YANG Xiao, WEN Qun. Dynamic and Quasi-Static Bending of Saturated Poroelastic Timoshenko Cantilever Beam[J]. Applied Mathematics and Mechanics, 2010, 31(8): 949-960. doi: 10.3879/j.issn.1000-0887.2010.08.008
Citation: YANG Xiao, WEN Qun. Dynamic and Quasi-Static Bending of Saturated Poroelastic Timoshenko Cantilever Beam[J]. Applied Mathematics and Mechanics, 2010, 31(8): 949-960. doi: 10.3879/j.issn.1000-0887.2010.08.008

Dynamic and Quasi-Static Bending of Saturated Poroelastic Timoshenko Cantilever Beam

doi: 10.3879/j.issn.1000-0887.2010.08.008
  • Received Date: 1900-01-01
  • Rev Recd Date: 2010-06-27
  • Publish Date: 2010-08-15
  • Based on the three-dmiensional Gurtin-type variational principle of the incompressible saturated porousmedia, first, a one-dimensionalm athematical model for dynamics of the saturated poroelastic Timoshenko Cantilever beam was established with a ssumptions of deformatin of the classical single phase Tmioshenko beam and the movement of pore fluid only in the axial direction of the saturated poroelasic beam. This mathematical model can be degene rated into the Euler-Bernoullim odel, Rayleigh model and Shear model of the saturated poroelastic beam, respe ctively, under some specialcases. Secondly, dynamic and quasi-static behavior of a saturated poroelastic Tmioshenko cant ilever beam with mipermeable and permeable at its fixed and free end, respectively, subjected to a step load at its free end, was analyzed by the Laplace transform. The variations of the deflections at the beam free end against the tmie were shown in figures, and the influences of the in teraction coefficient between the porefluid and solid skele to naswellas the slenderness ratio of the beam on the dynamic/quasi-static performances of the beam were examined. It is shown that the quasi-static deflections of the saturated poroela stic beam possess the creep behavior smiilar to that of viscoelastic beam. In dynamic responses, with the slenderness ratio increasing, the vibration periods and amplitudes of the deflections at the free end increase, and the tmie needed for deflections to approachits stationary values also increases. Whereas, with the interaction coefficient increasing, the vibrations of the beam deflections decay more strongly, and, eventually, the deflections of the saturated poroelastic beam converge to the static deflections of the classic single phase Tmioshenko beam.
  • loading
  • [1]
    Zhang D, Cowin S C. Oscillatory bending of a poroelastic beam[J]. Journal of the Mechanics and Physics of Solids, 1994, 42(10): 1575-1599. doi: 10.1016/0022-5096(94)90088-4
    [2]
    Kameo Y, Adachi T, Hojo M. Transient response of fluid pressure in a poroelastic material under uniaxial cyclic loading[J]. Journal of the Mechanics and Physics of Solids, 2008, 56(5): 1794-1805. doi: 10.1016/j.jmps.2007.11.008
    [3]
    Wang Z H, Prevost J H, Coussy O. Bending of fluid-saturated poroelastic beams with compressible constitutes[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2009, 33(4): 425-447. doi: 10.1002/nag.722
    [4]
    Li L P, Schulgasser K, Cederbaum G. Theory of poroelastic beams with axial diffusion[J]. Journal of the Mechanics and Physics of Solids, 1995, 43(12): 2023-2042. doi: 10.1016/0022-5096(95)00056-O
    [5]
    Li L P, Schulgasser K, Cederbaum G. Large deflection analysis of poroelastic beams[J]. International Journal of Non-Linear Mechanics, 1998, 33(1): 1-14. doi: 10.1016/S0020-7462(97)00003-6
    [6]
    Cederbaum G, Schulgasser K, Li L P. Interesting behavior patterns of poroelastic beams and columns[J]. International Journal of Solids and Structures, 1998, 35(34): 4931-4943. doi: 10.1016/S0020-7683(98)00102-4
    [7]
    Chakraborty A. Wave propagation in anisotropic poroelastic beam with axial-flexural coupling[J]. Computation Mechanics, 2009, 43(6):755-767. doi: 10.1007/s00466-008-0343-6
    [8]
    WANG Zhi-hua, Pr′evost Jean H, Coussy Olivier. Bending of fluid-saturated linear poroelastic beams with compressible constituents[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2009, 33(4):425-447. doi: 10.1002/nag.722
    [9]
    YANG Xiao, CHENG Chang-jun. Gurtin variational principle and finite element simulation for dynamical problems of fluid-saturated porous media[J]. Acta Mechanica Solida Sinica, 2003, 16(1): 24-32.
    [10]
    YANG Xiao, HE Lu-wu. Variational principles of fluid-saturated incompressible porous media[J]. Journal of Lanzhou University, 2003, 39(6): 24-28.
    [11]
    杨骁, 李丽. 不可压饱和多孔弹性梁、杆动力响应的数学模型[J]. 固体力学学报, 2006, 27(2): 159-166.
    [12]
    杨骁, 王佩菁. 不可压流体饱和多孔弹性梁的变分原理及有限元方法[J]. 固体力学学报, 2009, 30(1): 54-60.
    [13]
    杨晓,王琛. 不可压饱和多孔弹性梁的大桡度非线性数学模型[J]. 应用数学和力学, 2007, 28(12): 1417-1424.
    [14]
    de Boer R. Theory of Porous Media: Highlights in the Historical Development and Current State[M]. Berlin, Heidelberg: Springer-Verlag, 2000.
    [15]
    Timoshenko S, Young D N. Vibration Problems in Engineering[M]. Princeton, NY: Van Nostrand, 1955: 329-331.
    [16]
    Han S M, Benaroya H, Weik T. Dynamics of transversely vibrating beams using four engineering theories[J]. Journal of Sound and Vibration, 1999, 225(5): 935-988. doi: 10.1006/jsvi.1999.2257
    [17]
    Crump K S. Numerical inversion of Laplace transforms using a Fourier series approximation[J]. Journal of Association for Computing Machinery, 1976, 23(1): 89-96. doi: 10.1145/321921.321931
    [18]
    Abbas I. Natural frequencies of a poroelastic hollow cylinder[J]. Acta Mechanics, 2006, 186(1/4): 229-237. doi: 10.1007/s00707-006-0314-y
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1785) PDF downloads(745) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return