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In this paper, the effect of shear deformation is considered into flexural deflection of the geometrically nonlinear deformation of a flexible beam. Then, considering the coupling effect of deformation in to the extensional and flexural deflection, the second-order coupling terms of deformation in two displacement fields are developed and the axial inertial force and transverse distributed force are considered. The finite element method is used for the system discretization and the coupling dynamic equations of flexible beam are obtained by Lagrange’s equations. In this way, the new governing differential equations of the beam in the geometrically non-linear kinematics of deformation are derived. Numerical examples of a flexible beam are studied to analyze the effect of shear deformation on the dynamic character and to investigate the coupling effect. Furthermore, from this present method, a moving Timoshenko beam can also produce the dynamic stiffening phenomenon and some new properties can be shown.
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Keywords:
- non-inertial reference frame /
- shear deformation /
- flexible beam /
- dynamic modeling
[1] He X S, Deng F Y 2010 Acta Phys. Sin. 59 25 (in Chinese) [和兴锁、 邓峰岩 2010 物理学报 59 25]
[2] Deng F Y, He X S, Li L, Zhang J 2007 Multibody Syst. Dyn. 18 559
[3] Liu Y Z 2009 Chin. Phys. B 18 1
[4] He X S,Deng F Y 2010 Acta Phys. Sin. 59 1428 (in Chinese)[和兴锁、 邓峰岩 2010 物理学报 59 1428]
[5] Bai C L, Zhang X, Zhang L H 2009 Chin. Phys. B. 18 475
[6] Zhang S Q 2008 Acta Phys. Sin. 57 1335 (in Chinese) [张善 卿 2008 物理学报 57 1335] 〖7] Bai C L, Zhang X, Zhang L H 2009 Chin. Phys. B 18 475
[7] Meng Z, Liu B 2008 Acta Phys. Sin. 57 1329 (in Chinese) [孟 宗、 刘 彬 2008 物理学报 57 1329]
[8] Yang H 2002 PhD thesis (Shanghai Jiaotong Uni., Shanghai, China) (in Chinese) [杨 辉 2002 博士毕业论文, 上海: 上海交通大学]
[9] Fu J L, Chen B Y, Tang Y F, Fu H 2008 Chin. Phys. B 17 3942
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[1] He X S, Deng F Y 2010 Acta Phys. Sin. 59 25 (in Chinese) [和兴锁、 邓峰岩 2010 物理学报 59 25]
[2] Deng F Y, He X S, Li L, Zhang J 2007 Multibody Syst. Dyn. 18 559
[3] Liu Y Z 2009 Chin. Phys. B 18 1
[4] He X S,Deng F Y 2010 Acta Phys. Sin. 59 1428 (in Chinese)[和兴锁、 邓峰岩 2010 物理学报 59 1428]
[5] Bai C L, Zhang X, Zhang L H 2009 Chin. Phys. B. 18 475
[6] Zhang S Q 2008 Acta Phys. Sin. 57 1335 (in Chinese) [张善 卿 2008 物理学报 57 1335] 〖7] Bai C L, Zhang X, Zhang L H 2009 Chin. Phys. B 18 475
[7] Meng Z, Liu B 2008 Acta Phys. Sin. 57 1329 (in Chinese) [孟 宗、 刘 彬 2008 物理学报 57 1329]
[8] Yang H 2002 PhD thesis (Shanghai Jiaotong Uni., Shanghai, China) (in Chinese) [杨 辉 2002 博士毕业论文, 上海: 上海交通大学]
[9] Fu J L, Chen B Y, Tang Y F, Fu H 2008 Chin. Phys. B 17 3942
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