Диссертация (Повышение вибропрочности трубных пучков теплообменных аппаратов при гидроупругом возбуждении колебаний), страница 14

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ТаблицыМатрицы линейной гидродинамической связи в случае обтекания ряда из трехтрубокТаблица 1Матрица 1, ω0=0.20.174 - 0.133 I-0.094 - 0.086 I0.002 + 0.05 I-0.1 - 0.163 I000.089 + 0.148 I0.02 + 0.061 I-0.074 - 0.125 I0.130 + 0.077 I000.139 - 0.066 I0.026 + 0.141 I-0.04 - 0.06 I00.139 - 0.066 I-0.022 - 0.141 I0.064 + 0.019 I-0.032 + 0.028 I0-0.286 + 0.171 I-0.064 - 0.019 I-0.032 + 0.028 I000.037 + 0.04 I0.088 + 0.132 I0.174 - 0.133 I0.094 + 0.086 I000.111 + 0.127 I0.107 - 0.019 I-0.089 - 0.148 I0.02 + 0.061 IМатрица 2, ω0=0.3-0.049 - 0.12 I0.037 + 0.259 I0.084 - 0.051 I-0.007 - 0.319 I000.197 + 0.044 I-0.164 - 0.272 I-0.216 + 0.099 I0.047 + 0.24 I00-0.007 - 0.144 I0.223 + 0.218 I-0.063 - 0.183 I0-0.007 - 0.144 I-0.223 - 0.218 I0.201 - 0.066 I0.316 + 0.108 I0-0.624 - 0.347 I-0.201 + 0.066 I0.316 + 0.108 I000.111 - 0.081 I-0.182 + 0.222 I-0.049 - 0.120 I-0.037 - 0.259 I000.207 - 0.065 I0.043 + 0.107 I-0.197 - 0.044 I-0.164 - 0.273 IСобственные числа матрицы 1Собственные числа матрицы 2-0.269 + 0.213i-0.076 - 0.64i0.236 - 0.2i-0.289 - 0.075i0.271 - 0.1i-0.133 + 0.118i-0.225 + 0.099i-0.608 - 0.496i0.11 - 0.126i0.068 - 0.157i-0.062 + 0.08i-0.074 - 0.056i101Таблица 2Матрица 3, ω0=0.40.012 - 0.501 I0.155 + 0.131 I0.197 - 0.146 I-0.081 - 0.451 I000.065 + 0.157 I-0.277 - 0.285 I-0.279 + 0.089 I0.134 + 0.297 I000.120 - 0.103 I0.27 + 0.169 I-0.043 - 0.281 I00.12 - 0.103 I-0.27 - 0.169 I0.12 - 0.062 I0.295 + 0.195 I0-0.831 - 0.363 I-0.12 + 0.062 I0.296 + 0.195 I000.177 - 0.056 I0.064 + 0.407 I0.012 - 0.501 I-0.155- 0.131 I000.241 - 0.062 I0.089 + 0.35 I-0.065 - 0.157 I-0.277 - 0.285 IМатрица 4, ω0=0.5-0.043 - 0.543 I0.144 + 0.112 I0.155 - 0.093 I-0.031 - 0.323 I000.138 + 0.253 I-0.305 - 0.254 I-0.21 + 0.057 I0.094 + 0.39 I000.064 - 0.274 I0.203 + 0.267 I-0.027 - 0.417 I00.064 - 0.274 I-0.203 - 0.267 I-0.016 - 0.032 I0.23 + 0.117 I0-0.728 - 0.449 I0.016 + 0.032 I0.23 + 0.117 I000.24 - 0.183 I0.05 + 0.334 I-0.043 - 0.543 I-0.144 - 0.112 I000.32 + 0.016 I0.163 + 0.389 I-0.138 - 0.253 I-0.305 - 0.254 IСобственные числа матрицы 3:Собственные числа матрицы 4:-0.764 - 0.688i-0.84 - 0.802i-0.016 - 0.716i0.092 - 0.947i-0.025 - 0.429i-0.433 + 0.036i-0.04 - 0.428i-0.048 - 0.395i-0.306 - 0.029i-0.028 - 0.306i-0.252 + 0.075i-0.195 - 0.047i102Таблица 3Матрица 5, ω0=1.20.571 - 1.156 I0.172 + 0.247 I0.463 - 0.229 I0.084 - 0.437 I000.128 + 0.794 I0.182 + 0.38 I0.734 + 0.72 I1.236 + 0.271 I000.16 - 0.517 I0.283 + 0.646 I1.065 - 1.4 I00.16 - 0.517 I-0.283 - 0.646 I-0.095 + 0.173 I0.394 + 0.138 I0-0.805 - 0.043 I0.095 - 0.173 I0.394 + 0.138 I000.54 - 0.355 I-0.12 + 0.421 I0.571 - 1.156 I-0.172 - 0.247 I00-0.991 - 0.399I1.174 + 0.3I-0.128 - 0.794I0.182 + 0.38IМатрица 6, ω0=1.61.06 - 1.48 I0.474 + 0.425 I0.693 - 0.821 I0.06 - 1.07 I000.793 + 0.585 I1.266 + 0.705 I1.413 - 0.719 I1.145 - 1.126 I000.185 - 0.811 I0.6 + 0.789 I1.394 - 2.102 I00.185 - 0.811 I-0.6 - 0.789 I-0.283 - 0.084 I0.59 - 0.296 I00.809 + 1.178 I0.283 + 0.084 I0.59 - 0.296 I000.684 - 0.656 I0.036 + 0.811 I1.06 - 1.48 I-0.474 - 0.425 I00-1.427 + 0.264 I0.639 - 0.587 I-0.793 - 0.584 I1.266 + 0.705 IСобственные числа матрицы 5:Собственные числа матрицы 6:0.84 - 1.967i1.25 - 2.391i-1.373 - 0.225i2.367 + 0.037i0.444 - 1.147i2.2 + 0.256i0.991 + 0.562i0.277 + 1.722i0.88 + 0.54i0.619 - 1.455i-0.017 - 0.758i0.14 - 0.644i103Таблица 4Матрица 7, ω0=1.81.33 - 1.627 I0.61 + 0.517 I0.453 - 0.683 I-0.296 - 1.045 I000.782 + 0.475 I2.215 + 1.224 I0.339 - 0.746 I0.134 - 1.084 I000.2 - 0.858 I0.698 + 0.859 I1.488 - 2.22 I00.2 - 0.858 I-0.698 - 0.859 I-0.348 + 0.563 I0.353 - 0.382 I01.382 + 1.649 I0.348 - 0.563 I0.353 - 0.382 I000.561 - 0.837 I0.139 + 1.187 I1.331 - 1.627 I-0.61 - 0.517 I00-0.721 + 0.947 I0.692 - 1.458 I-0.782 - 0.475 I2.215 + 1.224 IМатрица 8, ω0=2.01.57 - 1.39 I1.2 + 0.215 I0.514 - 0.889 I-0.669 - 1.066 I000.257 + 0.699 I3.605 + 0.062 I0.409 - 1.173 I-0.547 - 1.105 I000.201 - 0.817 I0.713 + 0.745 I1.837 - 2.368 I00.201 - 0.817 I-0.716 - 0.745 I-0.072 + 0.65 I-0.513 - 0.355 I03.076 + 1.363 I0.072 - 0.65 I-0.513 - 0.355 I000.605 - 0.788 I0.513 + 1.141 I1.57 - 1.39 I-1.201 - 0.215 I00-0.732 + 0.774 I-0.305 - 1.268 I-0.257 - 0.699 I3.605 + 0.062 IСобственные числа матрицы 7:Собственные числа матрицы 8:1.727 - 2.704i4.197 + 1.395i2.844 + 0.444i4.055 - 0.19i2.54+ 0.583i2.164 - 2.673i1.295 + 2.115i2.847 - 0.103i0.868 - 1.323i1.201 - 1.256i0.688 - 0.492i0.799 - 0.834i104Таблица 5Матрица 9, ω0=2.22.216 - 1.5 I1.3 - 0.063 I0.567 - 0.953 I-0.551 - 1.03 I000.477 + 0.85 I4.41 - 0.046 I0.345 - 1.172 I-0.683 - 0.997 I000.384 - 0.741 I0.849 + 0.678 I2.345 - 