The Properties of Structures with Two Planes of Symmetry
Abstract
:1. Introduction
2. Methods
- —the inertial matrix for the subsystems ;
- —the inertial coupling matrix between the two identical parts and the system ;
- —the inertial matrix for the subsystem ;
- —the stiffness matrix for the subsystems ;
- —the stiffness coupling matrix between the two identical parts and the system ;
- —the stiffness matrix for the subsystem ;
- —the damping matrix for the subsystems ;
- —the damping coupling matrix between the two identical parts and the system ;
- —the damping matrix for the subsystem ;
- —the vector of independent coordinates for the subsystem on the left side;
- —the vector of independent coordinates for the subsystem on the right side;
- —the vector of independent coordinates for the subsystem .
3. Results
- -
- The lower sole and the upper sole of the lattice beams are made of hot-rolled square pipe with a section of 30 × 2 mm;
- -
- The uprights—hot-rolled square pipe with a section of 20 × 2 mm;
- -
- The diagonals—hot-rolled square pipe with a section of 20 × 2 mm;
- -
- The uprights at the ends of the beams with lattices that also fulfill the role of pillars are made of hot-rolled square pipe with a section of 40 × 2.5 mm;
- -
- The other elements are made of laminated profiles with the U65 section.
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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FULL | HALF_X | HALF_Z | QUARTER | ||||
---|---|---|---|---|---|---|---|
A1 | A2 | A3 | A4 | ||||
Mode | Eigenfrequency [Hz] | Mode | Eigenfrequency [Hz] | Mode | Eigenfrequency [Hz] | Mode | Eigenfrequency [Hz] |
1 | 4.90 | 1 | 4.90 | ||||
2 | 9.29 | ||||||
3 | 10.74 | 1 | 10.74 | ||||
4 | 13.78 | 2 | 13.78 | ||||
5 | 16.37 | ||||||
6 | 16.87 | 3 | 16.87 | ||||
7 | 18.81 | 2 | 18.81 | ||||
8 | 19.70 | ||||||
9 | 22.60 | ||||||
10 | 23.50 | 4 | 23.50 | ||||
11 | 26.11 | ||||||
12 | 27.48 | 3 | 27.48 | 5 | 27.48 | 1 | 27.48 |
13 | 27.56 | ||||||
14 | 29.22 | 4 | 29.22 | ||||
15 | 29.89 | 5 | 29.89 | 6 | 29.89 | 2 | 29.89 |
16 | 31.00 | 6 | 31.00 | 7 | 31.00 | 3 | 31.00 |
17 | 31.00 | 7 | 31.00 | ||||
18 | 31.56 | 8 | 31.56 | ||||
19 | 32.17 | 9 | 32.17 | 8 | 32.17 | 4 | 32.17 |
20 | 32.54 | 9 | 32.54 | ||||
21 | 32.85 | 10 | 32.85 | ||||
22 | 33.01 | 11 | 33.01 | 10 | 33.01 | 5 | 33.01 |
23 | 33.96 | 12 | 33.96 | 11 | 33.96 | 6 | 33.96 |
24 | 34.17 | 13 | 34.17 | ||||
25 | 34.26 | 14 | 34.26 | 12 | 34.26 | 7 | 34.26 |
26 | 34.26 | 15 | 34.26 | ||||
27 | 34.54 | 16 | 34.54 | ||||
28 | 35.52 | 17 | 35.52 | 13 | 35.52 | 8 | 35.52 |
29 | 36.54 | 18 | 36.54 | 14 | 36.54 | ||
30 | 37.72 | 19 | 37.72 | 9 | 36.54 | ||
31 | 39.81 | 20 | 39.81 | 15 | 39.81 | 10 | 39.81 |
32 | 43.11 | ||||||
33 | 46.96 | 46.96 | 16 | 46.96 | 11 | 46.96 | |
34 | 47.21 | ||||||
35 | 52.38 | ||||||
36 | 52.56 | 52.56 | 17 | 52.56 | 12 | 52.56 | |
37 | 52.78 | ||||||
38 | 54.09 | 18 | 54.09 | ||||
39 | 61.29 | ||||||
40 | 65.36 | 65.36 | 19 | 65.36 | 13 | 65.36 | |
41 | 65.64 | 20 | 65.64 | ||||
42 | 67.96 | ||||||
43 | 68.32 | ||||||
44 | 70.33 | 70.33 | 70.33 | 14 | 70.33 | ||
45 | 70.42 | ||||||
46 | 71.00 | ||||||
47 | 71.74 | 71.74 | 71.74 | 15 | 71.74 | ||
48 | 72.23 | ||||||
49 | 72.88 | ||||||
50 | 73.72 | 73.72 | 73.72 | 16 | 73.72 |
Type of Symmetry | |||
---|---|---|---|
Full System | Half System X | Half System Z | Quarter |
Mode 1: 4.90 Hz | Mode 1: 4.90 Hz | ||
Mode 3: 10.74 Hz | Mode 1: 10.74 Hz | ||
Mode 4: ν = 13.78 Hz | Mode 2: ν = 13.78 Hz | ||
Mode 6: ν = 16.87 Hz | Mode 3: ν = 16.87 Hz | ||
Mode 7: ν = 18.81 Hz | Mode 2: ν = 18.81 Hz | ||
Mode 10: ν = 23.50 Hz | Mode 4: ν = 23.50 Hz | ||
Mode 12: ν = 27.48 Hz | Mode 3: ν = 27.48 Hz | Mode 5: ν = 27.48 Hz | Mode 1: ν = 27.48 Hz |
Mode 14: ν = 29.22 Hz | Mode 4: ν = 29.22 Hz | ||
Mode 15: ν = 29.89 Hz | Mode 5: ν = 29.89 Hz | Mode 6: ν = 29.89 Hz | Mode 2: ν = 29.89 Hz |
Mode 16: ν = 31.00 Hz | Mode 6: ν = 31.00 Hz | Mode 7: ν = 31.00 Hz | Mode 3: ν = 31.00 Hz |
Mode 17: ν = 31.00 Hz | Mode 7: ν = 31.00 Hz |
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Vlase, S.; Itu, C. The Properties of Structures with Two Planes of Symmetry. Symmetry 2024, 16, 1075. https://doi.org/10.3390/sym16081075
Vlase S, Itu C. The Properties of Structures with Two Planes of Symmetry. Symmetry. 2024; 16(8):1075. https://doi.org/10.3390/sym16081075
Chicago/Turabian StyleVlase, Sorin, and Calin Itu. 2024. "The Properties of Structures with Two Planes of Symmetry" Symmetry 16, no. 8: 1075. https://doi.org/10.3390/sym16081075