | 24.2933 | 24.2888 | ||
3 | 23.1672 | 23.1473 | 23.1356 | 23.1295 | 23.1672 | 23.1473 | 23.1356 | 23.1295 | ||
1 | 0 | 26.0404 | 25.9977 | 25.9725 | 25.9593 | 26.0404 | 25.9977 | 25.9725 | 25.9593 | |
1 | 25.4515 | 25.3964 | 25.3639 | 25.3470 | 25.4515 | 25.3964 | 25.3639 | 25.3470 | ||
3 | 24.5520 | 24.4779 | 24.4342 | 24.4114 | 24.5520 | 24.4779 | 24.4342 | 24.4114 |
\(\frac{L}{h}\) | A | \({\hat{\mu }}_{0}^{2}\) | \(\hbox {DQM}^{*}\) | WQEM | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(n_{k}\quad \)1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | |||
HH boundary condition | ||||||||||
4 | 0.5 | 0 | 14.0539 | 14.0294 | 14.0137 | 14.0052 | 14.0539 | 14.0294 | 14.0137 | 14.0052 |
1 | 13.7709 | 13.7470 | 13.7318 | 13.7235 | 13.7709 | 13.7470 | 13.7318 | 13.7235 | ||
3 | 13.3224 | 13.2994 | 13.2849 | 13.2769 | 13.3225 | 13.2995 | 13.2850 | 13.2771 | ||
1 | 0 | 15.5572 | 15.4943 | 15.4561 | 15.4358 | 15.5572 | 15.4943 | 15.4561 | 15.4358 | |
1 | 15.3063 | 15.2433 | 15.2051 | 15.1848 | 15.3063 | 15.2433 | 15.2051 | 15.1848 | ||
3 | 14.9102 | 14.8469 | 14.8085 | 14.7882 | 14.9111 | 14.8479 | 14.8097 | 14.7894 | ||
5 | 0.5 | 0 | 14.2251 | 14.2031 | 14.1892 | 14.1817 | 14.2251 | 14.2031 | 14.1892 | 14.1817 |
1 | 13.9353 | 13.9136 | 13.8999 | 13.8925 | 13.9353 | 13.9136 | 13.8999 | 13.8925 | ||
3 | 13.4760 | 13.4546 | 13.4414 | 13.4342 | 13.4760 | 13.4547 | 13.4414 | 13.4342 | ||
1 | 0 | 15.7328 | 15.6715 | 15.6345 | 15.6149 | 15.7328 | 15.6715 | 15.6345 | 15.6149 | |
1 | 15.4752 | 15.4134 | 15.3763 | 15.3566 | 15.4752 | 15.4134 | 15.3763 | 15.3566 | ||
3 | 15.0691 | 15.0066 | 14.9691 | 14.9492 | 15.0694 | 15.0069 | 14.9694 | 14.9496 | ||
8 | 0.5 | 0 | 14.4276 | 14.4091 | 14.3978 | 14.3918 | 14.4276 | 14.4091 | 14.3978 | 14.3918 |
1 | 14.1298 | 14.1112 | 14.1000 | 14.0939 | 14.1298 | 14.1112 | 14.1000 | 14.0939 | ||
3 | 13.6576 | 13.6389 | 13.6276 | 13.6216 | 13.6576 | 13.6389 | 13.6276 | 13.6216 | ||
1 | 0 | 15.9408 | 15.8821 | 15.8471 | 15.8287 | 15.9408 | 15.8821 | 15.8471 | 15.8287 | |
1 | 15.6751 | 15.6156 | 15.5802 | 15.5616 | 15.6751 | 15.6156 | 15.5802 | 15.5616 | ||
3 | 15.2567 | 15.1959 | 15.1597 | 15.1407 | 15.2567 | 15.1959 | 15.1597 | 15.1407 | ||
