基于Chebyshev-Ritz法分析多裂纹梁自振特性
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赵佳雷,周叮,张建东,胡朝斌
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Free vibration characteristics of multi-cracked beam based on Chebyshev-Ritz method
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Jia-lei ZHAO,Ding ZHOU,Jian-dong ZHANG,Chao-bin HU
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| 表 1 固支梁前8阶的频率参数Ω的收敛性 |
| Tab.1 Convergence of first-eighth frequency parameters Ω of fixed beam |
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| h/L | mn | Ω1 | Ω2 | Ω3 | Ω4 | Ω5 | Ω6 | Ω7 | Ω8 | | 0.1 | 40×10 | 0.183 7 | 0.488 4 | 0.831 2 | 0.987 1 | 1.341 8 | 1.774 1 | 1.949 6 | 2.397 6 | | 0.1 | 50×10 | 0.183 3 | 0.488 2 | 0.828 5 | 0.986 8 | 1.341 2 | 1.769 8 | 1.948 7 | 2.397 0 | | 0.1 | 50×15 | 0.183 3 | 0.488 2 | 0.828 5 | 0.986 8 | 1.341 1 | 1.769 8 | 1.948 7 | 2.397 0 | | 0.1 | 60×15 | 0.183 1 | 0.488 0 | 0.826 7 | 0.986 6 | 1.340 7 | 1.766 8 | 1.948 1 | 2.396 6 | | 0.2 | 40×10 | 0.436 8 | 1.055 1 | 1.379 3 | 1.611 6 | 2.536 7 | 2.620 4 | 3.272 4 | 4.115 9 | | 0.2 | 50×10 | 0.436 3 | 1.054 7 | 1.378 7 | 1.608 7 | 2.535 7 | 2.617 3 | 3.271 2 | 4.113 8 | | 0.2 | 50×15 | 0.436 2 | 1.054 6 | 1.378 6 | 1.608 5 | 2.535 7 | 2.617 1 | 3.271 1 | 4.113 6 | | 0.2 | 60×15 | 0.435 8 | 1.054 4 | 1.378 2 | 1.606 6 | 2.535 0 | 2.614 9 | 3.270 3 | 4.112 2 | | 0.3 | 40×10 | 0.669 8 | 1.483 6 | 1.684 9 | 2.128 9 | 3.150 1 | 3.347 0 | 4.017 4 | 4.273 0 | | 0.3 | 50×10 | 0.669 2 | 1.482 9 | 1.684 4 | 2.125 6 | 3.147 7 | 3.344 5 | 4.016 5 | 4.271 3 | | 0.3 | 50×15 | 0.669 2 | 1.482 8 | 1.684 3 | 2.125 2 | 3.147 4 | 3.344 4 | 4.016 4 | 4.271 1 | | 0.3 | 60×15 | 0.668 8 | 1.482 3 | 1.684 0 | 2.123 0 | 3.145 7 | 3.342 5 | 4.015 7 | 4.270 0 |
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