Acta Aeronautica et Astronautica Sinica ›› 2024, Vol. 45 ›› Issue (22): 230280.doi: 10.7527/S1000-6893.2024.30280
• Solid Mechanics and Vehicle Conceptual Design • Previous Articles
Ke WU1,2, Qibo PENG1(), Xinfeng WU1, Pengbo LIU3, Yajun KOU1
Received:
2024-02-02
Revised:
2024-03-28
Accepted:
2024-05-30
Online:
2024-07-25
Published:
2024-06-14
Contact:
Qibo PENG
E-mail:poochie003@163.com
CLC Number:
Ke WU, Qibo PENG, Xinfeng WU, Pengbo LIU, Yajun KOU. Analytical method for vibration analysis of multi-cracked Timoshenko beam structures with elastic foundations[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(22): 230280.
Table 1
First order normalized natural frequencies of undamaged simply supported beams with elastic foundations
无量纲自然频率 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
本文 | 文献[ | 文献[ | 本文 | 文献[ | 本文 | 文献[ | |||||
0 | 0 | 3.141 40 | 3.141 43 | 3.141 5 | 3.129 91 | 3.130 24 | 3.045 33 | 3.047 99 | |||
0.5 | 3.476 59 | 3.476 59 | 3.476 7 | 3.467 11 | 3.466 71 | 3.398 64 | 3.394 58 | ||||
1.0 | 3.735 87 | 3.735 87 | 3.736 0 | 3.727 40 | 3.726 56 | 3.667 05 | 3.658 02 | ||||
2.5 | 4.296 89 | 4.296 86 | 4.297 0 | 4.289 72 | 4.288 09 | 4.239 47 | 4.218 34 | ||||
102 | 0 | 3.748 23 | 3.748 23 | 3.748 3 | 3.739 80 | 3.738 94 | 3.679 77 | 3.670 50 | |||
0.5 | 3.960 68 | 3.960 67 | 3.960 8 | 3.952 86 | 3.951 68 | 3.897 52 | 3.883 97 | ||||
1.0 | 4.143 58 | 4.143 56 | 4.143 7 | 4.136 15 | 4.134 71 | 4.083 87 | 4.066 36 | ||||
2.5 | 4.582 28 | 4.582 26 | 4.582 4 | 4.575 46 | 4.573 47 | 4.527 93 | 4.499 13 | ||||
104 | 0 | 10.024 1 | 10.024 0 | 10.024 | 10.015 0 | 9.995 82 | 7.376 58 | 7.340 81 | |||
0.5 | 10.036 1 | 10.036 1 | 10.036 | 10.027 0 | 10.007 7 | 7.376 58 | 7.340 88 | ||||
1.0 | 10.048 2 | 10.048 1 | 10.048 | 10.039 0 | 10.019 6 | 7.376 58 | 7.340 95 | ||||
2.5 | 10.084 0 | 10.083 9 | 10.084 | 10.074 8 | 10.055 1 | 7.376 58 | 7.341 16 | ||||
106 | 0 | 31.623 0 | 31.621 7 | 31.623 | 12.776 6 | 12.772 2 | 7.356 58 | 7.350 81 | |||
0.5 | 31.623 4 | 31.622 1 | 31.623 | 12.776 6 | 12.772 2 | 7.356 58 | 7.350 81 | ||||
1.0 | 31.623 8 | 31.622 4 | 31.624 | 12.776 6 | 12.772 2 | 7.356 58 | 7.350 81 | ||||
2.5 | 31.625 0 | 31.623 6 | 31.625 | 12.776 6 | 12.772 2 | 7.356 58 | 7.350 81 |
Table 2
Normalized natural frequencies of first three and 100th order for different boundaries of undamaged beams with elastic foundations (K¯w=1/30, α1=0, h/L=0.2, v=0.3, κ=5/6)
边界 | 方法 | 无量纲自然频率 | |||||
---|---|---|---|---|---|---|---|
H-H | 0 | 0 | 本文 | 9.275 | 32.166 | 61.458 | 1 443.213 |
LSM(n=20) | 9.274 | 32.15 | 61.29 | ||||
LSM(n=100) | 9.274 | 32.17 | 61.45 | ||||
TMM | 9.274 | 32.17 | 61.46 | ||||
1/2 | 0 | 本文 | 9.531 9 | 32.239 | 61.495 | 1 443.214 | |
LSM(n=20) | 9.531 | 32.22 | 61.33 | ||||
LSM(n=100) | 9.532 | 32.24 | 61.49 | ||||
TMM | 9.532 | 32.24 | 61.49 | ||||
1/2 | 本文 | 11.681 | 34.730 | 64.458 | 1 469.177 | ||
LSM(n=20) | 11.67 | 34.41 | 64.40 | ||||