2.397 I00.384 - 0.741 I-0.849 - 0.678 I-0.108 + 0.769 I-0.697 - 0.596 I03.968 + 1.11 I0.108 - 0.769 I-0.697 - 0.596 I000.665 - 0.762 I0.655 + 1.109 I2.216 - 1.5 I-1.296 + 0.063 I00-0.427 + 0.862 I-0.671 - 1.072 I-0.477 - 0.85 I4.41 - 0.046 IМатрица 10, ω0=2.42.86 - 1.787 I1.071 - 0.181 I0.687 - 0.85 I-0.757 - 0.801 I000.73 + 0.831 I4.847 - 0.484 I0.311 - 1.306 I-1.185 - 0.761 I000.637 - 0.797 I0.84 + 0.733 I2.827 - 2.463 I00.637 - 0.797 I-0.84 - 0.733 I-0.138 + 0.745 I-1.008 - 0.337 I05.413 + 0.364 I0.138 - 0.745 I-1.008 - 0.337 I000.748 - 0.829 I0.984 + 0.806 I2.86 - 1.787 I-1.071 + 0.181 I00-0.357 + 1.156 I-1.416 - 0.716 I-0.73 - 0.831 I4.847 - 0.484 IСобственные числа матрицы 9:Собственные числа матрицы 10:5.319 + 1.415i7.013 + 0.52i4.92 - 0.406i5.461 - 1.125i2.906 - 2.73i3.702 - 2.732i3.8 - 0.555i4.018 - 1.042i1.474 - 1.29i2.09 - 1.383i1.146 - 0.81i1.369 - 0.879i105Таблица 6Матрица 11, ω0=2.63.682 - 1.82 I1.203 - 0.372 I0.723 - 0.813 I-0.833 - 0.725 I000.568 + 0.893 I5.635 - 0.882 I0.174 - 1.184 I-1.652 - 0.604 I000.801 - 0.767 I0.861 + 0.723 I3.453 - 2.556 I00.801 - 0.767 I-0.861 - 0.723 I0.079 + 0.732 I-1.176 - 0.385 I06.224 + 0.004 I-0.079 - 0.732 I-1.176 - 0.385 I000.717 - 0.879 I0.827 + 0.825 I3.682 - 1.816 I-1.203 + 0.372 I00-0.1 + 1.397 I-1.53 - 0.655 I-0.568 - 0.893 I5.635 - 0.882 IМатрица 12, ω0=2.44.308 - 2.164 I1.062 - 0.448 I0.862 - 0.741 I-0.771 - 0.76 I000.778 + 0.753 I6.392 - 1.154 I-0.121 - 1.159 I-1.698 - 0.245 I000.848 - 0.864 I0.851 + 0.791 I4.103 - 2.714 I00.848 - 0.864 I-0.851 - 0.791 I0.02 + 0.893 I-1.636 - 0.192 I06.72 - 0.703 I-0.02 - 0.893 I-1.636 - 0.192 I000.929 - 0.744 I0.752 + 0.780 I4.308 - 2.164 I-1.062 + 0.449 I00-0.019 + 1.22 I-1.636 - 0.323 I-0.778 - 0.753 I6.392 - 1.154 IСобственные числа матрицы 11:Собственные числа матрицы 12:7.97 + 0.159i9.077 - 0.731i6.087 - 1.472i6.857 - 1.804i4.763 - 2.771i5.534 - 3.115i4.896 - 1.365i5.311 - 1.835i2.678 - 1.488i3.03 - 1.454i1.917 - 1.01i2.413 - 1.113i106Таблица 7Матрица 13, ω0=0.60.123 – 0.548 I0.129+0.198 I0.163 - 0.193 I-0.166 - 0.27 I000.037 + 0.186 I-0.366 – 0.372 I-0.271+ 0.083 I0.094+ 0.623 I000.232 - 0.457 I0.249 + 0.235 I0.332 – 0.611 I00.232 - 0.457 I-0.249 - 0.235 I0.138- 0.109 I0.26+ 0.215 I0-0.856 - 0.37 I-0.138+ 0.109 I0.26+ 0.215 I000.129 - 0.254 I0.238 + 0.273 I0.123 - 0.548I-0.128- 0.198 I00-0.388 – 0.046 I0.249+ 0.403 I-0.037 - 0.186 