Nonlinear Vibration for the Moderate Thickness Rectangular Cracked Plates Including the Coupled Effect of Elastic Foundation
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摘要: 基于Reissner板理论和Hamilton变分原理，建立了双参数地基上具有表面横向贯穿裂纹的中厚矩形板的非线性运动控制方程．在周边自由的条件下,提出了一组满足问题全部边界条件和裂纹处连续条件的试函数．且利用Galerkin法和谐波平衡法对方程进行求解，分析了考虑地基耦合效应的中厚矩形裂纹板的非线性振动特性．数值计算中， 讨论了不同裂纹位置、 裂纹深度、 板的结构参数和地基物理参数对弹性地基上具裂纹的四边自由中厚矩形板的非线性幅频响应的影响．Abstract: Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-parameter foundation. Under the condition of free boundary, aset of trial functions satisfying all boundary conditions and crack's continuous conditions were proposed. By employing the Galerkin method and the harmonic balance method, the nonlinear vibration equations were solved and the nonlinear vibration behaviors of the plate were analyzed. In numerical computation, the effects of the different location and depth of crack, the different structural parameters of plates and the different physical parameters of foundation on the nonlinear amplitue frequency response curves of the plate were discussed.
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Key words:
- moderate thickness rectangular plate /
- elastic foundation /
- crack /
- nonlinear vibration
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[1] Szilard R.Theory and Analysis of Plates Classical and Numerical Method[M].Englewood Chiffs,New Jersey:Prentice-Hall,Inc,1974. [2] Faw T F,Shi X P,Tan S A.Use of pasternak foundation in concrete pavement analysis[J].Journal of Transportation Engineering,1996(July/Aug):323—328. [3] 李正良，邓安福.双参数地基上板弯曲问题的边界积分方程[J].应用数学和力学，1992,13(7):633—643. [4] 王建国，黄茂光.双参数弹性地基板的边界元分析[J].土木工程学报，1992,25(3):51—59. [5] Sonzogni V E,Idelsohn S R.Free vibration of rectangular plates of exponentially varying thickness and with a free edge[J].Journal of Sound and Vibration,1990,140(3):513—522. doi: 10.1016/0022-460X(90)90764-Q [6] Bhaskar A,Dumir P C.Non-linear vibration of orthotropic thin rectangular plates on elastic foundations[J].Journal of Sound and Vibration,1988,125(1):1—11. doi: 10.1016/0022-460X(88)90410-5 [7] Saliba H T.Transverse free vibration of fully clamped symmetrical trapezoidal plates[J].Journal of Sound and Vibration,1988,126(1):237—247. doi: 10.1016/0022-460X(88)90238-6 [8] 梁兴复,章权，曲蕾，等.用伽辽金法解弹性地基上自由矩形板弯曲、稳定和振动问题[J].青岛建筑工程学院学报，1994,15(1):6—12. [9] Khadem S E,Rezaee M.An analytical approach for obtaining the location and depth of an all-over part-throuch crack on externally in-plane loaded rectangular plate using vibration analysis[J].Journal of Sound and Vibration,2000,230(2):291—308. doi: 10.1006/jsvi.1999.2619 [10] 曾亚.混凝土刚性路面板静、动力特性及损伤诊断研究[D].博士学位论文.长沙：湖南大学，1998，61—69. -
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