Lagrangianlized Nonlinear Dynamic Equation of Timoshenko Beam and Application

Abstract:

Base on Hamilton's principle, under the continuity conditions of generalized coordinator, generalized force and the deformation, provide nonlinear deformation problem of Timoshenko beam’s Lagrangianlized basic elastic equation and its generalized boundary condition. Lagrangianlized basic elastic equation makes it possible to avoid indirect problem for the variation principle of continuum, which not only simplify the solving of direct problem but also stylize the solving process. The YUQING ancient bridge (in ShangHai) is taken as an example, calculating the kinetics characteristics and making damage diagnosis combined with the pulsation experimental result data.

• Periodical: Applied Mechanics and Materials (Volumes 157-158)
• Pages: 1115-1120
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.157-158.1115
• Online since: February 2012
• Authors: Pei Tan, Lian Wang Chen, Yu Jiang Li
• Keywords: Damage Diagnosis, Dynamical Analysis, Hamilton Theory, Lagrangianlized, Nonlinear, Pulse Experiment

References

[1] Liu Yan-Zhu，Planar vibration of a thin elastic rod with circular cross section in viscous medium，2005，Acta Physica Sinica，Vol. 54, No. 11；

DOI: 10.7498/aps.54.4989

[2] Zhang Yan, Zha Long-Long, Dynamical big deflection of linear-elasticity Timoshenko beam，2005，Journal of Liaoning Technical University (Natural Science Edition), Vol.24, Suppl.

[3] Cheng Chang-Jun, Lu Yong-Hua, The variational principle of Viscoelastic Timoshenko beams and static dynamic behavior analysis [J], Acta Mechnica Solida Sinica，2002，(2): 190-196

[4] Zhang Yan, Xie Meng-Yao, Static buckling and bifurcation of nonlinear-elastic beams and application，2005，Journal of Liaoning Technical University (Natural Science Edition), Vol.24, N0.4；

[5] Zhang Yan, Sheng Dong-Fa, Cheng Chang-Jun, Dynamical Behavior of Nonlinear Viscoelastic Timoshenko Beams with Damage on a Viscoelastic Foundation. Journal of Shanghai University (English Edition)，2004，(2)：245-251；

DOI: 10.1007/s11741-004-0059-6

[6] Liang Li-Fu, Variation principle and its application, Harbin engineering university press (2005)

[7] Wang Xiang-Qiu, Yang De-Ling, Gao Wen-Hua, structural dynamic finite element analysis the track based on the variational principle, JOURNAL OF VIBRATION AND SHOCK, Vol. 24, No. 4.2005；

[8] Timoshenko S，Gem J．Mechanics of Materials [M]． ：ReinholdCompany，1972．

[9] Liu Yan-Zhu Mechanical problem on elastic Rod model of DNA [J]. Mechanics and Engineering,2003, 25(1):1-5.

[10] Love A E H. A treatise on mathematical theory of elasticity, 4-th ed[M].New York:Dover, 1944.

[11] Goriely A, Shipman P. Dynamics of helical strips[J]. Physical Review E,2000, 61(4): 4508-4517.2000,61(4):4508-4517..

DOI: 10.1103/physreve.61.4508

[12] Liu Yan-Zhu, Helical Equilibrium and Stability of a Thin Elastic Rod with Noncircular Cross-Section [J] Chinese Quarterly of Mechanics, 2003, 24(4):433-439.

[13] Xie Qifang, "Experimental Study and Theoretical Analysis on Strengthen for Chinese Ancient Timber Buildings," Xi an University of Architecture &Technology Ph.D. Dissertation; 2007.