【正文】 (32)其中 a1=s130λ330d310d330, a2=s440λ330+d150d310, a3=d150λ330+λ110d310, a4=s130d310d330s110, a5=s440d310+d150s110, a6=d150d310+λ110s110.將(26)式對x積分，得到u=x33k0C4z+C5+x22k0C1z+C2+g1(z)+xs4402C4λ330T1z+2C5λ330C3d310T0z+C7G0(z) 2d150C4d310T1z+C5d310C3s110T0(z)+C6G0(z)+C13z+C14 s13013C4λ330z3+(C5λ330C3d310)z2+d33013C4d310z3+C5d310C3s110z2(33)將(27)式對z積分,得到w= x2a1C4z22+C5zC3a4z+xa1C1z22+C2zC0a4z+g2(x)+(s330s130a1k0+d330a4k0)2C4λ330Y1z+2C5λ330C3d310Y0z+C7G1z+C8G0(z)+k0(s130a2+d330a5)2C4λ330T1z+2C5λ330C3d310T0z+C7G0(z)+2(s130a3+d330a6)C4d310T1z+C5d310C3s110T0z+C6G0(z) +(s130)2λ330+s130d330d310112C4λ330z4+13(C5λ330C3d310)z3+a1(C13z22+C14z)+s130d330λ330(d330)2d310112C4d310z4+13(C5d310C3s110)z3C12a4z (34)將(28),(33)和(34)式代到(6)式的第三式可求得:g2x=axx22C13x36k0C1x412k0C4+d (35)g1z=aza1C1z36+C2z22C0a4z22s440C1λ330T1z+C2λ330C0d310T0z+C10G0(z)+d150C1d310T1z+C2d310C0s110T0z+C9G0(z)+e (36)(22)~(36)式中各系數(shù)可由邊界條件(9)~(14)確定，見附錄考慮一功能梯度壓電懸臂梁(l=1m,h=)僅受均布壓力作用(P=0,M=0,q=1N/m2)的情況，假設(shè)梯度函數(shù)為Fz=exp?(αz/h)，其中α是梯度指數(shù)，在這里我們應(yīng)分別取α為0,1,2。 Journal of Applied Mechanics, ASME, 2004, 71(3): 421424[51]Shi Z. F. General solution of a density functionally gradient piezoelectric cantilever and its applications. Smart Material and Structures, 2002, 11(1): 122129[52]Shi Z. F., Chen Y. Functionally graded piezoelectric cantilever beam under load. Archive of Applied Mechanics, 2004, 74(34): 237–247附 錄由邊界條件(10),(11)及(9)的第一式,求得A=Pbk1H1h2H1(h2), B=q2k1H1h2H1(h2)C1=Pbλ330k1H0h2H0(h2) C4=q2λ330k1H0h2H0(h2)C7=ak1H1h2H0h2H1h2H0(h2),C8=qk1H0h2H0h2H1h2H1h2H1h2H0h2+ h2H1h2H0h2H1h2H0(h2)C10=Pbk1H1h2H0h2H1h2H0(h2),其中k1=H1h2H1(h2)H0h2H0(h2)+H0h2H0(h2)H1h2H1(h2)+H1h2H0h2H1h2H0(h2)h由邊界條件(12)和(13)得到C0=0, C3=0, C2=Aλ330, C5=Bλ330C6=d150λ330+d310λ110λ110G0h2G0(h2)C4T1h2T1h2+C5T0h2T0(h2)d1502λ110C7C9=d150λ330+d310λ110λ110G0h2G0(h2)C1T1h2T1(h2)+C2T0h2T0(h2)d150λ110C10,C12=d1502C4λ330T1h2+2C5λ330T0h2+C7G0(h2)2λ110C4d310T1h2+C5d310T0h2+C6G0(h2)由邊界條件(9),求得C13=A1H1h2H1(h2)A2H0h2H0(h2)Mbk0H0h2H0(h2)λ330k2,C14=A1H2h2H2(h2)+A2H1h2H1(h2)+Mbk0H1h2H1(h2)λ330k2,其中A1=a12C4λ330H11h2H11(h2)+2C5λ330H01h2H01(h2)+C8h+a22C4λ330N1h2N1(h2)+2C5λ330N0h2N0(h2)+C7G01h2G01(h2)+2a3C4d310N1h2N1(h2)+C5d310N0h2N0(h2)+C6G01h2G01(h2)+s130λ33013C4λ330H3h2H3(h2)+C5λ330H2h2H2(h2)d330λ33013C4d310H3h2H3h2+C5d310H2h2H2(h2)+C12d310H0h2H0(h2),A2=a12C4λ330H111h2H111(h2)+2C5λ330H011h2H011(h2)+C7h312+a22C4λ330N11h2N11(h2)+2C5λ330N10h2N10(h2)+C7G011h2G011h2+2a3C4d310N11h2N11(h2)+C5d310N01h2N01(h2)+C6G011h2G011(h2)+s130λ33013C4λ330H4h2H4(h2)+C5λ330H3h2H3(h2)d330λ33013C4d310H4h2H4(h2)+C5d310H3h2H3(h2)+C12d310H1h2H1(h2),k2=H1h2H1(h2)2H2h2H2(h2)H0h2H0(h2)由邊界條件(14)，求得：a=C13l+C1l22k0+C4l33k0 ，d=s330s130a1k0+d330a4k02C4λ330Y10+2C5λ330Y00+C7G10+C8G00k0(s130a2+d330a5)2C4λ330T10+2C5λ330T00+C7G0(0)+2(s130a3+d330a6)C4d310T10+C5d310T00+C6G0(0)C13l22C1l33k0C4l44k0e=l33k0C5l22k0C2+ls4402C4λ330T10+2C5λ330T00+C7G0(0)+2d150C4d310T10+C5d310T0+C6G0(0)C14+s440C1λ330T10+C2λ330T00+C10G0(0)+d150C1d310T10+C2d310T00+C9G0(0)致 謝本文在陳老師的多次指導(dǎo)下終于完稿，感激之情，溢于言表。圖表整潔，布局合理，文字注釋必須使用工程字書寫，不準(zhǔn)用徒手畫3）畢業(yè)論文須用A4單面打印，論文50頁以上的雙面打印4）圖表應(yīng)繪制于無格子的頁面上5）軟件工程類課題應(yīng)有程序清單，并提供電子文檔1）設(shè)計(jì)（論文）2）附件：按照任務(wù)書、開題報(bào)告、外文譯文、譯文原文（復(fù)印件）次序裝訂3）其它 第35頁 共35頁。開展對功能梯度材料相關(guān)結(jié)構(gòu)的實(shí)驗(yàn)研究，從實(shí)驗(yàn)結(jié)果方面進(jìn)一步驗(yàn)證本文得到的一些結(jié)果參 考 文 獻(xiàn)[1]于濤,，2006,36(5):518~529[2]向宏軍,北京:北京交通大學(xué),2007 [3]黃彬彬,，2002,19(4):107~113[4]陳盈,2004,25(2):242~245[5]黃德進(jìn),浙江:浙江大學(xué),2009[6]仲政,2010,40(5):529~541[7]方詩圣,合肥:合肥工業(yè)大學(xué),2006 [8] 李華東,2004,34(1):40~46[9]于濤,2006,27(1):16~20[10]向宏軍,2006,30(1):31~39 [11]劉婷婷,2004,28(1):48~50[12]楊永波,2004,36(3):306~310[13]王建哲,湖南:湖南大學(xué)，2012[14]黃德進(jìn),2007,28(7):764~768[15]張曉日，仲政. 功能梯度壓電圓板自由振動(dòng)問題的三維精確分析. 力學(xué)季刊，2005，26(1): 8186[16]伍曉紅, 沈亞鵬. 壓電功能梯度板自由振動(dòng)的三維解. 固體力學(xué)學(xué)報(bào), 2003, 24(1): 7582[17]仲政, 尚爾濤. 功能梯度熱釋電材料矩形板的三維精確分析. 力學(xué)學(xué)報(bào)，2003，35(5)：542552[18]Kashtalyan M. Threedimensional elasticity solution for bending of functionally graded rectangular plates. European Journal of Mechanics, A/Solids, 2004, 23(5): 853864[19]Yang J., Shen H. S. Vibration characteristics and transient response of sheardeformable functionally graded plates in thermal environments. Journal of Sound And Vibration, 2002, 255(3): 579602[20]Shen H. S. Nonlinear bending response of functionally graded plates subjected to transverse loads and in thermal environments. International Journal of Mechanical Sciences, 2002, 44 (3): 561584[21]Yang J., Shen H. S. Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels. Journal of Sound and Vibration, 2003, 261(5): 871893[22]Yang J., Kitipornchai S., Liew K. M. Nonlinear analysis of the thermoelectro mechanical behaviour of shear deformable FGM plates with piezoelectric actuators. International Journal for Numerical Methods in Engineering, 2004, 59 (