LSM(n=100) | 11.68 | 34.67 | 64.64 | ||||
TMM | 11.68 | 34.72 | 64.45 | ||||
1 | 0 | 本文 | 9.784 8 | 32.311 | 61.532 | 1 443.216 | |
LSM(n=20) | 9.784 | 32.29 | 61.38 | ||||
LSM(n=100) | 9.784 | 32.31 | 61.53 | ||||
TMM | 9.785 | 32.31 | 61.53 | ||||
1 | 本文 | 13.804 | 37.524 | 67.734 | 1 483.261 | ||
LSM(n=20) | 13.79 | 37.44 | 67.42 | ||||
LSM(n=100) | 13.80 | 37.52 | 67.72 | ||||
TMM | 13.80 | 37.52 | 67.73 | ||||
C-H | 2/3 | 本文 | 15.196 | 40.336 | 68.965 | 1 469.177 | |
LSM(n=20) | 15.18 | 40.09 | 68.40 | ||||
LSM(n=100) | 15.20 | 40.34 | 68.96 | ||||
TMM | 15.20 | 40.34 | 68.97 | ||||
C-C | 2/3 | 本文 | 19.225 | 42.246 | 70.305 | 1 483.623 | |
LSM(n=20) | 19.20 | 42.29 | 70.00 | ||||
LSM(n=100) | 19.22 | 42.24 | 70.31 | ||||
TMM | 19.22 | 42.24 | 70.31 |
Table 3
Natural frequencies of double-cracked beam with partially supported elastic foundation
边界 | 裂纹尺寸 | 无量纲自然频率 | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
LSM方法(n=100) | 本文方法 | ||||||||||||||
C-F | 0 | 0 | 0 | 0 | 0 | 3.410 | 18.36 | 43.71 | 72.56 | 3.409 7 | 18.363 | 43.709 | 72.567 | 1 441.97 | |
1/30 | 0 | 4.635 | 18.61 | 43.81 | 72.62 | 4.635 4 | 18.614 | 43.811 | 72.626 | 1 441.97 | |||||
1/30 | 7.563 | 24.58 | 50.07 | 79.59 | 7.563 3 | 24.583 | 50.073 | 79.609 | 1 467.70 | ||||||
0.2 | 0.1 | 0.2 | 0 | 0 | 3.212 | 17.27 | 39.68 | 69.82 | 3.213 2 | 17.252 | 39.678 | 69.937 | 1 428.00 | ||
3.211 2 | 17.173 | 39.544 | 69.341 | 1 412.10 | |||||||||||
1/30 | 0 | 4.491 | 17.53 | 39.79 | 69.89 | 4.491 7 | 17.518 | 39.789 | 69.998 | 1 428.01 | |||||
4.490 3 | 17.438 | 39.654 | 69.402 | 1 412.10 | |||||||||||
1/30 | 7.517 | 23.87 | 46.59 | 76.93 | 7.518 4 | 23.864 | 46.594 | 77.042 | 1 458.04 | ||||||
7.504 3 | 23.613 | 46.404 | 75.837 | 1 446.27 | |||||||||||
H-H | 0 | 0 | 0 | 0 | 0 | 9.274 | 32.17 | 61.45 | 93.24 | 9.274 0 | 32.166 | 61.458 | 93.259 | 1 443.21 | |
1/30 | 0 | 9.785 | 32.31 | 61.53 | 93.28 | 9.784 8 | 32.311 | 61.532 | 93.308 | 1 443.21 | |||||
1/30 | 13.80 | 37.52 | 67.72 | 100.6 | 13.804 | 37.524 | 67.734 | 100.62 | 1 483.26 | ||||||
0.2 | 0.1 | 0.2 | 0 | 0 | 8.345 | 29.03 | 60.03 | 91.26 | 8.340 4 | 29.047 | 60.107 | 91.139 | 1 442.66 | ||
8.401 2 | 28.940 | 59.671 | 90.416 | 1 419.19 | |||||||||||
1/30 | 0 | 8.909 | 29.18 | 60.11 | 91.31 | 8.904 3 | 29.205 | 60.183 | 91.189 | 1 442.66 | |||||
8.961 3 | 29.099 | 59.747 | 90.466 | 1 419.19 | |||||||||||
1/30 | 13.20 | 34.85 | 66.41 | 98.69 | 13.199 | 34.876 | 54.413 | 66.489 | 1 469.17 | ||||||
13.224 | 34.719 | 65.902 | 97.630 | 1 450.33 | |||||||||||
C-H | 0 | 0 | 0 | 0 | 0 | 13.44 | 36.88 | 65.19 | 95.75 | 13.436 | 36.877 | 65.195 | 95.769 | 1 456.50 | |
1/30 | 0 | 13.79 | 37.01 | 65.26 | 95.79 | 13.794 | 37.005 | 65.266 | 95.817 | 1 456.50 | |||||
1/30 | 17.14 | 41.74 | 71.18 | 102.9 | 17.140 | 41.742 | 71.186 | 102.95 | 1 483.26 | ||||||
0.2 | 0.1 | 0.2 | 0 | 0 | 12.67 | 34.07 | 63.64 | 93.84 | 12.662 | 34.074 | 63.711 | 93.728 | 1 442.94 | ||