CC boundary condition | ||||||||||
4 | 0.5 | 0 | 22.0435 | 21.8872 | 21.7853 | 21.7288 | 22.0435 | 21.8872 | 21.7853 | 21.7288 |
1 | 21.4002 | 21.2564 | 21.1625 | 21.1104 | 21.4003 | 21.2566 | 21.1627 | 21.1106 | ||
3 | 20.4413 | 20.3165 | 20.2349 | 20.1896 | 20.4440 | 20.3197 | 20.2385 | 20.1933 | ||
1 | 0 | 23.0556 | 22.8748 | 22.7587 | 22.6950 | 23.0556 | 22.8748 | 22.7587 | 22.6950 | |
1 | 22.5422 | 22.3654 | 22.2523 | 22.1904 | 22.5432 | 22.3664 | 22.2535 | 22.1915 | ||
3 | 21.7944 | 21.6215 | 21.5115 | 21.4513 | 21.8196 | 21.6510 | 21.5440 | 21.4857 | ||
5 | 0.5 | 0 | 22.9436 | 22.8219 | 22.7422 | 22.6979 | 22.9436 | 22.8219 | 22.7422 | 22.6979 |
1 | 22.2651 | 22.1519 | 22.0778 | 22.0367 | 22.2652 | 22.1520 | 22.0779 | 22.0368 | ||
3 | 21.2429 | 21.1425 | 21.0769 | 21.0405 | 21.2440 | 21.1438 | 21.0783 | 21.0420 | ||
1 | 0 | 23.9391 | 23.7905 | 23.6952 | 23.6429 | 23.9390 | 23.7905 | 23.6952 | 23.6429 | |
1 | 23.3994 | 23.2506 | 23.1558 | 23.1040 | 23.3998 | 23.2511 | 23.1564 | 23.1045 | ||
3 | 22.6038 | 22.4543 | 22.3599 | 22.3084 | 22.6124 | 22.4640 | 22.3704 | 22.3194 | ||
8 | 0.5 | 0 | 24.1381 | 24.0733 | 24.0309 | 24.0074 | 24.1381 | 24.0733 | 24.0309 | 24.0074 |
1 | 23.4180 | 23.3555 | 23.3148 | 23.2922 | 23.4181 | 23.3555 | 23.3148 | 23.2922 | ||
3 | 22.3196 | 22.2602 | 22.2219 | 22.2008 | 22.3199 | 22.2605 | 22.2222 | 22.2010 | ||
1 | 0 | 25.1194 | 25.0251 | 24.9654 | 24.9329 | 25.1194 | 25.0251 | 24.9654 | 24.9329 | |
1 | 24.5494 | 24.4484 | 24.3851 | 24.3508 | 24.5495 | 24.4485 | 24.3852 | 24.3509 | ||
3 | 23.6914 | 23.5800 | 23.5111 | 23.4739 | 23.6929 | 23.5815 | 23.5127 | 23.4756 |
\(\frac{L}{h}\) | \({\hat{k}}_{L}\) | \({\hat{\mu }}_{0}^2\) | DQM [36] | WQEM | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\({\hat{k}}_{S}\) | 0 | 50 | 0 | 50 | ||||||||||
\({\hat{k}}_{NL}\)10 | 50 | 100 | 10 | 50 | 100 | 10 | 50 | 100 | 10 | 50 | 100 | |||
HH boundary condition | ||||||||||||||
10 | 0 | 0 | 11.3200 | 12.5710 | 13.9823 | 24.8524 | 25.4457 | 26.1699 | 11.3200 | 12.5710 | 13.9823 | 24.8524 | 25.4457 | 26.1699 |
1 | 10.9344 | 12.2295 | 13.6849 | 24.6790 | 25.2770 | 26.0073 | 10.9344 | 12.2295 | 13.6849 | 24.6790 | 25.2771 | 26.0074 | ||
