功能梯度复合材料圆柱壳固有频率解-地震工程与工程振动.pdf

25 6 Vol. 25, No. 6 2005 12 EARTHQUAKE ENG INEERING AND ENG INEER ING VIBRATION Dec. 2005 : 1000-1 01( 2005) 06- 00 8- 05 曹志远 ( , 200092) :, , , : ; ; ; : P 15. 976 : A Natural frequen cy solution for functionally grad ed m aterial cylindrical sh ells Cao Zh iyuan ( School ofA erospace Engineering and AppliedM echanics, Tongj iU niversity, Shanghai 200092, China) Abs tract: The fundam entaldynam ic equations of functionally gradedmaterial cylindrical shell are established. Then its general solution of natural frequencies andmode shapes for various FGM cylindrical shells is given and as an ex- amp le the analytical expression of natural frequencies for cylindrical shellw ith smi ple boundary cond ition is presen- ted in th is paper. K ey w ord s: functional gradedmateria;l cylindrical shell; dynam ic equation; natural frequency ( FGM ), , , ; , , , , [ 1] 80, , [ 2] , ; / 86 0 / 97 0, , , , : 2005- 01- 24; : 2005- 04- 10 : ( 104 20 0) : ( 19 8- ), , , . 6 : 9 , , , , , , , [ ~ 6] , , , , , , , , , , , 1 1. 1 [ 7] , -, ( 1) : 0 9u 0 9v w 0 9v 9u E = , E = + , E = + ( 1a) x H xH 9x R9H R 9x R9H : 2