Acta Aeronautica et Astronautica Sinica ›› 2023, Vol. 44 ›› Issue (13): 227827-227827.doi: 10.7527/S1000-6893.2022.27827
• Solid Mechanics and Vehicle Conceptual Design • Previous Articles Next Articles
Yu WANG(), Hongda XU, Hao LI, Chang LI
Received:
2022-07-18
Revised:
2022-10-20
Accepted:
2022-11-09
Online:
2022-11-21
Published:
2022-11-17
Contact:
Yu WANG
E-mail:wangyu435@126.com
Supported by:
CLC Number:
Yu WANG, Hongda XU, Hao LI, Chang LI. Vibration analysis of rotating dual⁃functional gradient composite cylindrical shell reinforced with carbon nanotubes[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(13): 227827-227827.
Table 5
Influence of number of segments on natural frequency under S⁃S boundary condition
类型 | 模态(m,n) | 固有频率/Hz | ||||
---|---|---|---|---|---|---|
n0=0 | n0=1 | n0=2 | n0=3 | n0=4 | ||
FG-UD | (1,5) | 1 261 | 1 569 | 1 552 | 1 549 | 1 549 |
(2,5) | 2 765 | 3 208 | 3 331 | 3 283 | 3 282 | |
DFG-X | (1,5) | 1 366 | 1 669 | 1 652 | 1 649 | 1 648 |
(2,5) | 2 881 | 3 343 | 3 471 | 3 421 | 3 420 | |
DFG-O | (1,5) | 1 214 | 1 533 | 1 516 | 1 512 | 1 512 |
(2,5) | 2 766 | 3 209 | 3 333 | 3 285 | 3 284 | |
DFG-V | (1,5) | 1 283 | 1 595 | 1 578 | 1 575 | 1 575 |
(2,5) | 2 826 | 3 279 | 3 405 | 3 356 | 3 355 | |
DFG-A | (1,5) | 1 295 | 1 602 | 1 585 | 1 582 | 1 581 |
(2,5) | 2 809 | 3 257 | 3 381 | 3 333 | 3 332 |
Table 6
Influence of number of segments on natural frequency under C⁃C boundary condition
类型 | 模态(m,n) | 固有频率/Hz | ||||
---|---|---|---|---|---|---|
n0=0 | n0=1 | n0=2 | n0=3 | n0=4 | ||
FG-UD | (1,5) | 1 579 | 1 965 | 1 944 | 1 940 | 1 940 |
(2,5) | 2 988 | 3 466 | 3 579 | 3 548 | 3 547 | |
DFG-X | (1,5) | 1 700 | 2 077 | 2 057 | 2 053 | 2 052 |
(2,5) | 3 058 | 3 639 | 3 758 | 3 724 | 3 723 | |
DFG-O | (1,5) | 1 537 | 1 940 | 1 919 | 1 914 | 1 913 |
(2,5) | 3 013 | 3 442 | 3 554 | 3 523 | 3 522 | |
DFG-V | (1,5) | 1 615 | 2 008 | 1 986 | 1 983 | 1 982 |
(2,5) | 3 026 | 4 017 | 3 648 | 3 616 | 3 612 | |
DFG-A | (1,5) | 1 614 | 1 996 | 1 975 | 1 972 | 1 970 |
(2,5) | 3 027 | 3 510 | 3 623 | 3 592 | 3 592 |
Table 7
Influence of number of segments on natural frequency under C⁃F boundary condition
类型 | 模态(m,n) | 固有频率/Hz | ||||
---|---|---|---|---|---|---|
n0=0 | n0=1 | n0=2 | n0=3 | n0=4 | ||
FG-UD | (1,5) | 872 | 1 084 | 1 073 | 1 071 | 1 071 |
(2,5) | 1 860 | 2 158 | 2 220 | 2 208 | 2 208 | |
DFG-X | (1,5) | 980 | 1 197 | 1 185 | 1 183 | 1 183 |
(2,5) | 1 908 | 2 271 | 2 338 | 2 324 | 2 324 | |
DFG-O | (1,5) | 817 | 1 031 | 1 020 | 1 017 | 1 015 |
(2,5) | 1 870 | 2 136 | 2 209 | 2 187 | 2 183 | |
DFG-V | (1,5) | 899 | 1 115 | 1 103 | 1 101 | 1 101 |
(2,5) | 1 884 | 2 200 | 2 265 | 2 252 | 2 252 | |
DFG-A | (1,5) | 897 | 1 109 | 1 098 | 1 096 | 1 096 |
(2,5) | 1 886 | 2 187 | 2 260 | 2 238 | 2 238 |
Table 8
Comparison of traveling wave frequencies of rotating isotropic cylindrical shell
振型(m,n) | 行波频率 | 频率/Hz | RD/% | |
---|---|---|---|---|
文献[ | 本文 | |||
(1,20) | ff | 9 607 | 0.04 | |
fb | 9 627 | 0.04 | ||
(1,21) | ff | 10 566 | 0.04 | |