5 | 9.8283 | 11.2699 | 12.8693 | 24.2081 | 24.8194 | 25.5671 | 9.8283 | 11.2699 | 12.8693 | 24.2081 | 24.8187 | 25.5645 | ||
50 | 0 | 13.3319 | 14.4093 | 15.6558 | 25.8310 | 26.4023 | 27.1009 | 13.3319 | 14.4093 | 15.6558 | 25.8310 | 26.4023 | 27.1009 | |
1 | 13.0061 | 14.1124 | 15.3908 | 25.6641 | 26.2398 | 26.9440 | 13.0061 | 14.1124 | 15.3908 | 25.6641 | 26.2398 | 26.9441 | ||
5 | 12.0911 | 13.2895 | 14.6704 | 25.2117 | 25.7992 | 26.5193 | 12.0911 | 13.2895 | 14.6704 | 25.2117 | 25.7985 | 26.5168 | ||
100 | 0 | 15.0777 | 16.0383 | 17.1669 | 26.7738 | 27.3255 | 28.0010 | 15.0777 | 16.0383 | 17.1669 | 26.7738 | 27.3255 | 28.0010 | |
1 | 14.7904 | 15.7720 | 16.9255 | 26.6129 | 27.1684 | 27.8492 | 14.7904 | 15.7720 | 16.9255 | 26.6129 | 27.1684 | 27.8492 | ||
5 | 13.9926 | 15.0403 | 16.2734 | 26.1768 | 26.7432 | 27.4384 | 13.9926 | 15.0403 | 16.2734 | 26.1768 | 26.7425 | 27.4360 | ||
100 | 0 | 0 | 11.4053 | 12.6570 | 14.0696 | 24.9703 | 25.5655 | 26.2918 | 11.4053 | 12.6570 | 14.0696 | 24.9703 | 25.5655 | 26.2918 |
1 | 11.0158 | 12.3114 | 13.7676 | 24.7946 | 25.3946 | 26.1272 | 11.0158 | 12.3114 | 13.7676 | 24.7946 | 25.3946 | 26.1272 | ||
5 | 9.8982 | 11.3395 | 12.9381 | 24.3177 | 24.9303 | 25.6785 | 9.8982 | 11.3395 | 12.9381 | 24.3177 | 24.9303 | 25.6785 | ||
50 | 0 | 13.4193 | 14.4981 | 15.7464 | 25.9521 | 26.5252 | 27.2260 | 13.4193 | 14.4981 | 15.7464 | 25.9521 | 26.5252 | 27.2260 | |
1 | 13.0899 | 14.1974 | 15.4772 | 25.7831 | 26.3606 | 27.0671 | 13.0899 | 14.1974 | 15.4772 | 25.7831 | 26.3606 | 27.0671 | ||
5 | 12.1643 | 13.3634 | 14.7442 | 25.3248 | 25.9136 | 26.6342 | 12.1643 | 13.3634 | 14.7442 | 25.3248 | 25.9136 | 26.6342 | ||
100 | 0 | 15.1682 | 16.1304 | 17.2611 | 26.8981 | 27.4515 | 28.1292 | 15.1682 | 16.1304 | 17.2611 | 26.8981 | 27.4515 | 28.1292 | |
1 | 14.8775 | 15.8607 | 17.0159 | 26.7351 | 27.2924 | 27.9754 | 14.8775 | 15.8607 | 17.0159 | 26.7351 | 27.2924 | 27.9754 | ||
5 | 14.0701 | 15.1187 | 16.3520 | 26.2933 | 26.8610 | 27.5568 | 14.0701 | 15.1187 | 16.3520 | 26.2933 | 26.8610 | 27.5568 | ||
CC boundary condition | ||||||||||||||
10 | 0 | 0 | 22.5928 | 23.2288 | 24.0011 | 33.0229 | 33.4639 | 34.0078 | 22.5928 | 23.2288 | 24.0011 | 33.0229 | 33.4639 | 34.0078 |