I-0.366 – 0.372 IМатрица 14, ω0=0.80.12 – 0.899 I-0.038+0.153 I0.252 - 0.17 I-0.14 - 0.297 I00-0.088 + 0.42 I-0.465 – 0.275 I-0.018+ 0.25 I0.343+ 0.626 I000.106 - 0.465 I0.276 + 0.331 I0.455 – 0.736 I00.106 - 0.465 I-0.276 - 0.331 I-0.05- 0.066 I0.393+ 0.312 I0-0.56 - 0.334 I0.05- 0.065 I0.393+ 0.312 I000.194 - 0.163 I0.089 + 0.158 I0.12 - 0.899I0.038- 0.153 I00-0.253 – 0.568 I0.468+ 0.869 I0.088 - 0.42 I-0.465 – 0.275 IСобственные числа матрицы 13:Собственные числа матрицы 14:0.438-1.2 i-1.236- 1.023i-0.856- 0.887i0.388-1.429 i0.01-0.508 i0.125-0.866 i-0.194-0.286 i-0.07+0.388i-0.17-0.029i-0.252- 0.376i-0.24+0.09 i-0.048- 0.113i107Таблица 8Матрица 15, ω0=10.352 – 0.899 I0.0017+0.267 I0.232 - 0.246 I-0.245 - 0.22 I000.049 + 0.99 I-0.667+ 0.097 I0.191+ 0.397 I0.75+ 0.93 I000.111 - 0.324 I0.236 + 0.63 I0.791 – 1.142 I00.111 - 0.324 I-0.236 - 0.63 I-0.074+ 0.123 I0.703+ 0.258 I0-1 - 0.434 I0.074- 0.124 I0.703+ 0.258 I000.288 - 0.298 I0.032 + 0.267 I0.352 - 0.899I-0.0018- 0.267 I00-0.298 – 0.308 I0.831+ 0.506 I-0.049 - 0.99 I-0.667 – 0.097 IСобственные числа матрицы 15:-1.84 -0.912i0.512 - 1.67i0.19 +0.558i-0.407+ 0.062i0.325 – 0.872i0.385 -0.345i108Таблица 9.Расчетные точки для построения кривой устойчивости для ряда из трех труб№ω Im λп/пlg ( ) U=lg(U)10,20,2135,3254.180.62124,351,3820,30,1121,2440.977-0.0116,231,2130,40,0750,4690.368-0.43412,1751,0840,50,0360,1440.113-0.94479,740,98850,60,090,250,196-0,7088,1160,90960,80,3880,6060,476-0,3226,090,78710,5580,5580,438-0,3584,870,687581,20,5620,3900.306-0.5144,060,60891,61,720,6720.527-0.2783,040,483101,82,1150,6530.512-0.2912,710,433112,01,40,350.275-0.5612,430,386122,21,410,2910.229-0.642,210,344132,40,520,090.071-1.1482,030,307142,60,1580,0230.018-1.7451,870,272109Таблица 10.Расчетные точки для построения кривой устойчивости для ряда из пяти труб№ω(3)Im λ10,20,2294,490,6524,3471,3820,30,1361,1870,07416,231,2130,40,0620,304-0,51712,171,0840,50,0450,141-0,8509,740,98851,20,5830,318-0,4984,060,60861,61,770,543-0,2653,040,48371,82,20,533-0,2732,710,43382,01,790,352-0,4532,430,38692,21,930,313-0,52,210,344102,40,830,113-0,9472,030,307112,60,5250,061-1,621,870,272120,10,18614,61,1648,71,69130,60,150,326-0,4878,120,91140,80,3750,4579-0,3396,090,7841510,380,2985-0,5254,870,687U=lglg(U)110Таблица 11.