12.678 | 33.927 | 63.333 | 93.020 | 1 419.19 | |||||||||||
1/30 | 0 | 13.04 | 34.21 | 63.71 | 93.89 | 13.041 | 34.211 | 63.783 | 93.777 | 1 442.94 | |||||
13.056 | 34.063 | 63.405 | 93.069 | 1 419.19 | |||||||||||
1/30 | 16.59 | 39.27 | 69.77 | 101.1 | 16.591 | 39.284 | 69.842 | 100.95 | 1 469.17 | ||||||
16.581 | 39.076 | 69.317 | 100.02 | 1 456.21 | |||||||||||
C-C | 0 | 0 | 0 | 0 | 0 | 17.99 | 41.19 | 68.64 | 98.06 | 17.994 | 41.189 | 68.646 | 98.083 | 1 469.17 | |
1/30 | 0 | 18.27 | 41.31 | 68.71 | 98.11 | 18.265 | 41.305 | 68.714 | 98.130 | 1 469.17 | |||||
1/30 | 20.95 | 45.71 | 74.40 | 105.1 | 20.953 | 45.708 | 74.410 | 105.11 | 1 485.45 | ||||||
0.2 | 0.1 | 0.2 | 0 | 0 | 17.60 | 38.36 | 67.04 | 96.26 | 17.591 | 38.347 | 67.111 | 96.149 | 1 443.16 | ||
17.570 | 38.158 | 66.765 | 95.442 | 1 419.89 | |||||||||||
1/30 | 0 | 17.88 | 38.49 | 67.10 | 96.31 | 17.868 | 38.470 | 67.180 | 96.196 | 1 443.17 | |||||
17.847 | 38.279 | 66.834 | 95.489 | 1 419.89 | |||||||||||
1/30 | 20.62 | 43.23 | 72.95 | 103.3 | 20.616 | 43.229 | 73.023 | 103.17 | 1 469.17 | ||||||
20.569 | 42.954 | 72.544 | 102.25 | 1 465.25 |
Table 4
Modal frequencies of two-dimensional frame structures without cracks and elastic foundations
边界 (i-j-k-l) | 模态自然频率/Hz | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
FEM方法 | 本文方法(5组件) | ||||||||||
260单元 | 1 721单元 | ||||||||||
C-H-H-C | 63.887 | 113.156 | 130.954 | 148.367 | 23 867.01 | 23 723.38 | 63.886 | 113.151 | 130.951 | 148.360 | 23 629.031 |
C-C-C-C | 64.108 | 125.551 | 150.633 | 179.262 | 23 877.11 | 23 761.48 | 64.107 | 125.549 | 150.625 | 179.257 | 23 642.645 |
H-H-H-H | 44.102 | 86.858 | 116.941 | 142.524 | 23 570.97 | 23 403.27 | 44.101 | 86.857 | 116.935 | 142.519 | 23 298.577 |
H-C-C-H | 44.211 | 87.704 | 139.165 | 154.692 | 23 879.99 | 23 757.23 | 44.210 | 87.702 | 139.161 | 154.685 | 23 634.636 |
Table 5
Modal frequencies of multi-segment elastic foundation and multi-crack frame structures
边界 | 裂纹尺寸 | 自然模态频率/Hz | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
C-H-H-C | 0 | 0 | 0 | 0 | 0.1 | 0.1 | 0.1 | 0.1 | 63.867 | 113.084 | 130.930 | 148.272 | 23 628.63 |
1/30 | 0 | 1/30 | 0 | 0 | 0 | 0 | 0 | 120.543 | 148.866 | 215.241 | 462.730 | 39 557.27 | |
1/30 | 1/30 | 0 | 0 | 0 | 0 | 120.631 | 148.901 | 215.258 | 462.869 | 40 546.91 | |||
0 | 0 | 0 | 0 | 0.2 | 0.2 | 0.2 | 0.2 | 63.812 | 112.890 | 130.869 | 148.020 | 23 627.67 | |
1/30 | 0 | 1/30 | 0 | 0.2 | 0.3 | 0.3 | 0.2 | 120.024 | 148.377 | 215.058 | 460.048 | 39 405.16 | |
1/30 | 1/30 | 0.3 | 0.4 | 0.4 | 0.3 | 119.560 | 147.865 | 214.874 | 457.645 | 39 300.34 | |||
C-C-C-C | 0 | 0 | 0 | 0 | 0.1 | 0.1 | 0.1 | 0.1 | 64.089 | 125.542 | 150.553 | 179.248 | 23 639.87 |
1/30 | 0 | 1/30 | 0 | 0 | 0 | 0 | 0 | 153.416 | 216.941 | 259.464 | 526.709 | 40 373.36 | |
1/30 | 1/30 | 0 | 0 | 0 | 0 | 153.518 | 216.990 | 259.464 | 526.872 | 40 381.05 | |||
