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Table 4 The first three linear frequency parameters of clamped FG AL/AL2O3 isosceles triangular plate

From: Linear and non-linear vibration analysis of moderately thick isosceles triangular FGPs using a triangular finite p-element

β h/b Mode n
ceramic 0.1 0.5 1 2 5 10 metal
30° 0.05 ΩL1 5.0681 4.8827 4.3399 3.9585 3.6367 3.4112 3.2521 2.5773
ΩL2 7.9247 7.6385 6.8050 6.2214 5.7244 5.3517 5.0840 4.0300
ΩL3 10.768 10.382 9.2453 8.4385 7.7440 7.2297 6.8741 5.4761
0.1 ΩL1 9.1144 8.7992 7.8656 7.1908 6.5871 6.0926 5.7606 4.6349
ΩL2 13.729 13.267 11.904 10.916 10.009 9.1978 8.6491 6.9818
ΩL3 18.122 17.522 15.727 14.401 13.158 12.049 11.330 9.2160
0.15 ΩL1 11.960 11.571 10.404 9.5364 8.7114 7.9458 7.4521 6.0824
ΩL2 17.422 16.873 15.237 14.013 12.812 11.599 10.814 8.8598
ΩL3 22.452 21.759 19.656 18.046 16.436 14.823 13.822 11.418
60° 0.05 ΩL1 9.0322 8.7089 7.7700 7.1137 6.5499 6.1081 5.7894 4.5931
ΩL2 16.471 15.893 14.197 12.987 11.922 11.066 10.472 8.3760
ΩL3 16.471 15.895 14.220 13.039 11.998 11.121 10.501 8.3760
0.1 ΩL1 15.290 14.785 13.290 12.200 11.179 10.225 9.5914 7.7757
ΩL2 26.023 25.197 22.727 20.880 19.081 17.304 16.159 13.233
ΩL3 26.023 25.197 22.734 20.895 19.098 17.307 16.159 13.233
0.15 ΩL1 19.048 18.460 16.696 15.361 14.020 12.629 11.751 9.6867
ΩL2 30.889 29.973 27.193 25.036 22.785 20.357 18.876 15.708
ΩL3 30.889 29.974 27.208 25.070 22.840 20.408 18.904 15.708
90° 0.05 ΩL1 16.158 15.597 13.957 12.793 11.760 10.885 10.273 8.2171
ΩL2 25.654 24.788 22.260 20.454 18.802 17.278 16.227 13.046
ΩL3 30.842 29.806 26.705 24.420 22.326 20.519 19.338 15.684
0.1 ΩL1 25.141 24.354 22.002 20.236 18.487 16.701 15.561 12.785
ΩL2 37.407 36.275 32.868 30.265 27.597 24.749 22.981 19.022
ΩL3 43.879 42.565 38.556 35.441 32.237 28.877 26.830 22.314
0.15 ΩL1 29.543 28.682 26.067 24.026 21.861 19.453 17.991 15.023
ΩL2 42.470 41.260 37.557 34.620 31.440 27.861 25.732 21.597
ΩL3 49.166 47.778 43.507 40.090 36.371 32.198 29.726 25.002