Abstract and Applied Analysis / 2012 / Article / Tab 5 / Research Article
Structural-Electrical-Coupled Formulation for the Free Vibration of a Piezoelectric-Laminated Plate Using the Analytical Arbitrary Quadrilateral p Element Table 5 Natural frequencies (Hz) of the aluminum trapezoidal plates with a top and a bottom PZT-5H layers.
degreeMode 1 Mode 2 Mode 3 Mode 4 Mode 5 CFFF 0.4 1 0 973.25 3453.32 5008.23 8766.12 12533.2 16.70* 1012.18 3593.01 5054.03 9450.83 12505.7 30 977.83 3471.64 5015.1 8848.56 12546.9 0.4 2 0 254.19 1305.3 1603 3402.94 4021.24 8.53* 258.77 1335.07 1586.97 3499.12 3991.47 30 2285.42 1149.58 1605.29 2970.13 4028.11 0.6 1 0 897.68 2764.03 4863.96 7820.35 10630.2 11.31* 916 2805.25 4907.47 8118.05 10327.9 30 856.46 2670.14 4742.59 7284.49 11111.1 0.6 2 0 229 1218.28 1300.72 3295.31 3528.89 5.71* 231.29 1238.89 1289.27 3389.2 3460.19 30 199.23 1028.21 1314.46 2697.62 3588.43 FFFF (exclude rigid body) 0.4 1 0 3751.02 5081.51 7227.24 8855.43 12778.2 16.70* 4451.76 4829.61 6826.49 9817.23 12464.5 30 3817.43 5072.35 7192.89 8949.32 12759.9 0.4 2 0 1232.02 2244.2 3311.34 4476.95 6100.56 8.53* 1264.08 2241.91 3412.1 4483.82 6086.82 30 1046.53 2225.88 2814.41 4341.84 5257.84 0.6 1 0 3531.18 4795.26 6657.03 8273.77 11532.4 11.31* 3757.89 4763.2 6469.25 8660.78 11502.7 30 3137.3 4788.39 6705.12 7939.43 11502.7 0.6 2 0 1229.73 1884.67 3329.66 3938.8 5896.75 5.71* 1245.76 1880.09 3396.07 3915.9 5860.11 30 973.25 1921.31 2571.67 3959.41 4738.01 CCCC 0.4 1 0 11972.1 18409.3 23380.9 26724.3 31304.3 16.70* 11527.9 18338.3 22439.7 27022 30731.8 30 11908 18391 23266.4 26747.2 31258.5 0.4 2 0 8440.94 11415.7 14477.4 17653.6 18326.9 8.53* 8326.44 11312.6 14397.2 17678.8 17994.8 30 9247.02 12159.9 15084.2 17999.4 20069.6 0.6 1 0 9867.61 16105.6 20005.4 24434.3 26701.4 11.31* 9695.86 16169.7 19492.5 25235.8 25762.5 30 10309.6 16075.8 21104.6 23884.7 27731.9 0.6 2 0 7346.32 9395.87 11756.9 14912.5 16565.9 5.71* 7295.94 9350.07 11731.7 14930.8 16444.5 30 8418.04 10405.8 12455.3 14958.3 17976.5
* Symmetric trapezoidal plates.