0 | 0 | 0 | 0 | 0.2 | 0.2 | 0.2 | 0.2 | 64.036 | 125.521 | 150.343 | 179.223 | 23 637.89 | |
1/30 | 0 | 1/30 | 0 | 0.2 | 0.3 | 0.3 | 0.2 | 152.837 | 216.050 | 259.059 | 523.455 | 40 217.22 | |
1/30 | 1/30 | 0.3 | 0.4 | 0.4 | 0.3 | 152.361 | 215.156 | 258.586 | 520.579 | 40 087.45 | |||
H-H-H-H | 0 | 0 | 0 | 0 | 0.1 | 0.1 | 0.1 | 0.1 | 44.088 | 86.853 | 116.858 | 142.474 | 23 285.47 |
1/30 | 0 | 1/30 | 0 | 0 | 0 | 0 | 0 | 120.543 | 148.866 | 215.241 | 462.730 | 39 557.27 | |
1/30 | 1/30 | 0 | 0 | 0 | 0 | 120.631 | 148.901 | 215.258 | 462.869 | 39 561.00 | |||
0 | 0 | 0 | 0 | 0.2 | 0.2 | 0.2 | 0.2 | 44.047 | 86.841 | 116.634 | 142.343 | 23 247.32 | |
1/30 | 0 | 1/30 | 0 | 0.2 | 0.3 | 0.3 | 0.2 | 120.024 | 148.377 | 215.058 | 460.048 | 39 405.16 | |
1/30 | 1/30 | 0.3 | 0.4 | 0.4 | 0.3 | 119.560 | 147.865 | 214.874 | 457.645 | 39 300.34 | |||
H-C-C-H | 0 | 0 | 0 | 0 | 0.1 | 0.1 | 0.1 | 0.1 | 44.197 | 87.701 | 139.129 | 154.634 | 23 627.03 |
1/30 | 0 | 1/30 | 0 | 0 | 0 | 0 | 0 | 153.416 | 216.941 | 259.464 | 526.709 | 40 373.36 | |
1/30 | 1/30 | 0 | 0 | 0 | 0 | 153.518 | 216.990 | 259.464 | 526.872 | 40 381.05 | |||
0 | 0 | 0 | 0 | 0.2 | 0.2 | 0.2 | 0.2 | 44.157 | 87.699 | 139.037 | 154.490 | 23 604.17 | |
1/30 | 0 | 1/30 | 0 | 0.2 | 0.3 | 0.3 | 0.2 | 152.724 | 215.660 | 258.732 | 523.331 | 40 150.16 | |
1/30 | 1/30 | 0.3 | 0.4 | 0.4 | 0.3 | 152.361 | 215.156 | 258.586 | 520.579 | 40 087.45 |
1 | WINKLER E. Die Lehre von der Elasticitaet und Festigkeit: Mit besonderer Rücksicht auf ihre Anwendung in der Technik, für polytechnische schulen, bauakademien, ingenieure, maschinenbauer, architecten, etc[M]. Dominicus, 1867 (in German). |
2 | BHATTIPROLU U, BAJAJ A K, DAVIES P. An efficient solution methodology to study the response of a beam on viscoelastic and nonlinear unilateral foundation: Static response[J]. International Journal of Solids and Structures, 2013, 50(14-15): 2328-2339. |
3 | EISENBERGER M, YANKELEVSKY D Z, ADIN M A. Vibrations of beams fully or partially supported on elastic foundations[J]. Earthquake Engineering & Structural Dynamics, 1985, 13(5): 651-660. |
4 | MARZANI A, MAZZOTTI M, VIOLA E, et al. FEM formulation for dynamic instability of fluid-conveying pipe on nonuniform elastic foundation[J]. Mechanics Based Design of Structures and Machines, 2012, 40(1): 83-95. |
5 | ONISZCZUK Z. Free transverse vibrations of elastically connected simply supported double-beam complex system[J]. Journal of Sound and Vibration, 2000, 232(2): 387-403. |
6 | YOKOYAMA T. Vibration analysis of Timoshenko beam-columns on two-parameter elastic foundations[J]. Computers & Structures, 1996, 61(6): 995-1007. |
7 | FENG Z H, COOK R D. Beam elements on two-parameter elastic foundations[J]. Journal of Engineering Mechanics, 1983, 109(6): 1390-1402. |
8 | MATSUNAGA H. Vibration and buckling of deep beam-columns on two-parameter elastic foundations[J]. Journal of Sound and Vibration, 1999, 228(2): 359-376. |
