留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基本解方法求解简谐外力作用下的Kirchhoff-Love板反源问题

顾智杰 谭永基

顾智杰, 谭永基. 基本解方法求解简谐外力作用下的Kirchhoff-Love板反源问题[J]. 应用数学和力学, 2012, 33(12): 1411-1430. doi: 10.3879/j.issn.1000-0887.2012.12.004
引用本文: 顾智杰, 谭永基. 基本解方法求解简谐外力作用下的Kirchhoff-Love板反源问题[J]. 应用数学和力学, 2012, 33(12): 1411-1430. doi: 10.3879/j.issn.1000-0887.2012.12.004
GUZhi-jie, TAN Yong-ji. Fundamental solution method for inverse source problem of plate equation[J]. Applied Mathematics and Mechanics, 2012, 33(12): 1411-1430. doi: 10.3879/j.issn.1000-0887.2012.12.004
Citation: GUZhi-jie, TAN Yong-ji. Fundamental solution method for inverse source problem of plate equation[J]. Applied Mathematics and Mechanics, 2012, 33(12): 1411-1430. doi: 10.3879/j.issn.1000-0887.2012.12.004

基本解方法求解简谐外力作用下的Kirchhoff-Love板反源问题

doi: 10.3879/j.issn.1000-0887.2012.12.004
基金项目: 国家自然科学基金资助项目(11072141)
详细信息
    作者简介:

    顾智杰(1984—),男,江苏南通人,博士(联系人.E-mail: 071018028@fudan.edu.cn).

