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Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory

Fugen Liu
Fugen Liu
, 
Tenghao Zhang
Tenghao Zhang
, 
Daniyal M. Alghazzawi
Daniyal M. Alghazzawi
 y 
Mohamed Abdeldayem Ahmed Soltan
Mohamed Abdeldayem Ahmed Soltan
   | 22 nov 2021
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Publicado en línea: 22 nov 2021
Páginas: 277 - 284
Recibido: 17 jun 2021
Aceptado: 24 sept 2021
DOI: https://doi.org/10.2478/amns.2021.2.00089
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© 2021 Fugen Liu et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

The normalisation of the i mode shape and the reference degree of freedom r.
The normalisation of the i mode shape and the reference degree of freedom r.

Fig. 2

Three-span continuous beam/cm calculated by model modification simulation.
Three-span continuous beam/cm calculated by model modification simulation.

Fig. 3

Parameter (I2, I9, I12, I20) iterative process.
Parameter (I2, I9, I12, I20) iterative process.

Comparison of calculated and measured modal parameters before correction

Order Frequency calculation value Frequency measured value Frequency error Mode shape difference
1 18.503 15.674 18.05 2.7
2 39.549 33.74 17.22 12.69
3 46.472 39.854 16.61 10.2
4 68.545 58.921 16.33 11.2
5 78.746 71.885 9.54 -
6 122.81 103.85 18.26 17.78
7 153.04 133.7 14.47 38.55
8 167.12 146.14 14.36 36.81

Parameter modification results

Category Before correction × 10−4 After correction × 10−5 True value × 10−5 Error/%
1 Situation 1 1.33 9.309 9.31 0.011
Situation 2 9.204 1.138
2 Situation 1 1.33 7.974 7.98 0.075
Situation 2 7.788 2.4
3 Situation 1 1.33 6.624 6.65 0.391
Situation 2 6.61 0.6
4 Situation 1 1.33 7.899 7.98 1.015
Situation 2 7.937 0.53
5 Situation 1 2500 2997.1 3000 0.097
Situation 2 3031.6 1.05

Comparison of calculated and measured values of modal parameters after correction

Order Frequency calculation value Frequency measured value Frequency error Mode shape difference
1 Situation 1 15.672 15.674 0.010 0.089
Situation 2 15.433 1.540 0.330
2 Situation 1 33.725 33.740 0.040 0.650
Situation 2 33.089 1.929 0.260
3 Situation 1 39.842 39.854 0.030 0.540
Situation 2 39.103 1.880 0.310
4 Situation 1 58.932 58.921 0.020 0.170
Situation 2 57.933 1.677 0.500
5 Situation 1 71.922 71.885 0.050 -
Situation 2 71.510 0.521
6 Situation 1 103.850 103.850 0 0.11
Situation 2 102.280 1.512 0.93
7 Situation 1 133.750 133.700 0.04 0.15
Situation 2 131.350 1.758 0.72
8 Situation 1 146.170 146.140 0.02 0.45
Situation 2 143.700 1.67 0.91
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