9 | CHEN C N. Dqem vibration analyses of non-prismatic shear deformable beams resting on elastic foundations[J]. Journal of Sound and Vibration, 2002, 255(5): 989-999. |
10 | MALEKZADEH P, KARAMI G. A mixed differential quadrature and finite element free vibration and buckling analysis of thick beams on two-parameter elastic foundations[J]. Applied Mathematical Modelling, 2008, 32(7): 1381-1394. |
11 | MA X, BUTTERWORTH J W, CLIFTON G C. Static analysis of an infinite beam resting on a tensionless Pasternak foundation[J]. European Journal of Mechanics- A, 2009, 28(4): 697-703. |
12 | PAPADOPOULOS C A, DIMAROGONAS A D. Coupled longitudinal and bending vibrations of a rotating shaft with an open crack[J]. Journal of Sound and Vibration, 1987, 117(1): 81-93. |
13 | KHIEM N T, TOAN L K. A novel method for crack detection in beam-like structures by measurements of natural frequencies[J]. Journal of Sound and Vibration, 2014, 333(18): 4084-4103. |
14 | LIU J, ZHU W D, CHARALAMBIDES P G, et al. A dynamic model of a cantilever beam with a closed, embedded horizontal crack including local flexibilities at crack tips[J]. Journal of Sound and Vibration, 2016, 382: 274-290. |
15 | HAN H S, LIU L, CAO D Q. Analytical approach to coupled bending-torsional vibrations of cracked Timoshenko beam[J]. International Journal of Mechanical Sciences, 2020, 166: 105235. |
16 | ZHAO X, HU Q J, CROSSLEY W, et al. Analytical solutions for the coupled thermoelastic vibrations of the cracked Euler-Bernoulli beams by means of Green’s functions[J]. International Journal of Mechanical Sciences, 2017, 128-129: 37-53. |
17 | ZHAO X, ZHAO Y R, GAO X Z, et al. Green׳s functions for the forced vibrations of cracked Euler-Bernoulli beams[J]. Mechanical Systems and Signal Processing, 2016, 68-69: 155-175. |
18 | ATTAR M. A transfer matrix method for free vibration analysis and crack identification of stepped beams with multiple edge cracks and different boundary conditions[J]. International Journal of Mechanical Sciences, 2012, 57(1): 19-33. |
19 | HSU M H. Vibration analysis of edge-cracked beam on elastic foundation with axial loading using the differential quadrature method[J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194(1): 1-17. |
20 | MATBULY M S, RAGB O, NASSAR M. Natural frequencies of a functionally graded cracked beam using the differential quadrature method[J]. Applied Mathematics and Computation, 2009, 215(6): 2307-2316. |
21 | YANG B, TAN C A. Transfer functions of one-dimensional distributed parameter systems[J]. Journal of Applied Mechanics, 1992, 59(4): 1009-1014. |
22 | YANG B. Distributed transfer function analysis of complex distributed parameter systems[J]. Journal of Applied Mechanics, 1994, 61(1): 84-92. |
23 | ZHOU J, YANG B. Strip distributed transfer function method for analysis of plates[J]. International Journal for Numerical Methods in Engineering, 1996, 39(11): 1915-1932. |
