Dynamic stiffness approach and differential transformation for free vibration analysis of a moving Reddy-Bickford beam
作者： Baran Bozyigit , Yusuf Yesilce
DOI: 10.12989/SEM.2016.58.5.847
关键词: Structural engineering 、 Bending moment 、 Mathematics 、 Beam (structure) 、 Boundary value problem 、 Differential equation 、 Mathematical analysis 、 Timoshenko beam theory 、 Normal mode 、 Vibration 、 Equations of motion
摘要: In this study, the free vibration analysis of axially moving beams is investigated according to Reddy-Bickford beam theory (RBT) by using dynamic stiffness method (DSM) and differential transform (DTM). First all, governing equations motion in are derived Hamilton`s principle. The nondimensionalised multiplication factors for axial speed tensile force used investigate their effects on natural frequencies. frequencies calculated solving analytical (ANM). After ANM solution, solved DTM which based Finite Taylor Series. Besides DTM, DSM obtain beams. solution performed via Wittrick-Williams algorithm. For different boundary conditions, first three that tabulated tables compared with results where a very good proximity observed. mode shapes normalised bending moment diagrams presented figures.
koreascience.or.kr参考文章(37)
SM Bağdatli, E Özkaya, HR Öz, None, Dynamics of Axially Accelerating Beams With an Intermediate Support Journal of Vibration and Acoustics. ,vol. 133, pp. 031013- ,(2011) , 10.1115/1.4003205
J.R. Banerjee, W.D. Gunawardana, Dynamic stiffness matrix development and free vibration analysis of a moving beam Journal of Sound and Vibration. ,vol. 303, pp. 135- 143 ,(2007) , 10.1016/J.JSV.2006.12.020
Seval Çatal, Solution of free vibration equations of beam on elastic soil by using differential transform method Applied Mathematical Modelling. ,vol. 32, pp. 1744- 1757 ,(2008) , 10.1016/J.APM.2007.06.010
Yusuf Yesilce, Seval Catal, Free vibration of axially loaded Reddy-Bickford beam on elastic soil using the differential transform method Structural Engineering and Mechanics. ,vol. 31, pp. 453- 475 ,(2009) , 10.12989/SEM.2009.31.4.453
Li-Qun Chen, You-Qi Tang, C.W. Lim, Dynamic stability in parametric resonance of axially accelerating viscoelastic Timoshenko beams Journal of Sound and Vibration. ,vol. 329, pp. 547- 565 ,(2010) , 10.1016/J.JSV.2009.09.031
Seval Catal, Response of forced Euler-Bernoulli beams using differential transform method Structural Engineering and Mechanics. ,vol. 42, pp. 95- 119 ,(2012) , 10.12989/SEM.2012.42.1.095
M. Levinson, A new rectangular beam theory Journal of Sound and Vibration. ,vol. 74, pp. 81- 87 ,(1981) , 10.1016/0022-460X(81)90493-4
J.N. Reddy, C.M. Wang, K.H. Lee, Relationships between bending solutions of classical and shear deformation beam theories International Journal of Solids and Structures. ,vol. 34, pp. 3373- 3384 ,(1997) , 10.1016/S0020-7683(96)00211-9
Roshan Lal, Neha Ahlawat, Axisymmetric vibrations and buckling analysis of functionally graded circular plates via differential transform method European Journal of Mechanics A-solids. ,vol. 52, pp. 85- 94 ,(2015) , 10.1016/J.EUROMECHSOL.2015.02.004
P.R. Heyliger, J.N. Reddy, A higher order beam finite element for bending and vibration problems Journal of Sound and Vibration. ,vol. 126, pp. 309- 326 ,(1988) , 10.1016/0022-460X(88)90244-1