Li F L, Sun Z Z. A finite difference scheme for solving the Timoshenko beam equations with boundary feedback [J]. Journal of Computational and Applied Mathematics, 2007, 200(2): 606―627.
Zhao Qin, Tong Genshu. Moment amplification factors of cantilevers with variable axial forces and sectional rigidities [J]. Engineering Mechanics, 2011, 28(11): 1―6. (in Chinese)
[4]
Su Y, Ma C. Transient wave analysis of a cantilever Timoshenko beam subjected to impact loading by Laplace transform and normal mode methods [J]. International Journal of Solids and Structures, 2012, 49(9): 1158―1176.
Yang Xiao, He Guanghui. Exact finite element method for vibration and buckling of pile-soil-superstructure system in liquefied soil [J]. Chinese Quarterly of Mechanics, 2010, 31(4): 604―609. (in Chinese)
[7]
Olovssona L, Simonssonb K, Unossona M. Shear locking reduction in eight-noded tri-linear solid finite elements [J]. Computers and Structures, 2006, 84(7): 476―484.
[8]
Rong T Y, Lu A Q. Generalized mixed variational principles and solutions of ill-conditioned problems in computational mechanics: Part I. Volumetric locking [J]. Computer Methods in Applied Mechanics and Engineering, 2001, 191(3/5): 407―422.
Chen Taicong, Ma Haitao. Exact finite solutions of buckling analysis of frame structure [J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(6): 953―960. (in Chinese)
[11]
Ma H. Exact solution of vibration problems of frame structures [J]. International Journal for Numerical Methods in Biomedical Engineering, 2008, 26(5): 587―596.
[12]
Attarnejad R, Semnani S J, Shahba A. Basic displacement functions for free vibration analysis of non-prismatic Timoshenko beams [J]. Finite Elements in Analysis and Design, 2010, 46(10): 916―929.
[13]
Nguyen Q H, Martinelli E, Hjiaj M. Derivation of the exact stiffness matrix for a two-layer Timoshenko beam element with partial interaction [J]. Engineering Structures, 2011, 33(2): 298―307.
[14]
Grognec P L, Nguyen Q H, Hjiaj M. Exact buckling solution for two-layer Timoshenko beams with interlayer slip [J]. International Journal of Solids and Structures, 2012, 49(1): 143―150.
Xia Guiyun, Li Chuanxi, Zeng Qingyuan. Analysis for elastic foundation beam with double shear effect [J]. Journal of Hunan University (Natural Sciences Edition), 2011, 38(11): 19―24. (in Chinese)
[17]
Kerr A D. Elastic and viscoelastic foundation models [J]. Journal of Applied Mechanics, 1964, 31(3): 491―498.
Yang Xiao, He Guanghui. Analysis of horizontal vibration of pile-soil-superstructure system in layered liquefiable soil [J]. Journal of Shanghai University (Natural Science Edition), 2011, 17(6): 779―784. (in Chinese)
[20]
Timoshenko S. Vibration problems in engineering [M]. 2nd ed. New York: D. Van Nostrand Company, Inc., 1937: 189―192.
[21]
Adhikari S, Bhattacharya S. Dynamic instability of pile-supported structures in liquefiable soils during earthquakes [J]. Shock and Vibration, 2008, 15(6): 665―685.
[22]
Han S M, Benaroya H, Wei T. Dynamics of transversely vibraing beams using four engineering theories [J]. Journal of Sound and Vibration, 1999, 225(5): 935―988.
[23]
Antes H. Fundamental solution and integral equations for Timoshenko beams [J]. Computers and Structures, 2003, 81(6): 383―396.
[24]
Auciello N M, Ercolano A. A general solution for dynamic response of axially loaded non-uniform Timoshenko beams [J]. International Journal of Solids and Structures, 2004, 41(18/19): 4861―4874.
[25]
Tokimatsu K, Asaka Y. Effects of liquefaction-induced ground displacements on pile performance in the 1995 Hyogoken-Nambu earthquake [J]. Special Issue of Soils and Foundations, 1998, 38(2): 163―177.