24 | LIU S B, YANG B G. A closed-form analytical solution method for vibration analysis of elastically connected double-beam systems[J]. Composite Structures, 2019, 212: 598-608. |
25 | NOH K, YANG B. An augmented state formulation for modeling and analysis of multibody distributed dynamic systems[J]. Journal of Applied Mechanics, 2014, 81(5): 051011. |
26 | YANG B G, LIU S B. Closed-form analytical solutions of transient heat conduction in hollow composite cylinders with any number of layers[J]. International Journal of Heat and Mass Transfer, 2017, 108: 907-917. |
27 | FANG H F, YANG B G, DING H L, et al. Dynamic analysis of large in-space deployable membrane antennas[C]∥13th International Congress on Sound and Vibration (ICSV13-Vienna). Washington,D.C.:NASA,2006. |
28 | YANG B G, ZHANG Y C. A new method for mid- to high-frequency vibration analyses of beam structures[C]∥SAE Technical Paper Series. Warrendale: SAE International, 2019. |
29 | GIRIJA VALLABHAN C V, DAS Y C. Modified Vlasov model for beams on elastic foundations[J]. Journal of Geotechnical Engineering, 1991, 117(6): 956-966. |
30 | TADA H, PARIS P C, IRWIN G R. The stress analysis of cracks[M]. New York: ASME, 2000. |
31 | CHEN W Q, LÜ C F, BIAN Z G. A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation[J]. Applied Mathematical Modelling, 2004, 28(10): 877-890. |
32 | DE ROSA M A, MAURIZI M J. The influence of concentrated masses and Pasternak soil on the free vibrations of Euler beams—exact solution[J]. Journal of Sound and Vibration, 1998, 212(4): 573-581. |
33 | ATTAR M, KARRECH A, REGENAUER-LIEB K. Free vibration analysis of a cracked shear deformable beam on a two-parameter elastic foundation using a lattice spring model[J]. Journal of Sound and Vibration, 2014, 333(11): 2359-2377. |
[1] | Yulian GONG, Jianguo ZHANG, Zhigang WU, Guangyuan CHU, Xiaoduo FAN, Ying HUANG. Reliability algorithm of composite structure based on active learning basis-adaptive PC-Kriging model [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(8): 228982-228982. |
[2] | Ruiqing MA, Peng CHEN. Research and development trend of initial position identification methods for permanent magnet synchronous motors [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(3): 28776-028776. |
[3] | Dehui ZHANG, Xiaohong DING, Tiannan HU, Heng ZHANG. Optimization design of natural frequencies for thin-walled structures based on improved adaptive growth method [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(19): 228378-228378. |
[4] | Zhao KE, Yongxin SHI, Peng ZHANG, Kuo TIAN, Bo WANG. Vibration reduction optimization of complex thin-walled structures based on global POD reduced-order model [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(13): 227900-227900. |
