Skip to main content

Table 7 The first three linear frequency parameters of clamped FG AL/ZrO2 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 3.0021 2.9572 2.8416 2.7888 2.7883 2.8317 2.8112 2.5773
ΩL2 4.6942 4.6257 4.4505 4.3711 4.3692 4.4266 4.3896 4.0299
ΩL3 6.3787 6.2869 6.0482 5.9351 5.9251 5.9981 5.9503 5.4760
0.1 ΩL1 5.3989 5.3268 5.1359 5.0398 5.0174 5.0496 5.0015 4.6348
ΩL2 8.1325 8.0301 7.7590 7.6194 7.5751 7.5901 7.5050 6.9816
ΩL3 10.735 10.604 10.250 10.056 9.9768 9.9757 9.8654 9.2158
0.15 ΩL1 7.0850 7.0016 6.7739 6.6473 6.5896 6.5742 6.4964 6.0823
ΩL2 10.320 10.207 9.8999 9.7224 9.6219 9.5516 9.4211 8.8596
ΩL3 13.300 13.161 12.769 12.526 12.368 12.251 12.086 11.418
60° 0.05 ΩL1 5.3502 5.2734 5.0781 4.9894 4.9857 5.0425 4.9975 4.5931
ΩL2 9.7566 9.6227 9.2739 9.1052 9.0780 9.1532 9.0675 8.3758
ΩL3 9.7566 9.6232 9.2816 9.1224 9.0985 9.1668 9.0741 8.3758
0.1 ΩL1 9.0573 8.9471 8.6541 8.4990 8.4407 8.4359 8.3353 7.7755
ΩL2 15.415 15.244 14.774 14.500 14.358 14.268 14.081 13.233
ΩL3 15.415 15.244 14.777 14.509 14.362 14.270 14.082 13.233
0.15 ΩL1 11.283 11.165 10.838 10.642 10.517 10.414 10.266 9.6865
ΩL2 18.297 18.125 17.627 17.299 17.040 16.784 16.532 15.707
ΩL3 18.297 18.125 17.632 17.310 17.056 16.797 16.538 15.707
90° 0.05 ΩL1 9.5715 9.4422 9.1085 8.9487 8.9212 8.9816 8.8897 8.2169
ΩL2 15.196 15.003 14.502 14.254 14.185 14.215 14.050 13.045
ΩL3 18.269 18.040 17.419 17.086 16.970 17.004 16.829 15.684
0.1 ΩL1 14.892 14.732 14.291 14.033 13.882 13.769 13.580 12.785
ΩL2 22.158 21.938 21.319 20.930 20.650 20.390 20.091 19.022
ΩL3 25.992 25.741 25.014 24.537 24.177 23.847 23.505 22.313
0.15 ΩL1 17.500 17.340 16.880 16.571 16.314 16.039 15.785 15.023
ΩL2 25.157 24.943 24.305 23.848 23.428 22.966 22.596 21.596
ΩL3 29.123 28.883 28.152 27.614 27.104 26.542 26.113 25.002