1 | 21.5853 | 22.2663 | 23.0918 | 34.6531 | 35.0810 | 35.6096 | 21.5853 | 22.2663 | 23.0918 | 34.6531 | 35.0810 | 35.6096 | ||
5 | 18.8460 | 19.6745 | 20.6739 | 38.3348 | 38.7472 | 39.2540 | 18.8460 | 19.6745 | 20.6739 | 38.3349 | 38.7479 | 39.2559 | ||
50 | 0 | 23.6637 | 24.2716 | 25.0118 | 33.7649 | 34.1964 | 34.7288 | 23.6637 | 24.2716 | 25.0118 | 33.7649 | 34.1964 | 34.7288 | |
1 | 22.7012 | 23.3496 | 24.1381 | 35.3593 | 35.7787 | 36.2971 | 22.7012 | 23.3496 | 24.1381 | 35.3593 | 35.7787 | 36.2971 | ||
5 | 20.1071 | 20.8857 | 21.8297 | 38.9708 | 39.3766 | 39.8753 | 20.1071 | 20.8857 | 21.8297 | 38.9709 | 39.3773 | 39.8772 | ||
100 | 0 | 24.6882 | 25.2715 | 25.9832 | 34.4911 | 34.9136 | 35.4352 | 24.6882 | 25.2715 | 25.9832 | 34.4911 | 34.9136 | 35.4352 | |
1 | 23.7647 | 24.3848 | 25.1409 | 36.0516 | 36.4631 | 36.9719 | 23.7647 | 24.3848 | 25.1409 | 36.0516 | 36.4631 | 36.9719 | ||
5 | 21.2937 | 22.0304 | 22.9274 | 39.5966 | 39.9960 | 40.4872 | 21.2937 | 22.0304 | 22.9274 | 39.5967 | 39.9967 | 40.4890 | ||
100 | 0 | 0 | 23.2071 | 23.8323 | 24.5923 | 33.7209 | 34.1567 | 34.6943 | 23.2071 | 23.8323 | 24.5923 | 33.7209 | 34.1567 | 34.6943 |
1 | 22.1771 | 22.8480 | 23.6622 | 35.4379 | 35.8614 | 36.3848 | 22.1771 | 22.8480 | 23.6622 | 35.4379 | 35.8614 | 36.3848 | ||
5 | 19.3667 | 20.1872 | 21.1769 | 39.1219 | 39.5310 | 40.0378 | 19.3667 | 20.1872 | 21.1769 | 39.1219 | 39.5310 | 40.0378 | ||
50 | 0 | 24.2603 | 24.8590 | 25.5886 | 34.4542 | 34.8808 | 35.4075 | 24.2603 | 24.8590 | 25.5886 | 34.4542 | 34.8808 | 35.4075 | |
1 | 23.2769 | 23.9171 | 24.6960 | 36.1364 | 36.5518 | 37.0654 | 23.2769 | 23.9171 | 24.6960 | 36.1364 | 36.5518 | 37.0654 | ||
5 | 20.6170 | 21.3895 | 22.3260 | 39.7557 | 40.1583 | 40.6573 | 20.6170 | 21.3895 | 22.3260 | 39.7557 | 40.1583 | 40.6573 | ||
100 | 0 | 25.2697 | 25.8451 | 26.5476 | 35.1723 | 35.5903 | 36.1066 | 25.2697 | 25.8451 | 26.5476 | 35.1723 | 35.5903 | 36.1066 | |
1 | 24.3271 | 24.9403 | 25.6883 | 36.8216 | 37.2294 | 37.7338 | 24.3271 | 24.9403 | 25.6883 | 36.8216 | 37.2294 | 37.7338 | ||
5 | 21.7957 | 22.5278 | 23.4188 | 40.3795 | 40.7760 | 41.2675 | 21.7957 | 22.5278 | 23.4188 | 40.3795 | 40.7760 | 41.2675 |