[5] | FEI Zhongyang, JIANG Xiangwen, ZHAO Qijun. Design of helicopter target rotor based on similar dynamic RCS characteristics [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(7): 125465-125465. |
[6] | LIU Zhihui, NIU Junchuan, JIA Ruihao. Energy flow model for high-frequency vibration of beams in thermal-gradient environment [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(5): 425336-425336. |
[7] | XU Luopeng, HU Shi, LIU Qingsong, WANG Qingyuan. High-frequency fatigue infrared heat dissipation of new Al-Li alloy AA2198 [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(9): 224482-224482. |
[8] | XU Jinghui, QIAO Baijie, TENG Guangrong, YANG Zhibo, CHEN Xuefeng. Parameter identification of blade tip timing signal using compressed sensing [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(5): 524229-524229. |
[9] | PENG Zhenrui, CAO Mingming, LIU Mandong. Model updating method based on wavelet decomposition of acceleration frequency response function [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(7): 223548-223548. |
[10] | FAN Xinliang, WANG Tong, XIA Zunping. A finite element model updating method for local structures [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(12): 223834-223834. |
[11] | JIA Baohui, YU Lingjie, LU Xiang. Vibration characteristics analysis of pressurized repair hydraulic pipe of civil aircraft based on ANSYS Workbench [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(9): 222828-222828. |
[12] | TENG Xiaoyan, FENG Guobao, JIANG Xudong, ZHAO Hetao. Analytical model of high-frequency energy flow response for a beam with free layer damping [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(4): 222616-222616. |
[13] | CHEN Zhaolin, YANG Zhichun, WANG Yongyan, ZHANG Xinping. A high-frequency shock response analysis method based on energy finite element method and virtual mode synthesis and simulation [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(8): 221893-221893. |
[14] | FAN Gang, WU Shaoqing, LI Yanbin, FEI Qingguo, HAN Xiaolin. Identification of spatial distribution of modulus field of composite material based on frequency response function [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(8): 221024-221024. |
[15] | HE Erming, CHEN Bing, CAO Cunxian. Vibration mode evolution of 2D woven C/SiC composite panels in hot environment [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(7): 220553-220553. |
Viewed | ||||||||||||||||||||||||||||||||||||||||||||||||||
Full text 33
|
|
|||||||||||||||||||||||||||||||||||||||||||||||||
Abstract 83
|
|
|||||||||||||||||||||||||||||||||||||||||||||||||
Address: No.238, Baiyan Buiding, Beisihuan Zhonglu Road, Haidian District, Beijing, China
Postal code : 100083
E-mail:hkxb@buaa.edu.cn
Total visits: 6658907 Today visits: 1341All copyright © editorial office of Chinese Journal of Aeronautics
All copyright © editorial office of Chinese Journal of Aeronautics
Total visits: 6658907 Today visits: 1341