Mathematical Problems in Engineering / 2017 / Article / Tab 5 / Research Article
The Modified Fourier-Ritz Approach for the Free Vibration of Functionally Graded Cylindrical, Conical, Spherical Panels and Shells of Revolution with General Boundary Condition Table 5 Comparison of the first nine frequencies (Hz) of the functionally graded conical panels with different power-law index
. Method Mode number 1 2 3 4 5 6 7 8 9 0.6 Ref [3 ] 80.10 110.93 158.60 195.20 259.10 273.52 321.39 360.77 396.83 Ref [10 ] 80.15 111.03 158.61 195.49 259.31 273.52 321.38 361.16 397.06 Present 80.14 110.95 158.62 195.57 259.18 273.62 321.42 361.38 397.12 1 Ref [3 ] 79.89 110.56 158.15 194.72 258.36 272.88 320.38 359.84 395.97 Ref [10 ] 79.91 110.62 158.10 194.94 258.48 272.82 320.28 360.10 396.11 Present 79.91 110.54 158.11 195.02 258.36 272.91 320.31 360.33 396.18 5 Ref [3 ] 78.92 108.45 156.07 192.86 254.58 270.76 315.52 356.30 393.68 Ref [10 ] 78.86 108.39 155.87 192.87 254.45 270.51 315.12 356.20 393.55 Present 78.86 108.31 155.88 192.95 254.33 270.60 315.16 356.42 393.62 20 Ref [3 ] 77.81 106.72 153.93 190.43 250.80 267.51 311.11 351.98 389.27 Ref [10 ] 77.83 106.78 153.90 190.65 250.92 267.46 311.03 352.24 389.42 Present 77.83 106.70 153.91 190.73 250.80 267.56 311.07 352.46 389.48 50 Ref [3 ] 76.57 105.58 151.56 187.03 247.32 262.39 306.75 345.73 381.29 Ref [10 ] 76.63 105.69 151.60 187.34 247.57 262.43 306.81 346.17 381.56 Present 76.63 105.62 151.61 187.43 247.45 262.53 306.85 346.39 381.63 0.6 Ref [3 ] 79.87 110.71 158.27 194.75 258.47 272.88 320.85 360.10 395.93 Ref [10 ] 80.03 110.96 158.48 195.29 258.99 273.14 321.24 360.94 396.49 Present 80.03 110.88 158.49 195.37 258.86 273.23 321.27 361.16 396.56 1 Ref [3 ] 79.54 110.22 157.64 194.02 257.39 271.89 319.56 358.81 394.58 Ref [10 ] 79.73 110.51 157.90 194.63 257.99 272.21 320.05 359.76 395.23 Present 79.73 110.43 157.91 194.71 257.86 272.31 320.08 359.98 395.30 5 Ref [3 ] 78.23 107.82 155.00 191.47 252.65 268.67 313.79 354.27 390.76 Ref [10 ] 78.49 108.21 155.40 192.25 253.46 269.17 314.54 355.53 391.65 Present 78.49 108.13 155.41 192.33 253.34 269.26 314.58 355.75 391.71 20 Ref [3 ] 77.49 106.44 153.43 189.81 249.93 266.54 310.31 351.07 387.92 Ref [10 ] 77.67 106.70 153.67 190.37 250.47 266.83 310.75 351.94 388.52 Present 77.66 106.63 153.68 190.45 250.35 266.92 310.78 352.16 388.59 50 Ref [3 ] 76.43 105.46 151.35 186.76 246.94 261.96 306.41 345.34 380.70 Ref [10 ] 76.56 105.66 151.50 187.22 247.36 262.15 306.69 346.04 381.16 Present 76.56 105.59 151.52 187.30 247.25 262.25 306.73 346.26 381.24