Table 3 First three natural frequencies of damaged cantilever beam \(\text{(Hz)}\) for nine scenarios.
From: Identification of frame geometry and boundary conditions from free-vibration modal signatures
\(\mathfrak{L}\) | \({\mathfrak{D}}=100\) | \({\mathfrak{D}}=10\) | \({\mathfrak{D}}=1\) | ||||
|---|---|---|---|---|---|---|---|
Present | ANSYS | Present | ANSYS | Present | ANSYS | ||
0.2 | \({\omega }_{1}\) | 31.594 | 31.571 | 30.636 | 30.606 | 27.056 | 27.036 |
\({\omega }_{2}\) | 246.965 | 246.68 | 244.983 | 244.66 | 228.609 | 228.3 | |
\({\omega }_{3}\) | 649.299 | 648.28 | 641.264 | 640.13 | 593.901 | 593.0 | |
0.5 | \({\omega }_{1}\) | 37.894 | 37.868 | 37.481 | 37.451 | 35.581 | 35.551 |
\({\omega }_{2}\) | 204.904 | 204.72 | 200.722 | 200.52 | 187.135 | 186.96 | |
\({\omega }_{3}\) | 675.394 | 674.31 | 667.644 | 666.43 | 612.528 | 611.39 | |
0.8 | \({\omega }_{1}\) | 40.548 | 40.521 | 40.518 | 40.491 | 40.321 | 40.293 |
\({\omega }_{2}\) | 235.476 | 235.25 | 232.703 | 232.45 | 219.216 | 218.98 | |
\({\omega }_{3}\) | 572.961 | 572.29 | 562.484 | 561.77 | 533.370 | 532.75 | |