fb | 10 586 | 0.03 | ||
(1,22) | ff | 11 573 | 0.03 | |
fb | 11 591 | 0.03 | ||
(1,23) | ff | 12 626 | 0.02 | |
fb | 12 644 | 0.02 | ||
(1,24) | ff | 13 725 | 0.01 | |
fb | 13 742 | 0.01 | ||
(1,25) | ff | 14 872 | 0.01 | |
fb | 14 888 | 0.01 |
Table 9
Comparison of natural frequency of FG cylindrical shell
振型 (m,n) | 简支-简支 | 固支-自由 | ||||
---|---|---|---|---|---|---|
文献[ | 本文固有频率/Hz | RD/% | 文献[ | 本文固有频率/Hz | RD/% | |
(1,1) | 13.211 | 13.216 | 0.038 | 250.8 | 249.02 | 0.71 |
(1,2) | 4.48 | 4.481 | 0.022 | 151.53 | 150.02 | 1.01 |
(1,3) | 4.156 9 | 4.157 | 0.002 | 219.33 | 218.76 | 0.26 |
(1,4) | 7.038 2 | 7.038 | 0.003 | 382.85 | 386.91 | 1.05 |
(1,5) | 11.241 | 11.241 | 0 | |||
(1,6) | 16.454 | 16.455 | 0.006 | |||
(1,7) | 22.634 | 22.635 | 0.004 | |||
(1,8) | 29.77 | 29.771 | 0.003 | |||
(1,9) | 37.859 | 37.862 | 0.008 | |||
(1,10) | 46.901 | 46.905 | 0.009 |
Table 11
Natural frequencies of DFG⁃CNTRC cylindrical shell
阶次 | FG-UD | DFG-X | DFG-O | DFG-V | DFG-A | |||||
---|---|---|---|---|---|---|---|---|---|---|
振型(m,n) | 频率/Hz | 振型(m,n) | 频率/Hz | 振型(m,n) | 频率/Hz | 振型(m,n) | 频率/Hz | 振型(m,n) | 频率/Hz | |
1 | (1,5) | 1 549 | (1,5) | 1 649 | (1,5) | 1 512 | (1,5) | 1 575 | (1,5) | 1 582 |
2 | (1,4) | 1 713 | (1,4) | 1 769 | (1,6) | 1 651 | (1,4) | 1 741 | (1,4) | 1 738 |
3 | (1,6) | 1 728 | (1,6) | 1 893 | (1,4) | 1 713 | (1,6) | 1 763 | (1,6) | 1 778 |
4 | (1,7) | 2 136 | (1,3) | 2 356 | (1,7) | 2 019 | (1,7) | 2 187 | (1,7) | 2 205 |
5 | (1,3) | 2 306 | (1,7) | 2 374 | (1,3) | 2 340 | (1,3) | 2 351 | (1,3) | 2 343 |
6 | (1,8) | 2 691 | (1,8) | 3 007 | (1,8) | 2 534 | (1,8) | 2 760 | (1,8) | 2 780 |
7 | (2,6) | 3 048 | (2,6) | 3 230 | (2,6) | 2 996 | (2,6) | 3 114 | (2,6) | 3 094 |
8 | (2,7) | 3 112 | (2,7) | 3 363 | (2,7) | 3 004 | (2,7) | 3 180 | (2,7) | 3 169 |
Table 12
Influence of Coriolis force on frequency characteristics of rotating DFG⁃CNTRC cylindrical shell
结构模型 | 科氏力 | 类型 | 频率/Hz | |||||
---|---|---|---|---|---|---|---|---|
0 r/min | 2×103 r/min | 4×103 r/min | 6×103 r/min | 8×103 r/min | 1×104 r/min | |||
FG-UD | 无 | 动频 | 1 549 | 1 557 | 1 580 | 1 618 | 1 670 | 1 734 |
有 | 前行波 | 1 549 | 1 544 | 1 554 | 1 580 | 1 619 | 1 671 | |
后行波 | 1 549 | 1 570 | 1 606 | 1 657 | 1 722 | 1 800 | ||
DFG-X | 无 | 动频 | 1 649 | 1 656 | 1 678 | 1 714 | 1 763 | 1 824 |
有 | 前行波 | 1 649 | 1 643 | 1 652 | 1 675 | 1 712 | 1 760 | |
后行波 | 1 649 | 1 669 | 1 704 | 1 753 | 1 815 | 1 889 | ||
DFG-O | 无 | 动频 | 1 512 | 1 520 | 1 544 | 1 583 | 1 636 | 1 701 |
有 | 前行波 | 1 512 | 1 507 | 1 518 | 1 545 | 1 585 | 1 638 | |
后行波 | 1 512 | 1 533 | 1 570 | 1 622 | 1 688 | 1 767 | ||
DFG-V | 无 | 动频 | 1 575 | 1 583 | 1 605 | 1 643 | 1 694 | 1 757 |
有 | 前行波 | 1 575 | 1 570 | 1 579 | 1 604 | 1 642 | 1 692 | |
后行波 | 1 575 | 1 596 | 1 632 | 1 683 | 1 747 | 1 824 | ||
DFG-A | 无 | 动频 | 1 582 | 1 589 | 1 612 | 1 649 | 1 700 | 1 764 |
有 | 前行波 | 1 582 | 1 577 | 1 587 | 1 612 | 1 650 | 1 701 | |
后行波 | 1 582 | 1 602 | 1 638 | 1 688 | 1 752 | 1 828 |
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