Vibration and Stability of Hybrid Plate Based on Elasticity Theory
-
摘要: 通过将非线性应变位移关系引入Hellinger-Reissner变分原理,推导出了各向异性板基于弹性理论下的振动和屈曲控制方程.用精细积分法研究了四边简支混合矩形板.精细积分法与传统的有限差分法相比,可以给出计算机精度允许的很精确的数值结果.所以,给出的混合板的振动和稳定的结果可以看作是近似解析的.这些结果可以作为衡量各种板理论准确性的一个标准.而且,非对称层合板中出现的各种耦合影响,比如弯扭耦合,拉弯耦合等在同一组控制方程里被考虑了.Abstract: The governing equations of elasticity theory for natural vibration and buckling of anisotropic plate were derived from Hellinger-Reissner's variational principle with nonlinear strain-displacement relations.Simply supported rectangular hybrid plates were studied by precise integration method.This method,in contrast to the traditional finite difference approximation,gives highly precise numerical results which approach the full computer precision.So the results for natural vibration and stability of hybrid plates presented can be regarded as approximate analytical solutions.Furthermore,the several types of coupling effects,such as coupling between bending and twisting,coupling between extension and bending,etc.when the layer stacking sequence is not symmetric,are considered by only one set of governing equations.
-
Key words:
- vibration /
- buckling /
- precise integration method /
- hybrid plate /
- state space
-
[1] Mindlin R D.Influence of rotary inertia and shear on flexural motions of isotropic,elastic plates[J].Journal of Applied Mechanics,Transactions ASME,1951,18(1):31-38. [2] Reissner E,Stavsky Y.Bending and stretching of certain types of heterogenous aelotropic elastic plates[J].Journal of Applied Mechanics,Transactions ASME,1961,28(3):402-408. doi: 10.1115/1.3641719 [3] Reddy J N.Mechanics of Laminated Composite Plates: Theory and Analysis[M].Boca Raton: CRC Press,1997. [4] Dong S B,Nelson R B.On natural vibrations and waves in laminated orthotropic plates[J].Journal of Applied Mechanics,Transactions ASME,1972,39(3):739-745. doi: 10.1115/1.3422782 [5] Kulkarni S V,Pagano N J.Dynamic characteristics of composite laminates[J].Journal of Sound and Vibration,1972,23(1):127-143. doi: 10.1016/0022-460X(72)90793-6 [6] Nayak A K,Moy S S J.Free vibration analysis of composite sandwich plates based on Reddy's higher-order theory[J].Composites Part B,2002,33(7):505-519. doi: 10.1016/S1359-8368(02)00035-5 [7] Reddy J N,Phan N D.Stability and vibration of isotropic and laminated plates according to a higher-order shear deformation theory[J].Journal of Sound and Vibration,1985,98(2):157-170. doi: 10.1016/0022-460X(85)90383-9 [8] Vuksanovic D.Linear analysis of laminated composite plates using single layer higher-order discrete models[J].Composite Structures,2000,48(1/3):205-211. doi: 10.1016/S0263-8223(99)00096-3 [9] Rao K M,Desai Y M.Free vibrations of laminated beams using mixed theory[J].Composite Structures,2001,52(2):149-160. doi: 10.1016/S0263-8223(00)00162-8 [10] Kant T,Swaminathan K.Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory[J].Composite Structures,2002,56(4):329-344. doi: 10.1016/S0263-8223(02)00017-X [11] Lo K H,Christensen R M,Wu E M.A higher-order theory of plate deformation—part 2: laminated plates[J].Journal of Applied Mechanics,Transactions ASME,1977,44(4):669-676. doi: 10.1115/1.3424155 [12] Bert C W.A critical evaluation of new plate theories applied to laminated composites[J].Composite Structures,1984,2(4):329-347. doi: 10.1016/0263-8223(84)90004-7 [13] Barai A,Durvasula S.Vibration and buckling of hybrid laminated curved panels[J].Composite Structures,1992,21(1):15-27. doi: 10.1016/0263-8223(92)90076-O [14] Benjeddou A,Deu J F.A two-dimensional closed-form solution for the free-vibrations