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Table 6 The first three linear frequency parameters of clamped FG Ti-6AL-4 V/Aluminum oxide 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 4.8290 4.6023 4.0178 3.6640 3.3821 3.1477 2.9915 2.5775
ΩL2 7.5568 7.2037 6.2958 5.7453 5.3021 4.9231 4.6728 4.0305
ΩL3 10.275 9.7962 8.5595 7.8050 7.1942 6.6742 6.3363 5.4770
0.1 ΩL1 8.7224 8.3224 7.2851 6.6421 6.1042 5.6259 5.3293 4.6364
ΩL2 13.162 12.565 11.018 10.053 9.2288 8.4668 8.0039 6.9847
ΩL3 17.397 16.613 14.569 13.281 12.167 11.137 10.527 9.2205
0.15 ΩL1 11.497 10.982 9.6405 8.7886 8.0410 7.3389 6.9297 6.0858
ΩL2 16.783 16.041 14.109 12.873 11.761 10.679 10.060 8.8657
ΩL3 21.659 20.709 18.216 16.602 15.134 13.708 12.913 11.426
60° 0.05 ΩL1 8.6182 8.2172 7.1865 6.5606 6.0523 5.6101 5.3205 4.5939
ΩL2 15.743 15.016 13.139 11.986 11.033 10.193 9.6614 8.3781
ΩL3 15.743 15.017 13.149 12.006 11.058 10.209 9.6685 8.3781
0.1 ΩL1 14.679 14.018 12.303 11.225 10.290 9.4121 8.8890 7.7795
ΩL2 25.055 23.944 21.047 19.198 17.544 15.951 15.037 13.242
ΩL3 25.055 23.944 21.049 19.201 17.547 15.951 15.037 13.242
0.15 ΩL1 18.378 17.573 15.468 14.107 12.863 11.641 10.959 9.6939
ΩL2 29.880 28.591 25.201 22.974 20.887 18.802 17.675 15.721
ΩL3 29.880 28.591 25.209 22.991 20.911 18.818 17.682 15.721
90° 0.05 ΩL1 15.453 14.743 12.911 11.784 10.845 10.002 9.4702 8.2194
ΩL2 24.582 23.465 20.582 18.795 17.269 15.851 14.981 13.051
ΩL3 29.577 28.236 24.742 22.547 20.676 18.974 17.953 15.691
0.1 ΩL1 24.232 23.165 20.377 18.586 16.965 15.385 14.493 12.794
ΩL2 36.137 34.565 30.445 27.765 25.284 22.822 21.468 19.038
ΩL3 42.422 40.584 35.747 32.574 29.626 26.711 25.127 22.333
0.15 ΩL1 28.615 27.392 24.165 22.028 19.998 17.948 16.857 15.037
ΩL2 41.198 39.447 34.821 31.734 28.767 25.752 24.171 21.619
ΩL3 47.715 45.694 40.348 36.768 33.310 29.790 27.951 25.028