  • 中图分类号: O326; O151.2; O241.6

Fundamental solution method for inverse source problem of plate equation

  • 摘要: 主要考察弹性薄板在规则外力作用下的振动模型.在给定外力源项随时间变化模式的情况下,通过对薄板局部区域一段时间的振动位移观测数据,来反演外力大小的问题,也就是通常所谓的弹性薄板反源问题.给出了弹性薄板反源解的唯一性定理,并推导出板方程的基本解.取基本解方法和Tikhonov正则化方法的精髓,在简谐模式源项作用的情况下,构造了一套算法来反解源项.对Euler-Bernoulli杆和Kirchhoff-Love板的数值算例表明,无论源项是否光滑,测量是否带有误差,基本解方法都因其较好的计算效果,有着广泛的适用性.
  • [1] Yang Y, Lim C W. A new nonlocal cylindrical shell model for axisymmetric wave propagation in carbon nanotubes[J]. Advanced Science Letters, 2011, 4(1): 121-131.
    [2] Zhao X, Ng T Y, Liew K M. Free vibration of two-side simplysupported laminated cylindrical panels via the meshfree kpRitz method[J].International Journal of Mechanical Sciences, 2004, 46(1): 123-142.
    [3] Zhou D, Lo S H, Cheung Y K. 3-D vibration analysis of annular sector plates using the Chebyshev-Ritz method[J].Journal of Sound and Vibration, 2009, 320(1/2): 421-437.
    [4] Liu Y, Hon Y C, Liew K M. A meshfree Hermite-type radial point interpolation method for Kirchhoff plate problems[J].International Journal for Numerical Methods in Engineering, 2006, 66(7): 1153-1178.
    [5] Kurpa L, Pilgun G, Amabili M. Nonlinear vibrations of shallow shells with complex boundary: R-functions method and experiments[J].Journal of Sound and Vibration, 2007, 306(3/5): 580-600.
    [6] Qian L F, Batra R C, Chen L M. Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local PetrovGalerkin method[J].Composites Part B: Engineering, 2004, 35(6/8): 685-697.
    [7] Sladek J, Sladek V, Wen P H, Aliabadi M H. Meshless local PetrovGalerkin(MLPG) method for shear deformable shells analysis[J].Chinese Journal of Mechanical Engineering, 2006, 13(2): 103-117.
    [8]  
    [9] Krys’ko V A, Papkova I V, Soldatov V V. Analysis of nonlinear chaotic vibrations of shallow shells of revolution by using the wavelet transform[J].Mechanics of Solids, 2010, 45(1): 85-93.
    [10] 李善倾, 袁鸿. 简支梯形底扁球壳自由振动问题的准Green函数方法[J]. 应用数学和力学, 2010, 31(5): 602-608.(LI Shan-qing, YUAN Hong. Quasi-Green’s function method for free vibration of simply-supported trapezoidal shallow spherical shell[J].Applied Mathematics and Mechanics(English Edition), 2010, 31(5): 635-642.)  
    [11] Michaels J E, Pao Y H. The inverse source problem for an oblique force on an elastic plate[J]. Journal of the Acoustical Society of America, 1985, 77(6): 2005-2011.
    [12] Li S M, Miara B, Yamamoto M. A Carleman estimate for the linear shallow shell equation and an inverse source problem[J].Discrete and Continuous Dynamical Systems, 2009, 23(1/2): 367-.
    [13]  
    [14] Alves C, Silvestre A L, Takahashi T. Solving inverse source problems using observability applications to the EulerBernoulli plate equation[J].SIAM Journal on Control and Optimization, 2009, 48(3): 1632-1659.
    [15] Wang Y H. Global uniqueness and stability for an inverse plate problem[J].Journal of Optimization Theory and Applications, 2007, 132(1): 161-173.
    [16] Yang C Y. The determination of two heat sources in an inverse heat conduction problem[J]. International Journal of Heat and Mass Transfer, 1999, 42(2): 345-356.
    [17] Yang C Y. Solving the twodimensional inverse heat source problem through the linear least-squares error method[J].International Journal of Heat and Mass Transfer, 1998, 41(2): 393-398.
    [18] Fatullayev A G. Numerical solution of the inverse problem of determining an unknown source term in a heat equation[J].Mathematical and Computers in Simulation, 2002, 58(3): 247-253.
    [19] Le N C, Lefevre F. A parameter estimation approach to solve the inverse problem of point heat sources identification[J].International Journal of Heat and Mass Transfer, 2004, 47(4): 827-841.
    [20] Johansson B T, Lesnic D. A variational method for identifying a spacewisedependent heat source[J].IMA Journal of Applied Mathematics, 2007, 72(6): 748-760.
    [21] Yan L, Fu C L, Yang F L. The method of fundamental solutions for the inverse heat source problem[J].Engineering Analysis With Boundary Elements, 2008, 32(3): 216-222.
    [22] Jin B T, Marin L. The method of fundamental solutions for inverse source problems associated with the steadystate heat conduction[J].International Journal for Numerical Method in Engineering, 2007, 69(8): 1570-1589.
    [23] Yan L, Yang F L, Fu C L. A meshless method for solving an inverse spacewisedependent heat source problem[J].Journal of Computational Physics, 2009, 228(1): 123-136.
    [24] Johansson B T, Lesnic D, Reeve T. A method of fundamental solutions for the onedimensional inverse Stefan problem[J].Applied Mathematical Modelling, 2011, 35(9): 4367-4378.
    [25] Chen C W, Young D L, Tsai C C. The method of fundamental solutions for inverse 2D Stokes problems[J].Computational Mechanics, 2005, 37(1):2-14.
    [26] Marin L, Lesnic D. The method of fundamental solutions for inverse boundary value problems associated with the twodimensional biharmonic equation[J].Mathematical and Computer Modelling, 2005, 42(3/4): 261-278.
    [27] Alves C J S, Colaco M J, Leitao V M A, Martins N F M , Orlande H R B, Roberty Ni C. Recovering the source term in a linear diffusion problem by the method of fundamental solutions[J].Inverse Problems in Science and Engineering, 2008, 16(8): 1005-1021.
    [28] Love A E H. On the small free vibrations and deformations of elastic shells[J]. Philosophical Transactions of the Royal Society A, 1888, 179: 491-549.
    [29] Alves C J S. On the choice of source points in the method of fundamental solutions[J]. Engineering Analysis With Boundary Elements, 2009, 33(12): 1348-1361.
    [30] Kim S M, McCullough B F. Dynamic response of plate on viscous Winkler foundation to moving loads of varying amplitude[J].Engineering Structure, 2003, 25(9): 1179-1188.
    [31] Liew K M, Han J B, Xiao Z M. Differential quadrature method for Mindlin plates on Winkler foundations[J]. International Journal of Mechanical Sciences, 1996, 38(4): 405-421.
  • 加载中
计量
  • 文章访问数:  1802
  • HTML全文浏览量:  59
  • PDF下载量:  1205
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-02-10
  • 修回日期:  2012-05-10
  • 刊出日期:  2012-12-15

目录

    /

    返回文章
    返回