analysis of piezoelectric sandwich plates[J].International Journal of Solids and Structures,2002,39(6):1463-1486. doi: 10.1016/S0020-7683(01)00287-6 [15] Harras B,Nenamar R.White R G.Experimental and theoretical investigation of the linear and nonlinear dynamic behavior of a glare 3 hybrid composite panel[J].Journal of Sound and Vibration,2002,252(2):281-315. doi: 10.1006/jsvi.2001.3962 [16] Lee Y S,Kim Y W.Analysis of nonlinear vibration of hybrid composite plates[J].Composite Structures,1996,61(3):573-578. doi: 10.1016/0045-7949(96)00055-7 [17] Chen C S,Fung C P.Nonlinear vibration of an initially stressed hybrid composite plates[J].Journal of Sound and Vibration,2004,274(3/5):1013-1029. doi: 10.1016/S0022-460X(03)00661-8 [18] Brunell E J,Robertson S R.Initially stressed Mindlin plates[J].AIAA Journal,1974,12(10):1036-1045. doi: 10.2514/3.49407 [19] Brunell E J,Robertson S R.Vibrations of an initially stressed thick plate[J].Journal of Sound and Vibration,1976,45(3):405-416. doi: 10.1016/0022-460X(76)90395-3 [20] Yamaki N,Chiba M.Nonlinear vibrations of a clamped rectangular plate with initial deflection and initial edge displacement—part Ⅰ: theory[J].Thin-Walled Structures,1983,1(1):3-29. doi: 10.1016/0263-8231(83)90003-4 [21] Rogerson G A,Sandiford K J.On small amplitude vibrations of pre-stressed laminates[J].International Journal of Engineering Science,1996,34(8):853-872. doi: 10.1016/0020-7225(95)00138-7 [22] Cheung Y K,Zhu D S,Iu V P.Nonlinear vibration of thin plates with initial stress by spline finite strip method[J].Thin-Walled Structures,1998,32(4):275-287. doi: 10.1016/S0263-8231(98)00022-6 [23] Chen L W,Yang J Y.Dynamic stability of laminated composite plate by the finite element method[J].Composite Structures,1990,36(5):845-851. doi: 10.1016/0045-7949(90)90155-U [24] Chen L W,Ku D M.Note on sensitivity analysis to improve eigenvalue analysis[J].Comput Appl Numer Meth,1992,8(5):331-340. doi: 10.1002/cnm.1630080507 [25] Chen L W,Ku D M.Stability of nonconservatively elastic systems using eigenvalue sensitivity[J].Journal of Applied Mechanics,Transactions ASME,1994,116(2):168-172. [26] Doong J L,Chen T J,Chen L W.Vibration and stability of an initially stressed laminated plate based on a higher-order deformation theory[J].Composite Structures,1987,7(4):285-310. doi: 10.1016/0263-8223(87)90080-8 [27] Doong J L,Lee C,Fung C P.Vibration and stability of laminated plates based on a modified plate theory[J].Journal of Sound and Vibration,1991,151(2):193-201. doi: 10.1016/0022-460X(91)90851-A [28] Chen C S,Hwang J R,Doong J L.Nonlinear vibration of an initially stressed plate based on a modified plate theory[J].International Journal of Solids and Structures,2001,38(46/47):8563-8583. doi: 10.1016/S0020-7683(00)00226-2 [29] Chen C S,Cheng W S,Chien R D,et al.Large amplitude vibration of an initially stressed cross ply laminated plates[J].Applied Acoustics,2002,63(9):939-956. doi: 10.1016/S0003-682X(02)00015-4 [30] Chen C S,Fung C P,Chien R D.Analysis of an initially stressed hybrid plate based on a higher-order theory[J].Composite Structures,2006,74(3):343-353. doi: 10.1016/j.compstruct.2005.04.014 [31] 钟万勰.计算结构力学与最优控制[M].大连: 大连理工大学出版社,1993. [32] Washizu K.Variational Methods in Elasticity and Plasticity[M].Oxford: Pergamon Press Ltd,1968. [33] 唐立民.混合状态Hamiltonian元的半解析解和叠层板的计算[J].计算结构力学及其应用,1992,9(4):347-360. [34] Gallagher R H.Finite Element Analysis[M].New Jersey: Prentice-Hall,Inc,1975.[WT5”BZ]. Жнвожилов Β Β.Теория Упругости[M].Mocквa: Судпромгиз,1958.
点击查看大图
计量
- 文章访问数: 2721
- HTML全文浏览量: 92
- PDF下载量: 649
- 被引次数: 0