Расчетные точки для построения кривой устойчивости для ряда из семи трубU=lglg(U)№ω(3)Imλ10,20,234,5160,65524,3471,3820,30,1331,1610,06516,231,2130,40,0560,275-0,56112,171,0840,50,0340,107-0,9719,740,98851,20,5830,318-0,4984,060,60861,61,760,540-0,2683,040,48371,82,260,548-0,2612,710,43382,01,910,375-0,4262,430,38692,22,090,339-0,4702,210,344102,40,920,125-0,9022,030,307112,60,640,074-1,1291,870,272120.10,2217,2791,23848,71,69130.60,2250,491-0,3098,120,91140.80,370,454-0,3436,090,7841510,4560,358-0,4464,870,687111Таблица 12.Пример матрицы линейной гидродинамической связи в случае обтекания ряда из семи труб0.18 0.13i0.09 +0.15i0.14 0.07i0.06 +0.02i0-0.09 0.09i0.02 +0.06i0.02+0.14i-0.03+0.03i00000.002 +0.05i-0.07 0.13i-0.04 0.06i0-0.10.16i0.13+0.08i000.14 0.07i0.06 +0.02i0-0.29 +0.17i0.02+0.14i-0.03+0.03i00000000000000000000000000000000.14 0.07i-0.06 0.02i-0.04 0.06i0-0.02 0.14i-0.03 +0.03i000000000000000000.14 0.07i-0.06 0.02i-0.04 0.06i0-0.02 0.14i-0.03 +0.03i00000000000000.14 0.07i-0.06 0.02i-0.04 0.06i0-0.02 0.14i-0.03 +0.03i0000000000.14 0.07i-0.06 0.02i-0.04 0.06i0-0.02 0.14i-0.03 +0.03i000000.14 0.07i-0.06 0.02i0.17 0.13i-0.09 0.15i-0.02 0.14i-0.03 +0.03i0.09+0.09i0.02 +0.06i00.14 0.07i0.06 +0.02i0-0.29 +0.17i0.02+0.14i-0.03+0.03i000000000000000000000.14 0.07i0.06 +0.02i0-0.29 +0.17i0.02+0.14i-0.03+0.03i000000000000000.14 0.07i0.06 +0.02i0-0.29 +0.17i0.02+0.14i-0.03+0.03i00000.04 +0.04i0.11+0.13i-0.29 +0.17i0.09 +0.13i0.110.02i112Таблица 13.Примеры матриц линейной гидродинамической связи в случае обтекания пучкаиз пяти трубω=0,2ω=0,4Sxx=0.46-0.65iSyy=-0.57+1.07iRyx=-0.01Lxy=-0.37-0.54iDxx=0.10-0.20iDyy=0.64+0.92iUyx=-0.24-0.32iSxx=0.25-0.3iSyy=-1.27-0.03iRyx=-0.006-0.001Lxy=0.035-0.05iUxx=0.06- 0.09iUyy=0.094+ 0.073iDyx=-0.072 + 0.46iSxy=0.22+0.15iRxx=-0.07+0.15iRyy=0.35-1.0iLyx=0.31+0.25iDxy=0.04-0.02iUxx=0.11-0.18iUyy=0.11+1.30iSxy=0.025-0.004iRxx=0.003+0.09iRyy=0.26-0.16iLyx=0.12-0.04iUxy=-0.04 +0.085iDxx=0.088- 0.105iDyy=0.145+ 0.165iSyx=-0.23+0.12iRxy=-0.07-0.03iLxx=0.10+0.55iLyy=1.37-0.70iDyx=0.15+0.13iUxy=0.05+0.30iSyx=-0.01-0.035iRxy=-0.01+0.08iLxx=-0.25+0.27iLyy=0.2+0.81iUyx=0.012 - 0.47iDxy=0.067 + 0.04iТаблица 14.Расчетные точки для построения кривой устойчивости для пучка из 16 труб№ω(3)Im λU=lglg(U)Диагональные матрицы10,24,53891,9524,351,3920,40,4772,340,3712,171,0931,61,770,543-0,2563,0430,483113Таблица 15.Пример построения матрицы линейной гидродинамической связи для пучка из 16 труб114115116117.