Advanced SearchSearch Tips
Dynamic stiffness approach and differential transformation for free vibration analysis of a moving Reddy-Bickford beam
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Dynamic stiffness approach and differential transformation for free vibration analysis of a moving Reddy-Bickford beam
Bozyigit, Baran; Yesilce, Yusuf;
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 method (DTM). First of all, the governing differential equations of motion in free vibration are derived by using Hamilton`s principle. The nondimensionalised multiplication factors for axial speed and axial tensile force are used to investigate their effects on natural frequencies. The natural frequencies are calculated by solving differential equations using analytical method (ANM). After the ANM solution, the governing equations of motion of axially moving Reddy-Bickford beams are solved by using DTM which is based on Finite Taylor Series. Besides DTM, DSM is used to obtain natural frequencies of moving Reddy-Bickford beams. DSM solution is performed via Wittrick-Williams algorithm. For different boundary conditions, the first three natural frequencies that calculated by using DTM and DSM are tabulated in tables and are compared with the results of ANM where a very good proximity is observed. The first three mode shapes and normalised bending moment diagrams are presented in figures.
axially moving beam;Reddy-Bickford beam theory;dynamic stiffness method;differential transform method;free vibration analysis;natural frequency;
 Cited by
Arikoglu, A. and Ozkol, I. (2010), "Vibration analysis of composite sandwich beams with viscoelastic core by using differential transform method", Compos. Struct., 92, 3031-3039. crossref(new window)

Bagdatli, S.M., Ozkaya, E. and Oz, H.R. (2011), "Dynamics of axially accelerating beams with an intermediate support", J. Vib. Acoust., 133, 1-10.

Banerjee, J.R. (1997), "Dynamic stiffness for structural elements: A general approach", Comput. Struct., 63, 101-103. crossref(new window)

Banerjee, J.R. and Gunawardana, W.D. (2007), "Dynamic stiffness matrix development and free vibration analysis of a moving beam", J. Sound Vib., 303, 135-143. crossref(new window)

Banerjee, J.R. (2012), "Free vibration of beams carrying spring-mass systems-A dynamic stiffness approach", Comput. Struct., 104-105, 21-26. crossref(new window)

Banerjee, J.R. and Jackson, D.R. (2013), "Free vibration of a rotating tapered Rayleigh beam: A dynamic stiffness method of solution", Comput. Struct., 124, 11-20. crossref(new window)

Bao-hui, L., Hang-shan, G., Hong-bo, Z., Yong-shou, L. and Zhou-feng, Y. (2011), "Free vibration analysis of multi-span pipe conveying fluid with dynamic stiffness method", Nucl. Eng. Des., 241, 666-671. crossref(new window)

Bickford, W.B. (1982), "A consistent higher order beam theory", Develop. Theor. Appl. Mech., 11, 137-150.

Catal, S. and Catal, H.H. (2006), "Buckling analysis of partially embedded pile in elastic soil using differential transform method", Struct. Eng. Mech., 24(2), 246-269.

Catal, S. (2014), "Buckling analysis of semi-rigid connected and partially embedded pile in elastic soil using differential transform method", Struct. Eng. Mech., 52(5), 971-995. crossref(new window)

Catal, S. (2006), "Analysis of free vibration of beam on elastic soil using differential transform method", Struct. Eng. Mech., 24(1), 51-63. crossref(new window)

Catal, S. (2008), "Solution of free vibration equations of beam on elastic soil by using differential transform method", Appl. Math. Model., 32, 1744-1757. crossref(new window)

Catal, S. (2012), "Response of forced Euler-Bernoulli beams using differential transform method", Struct. Eng. Mech., 42(1), 95-119. crossref(new window)

Chen, C.K. and Ho, S. H. (1986), "Application of differential transformation to eigenvalue problems", Appl. Math. Comput., 79, 173-188.

Chen, L.Q., Tang, Y.Q. and Lim, C.W. (2010), "Dynamic stability in parametric resonance of axially accelerating viscoelastic Timoshenko beams", J. Sound Vib., 329, 547-565. crossref(new window)

Ebrahimi, F. and Salari, E. (2015), "Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method", Compos. Part B, 79, 156-169. crossref(new window)

Eisenberger, M. (2003), "An exact high order beam element", Comput. Struct., 81, 147-152. crossref(new window)

Eisenberger, M. (2003), "Dynamic stiffness vibration analysis using a high-order beam model", Int. J. Numer. Meth. Eng., 57, 1603-1614. crossref(new window)

Heyliger, P.R. and Reddy J.N. (1988), "A higher order beam finite element for bending and vibration problems", J. Sound Vib., 126, 309-326. crossref(new window)

Ho, S.H. and Chen, C.K. (2006), "Free transverse vibration of an axially loaded non-uniform spinning twisted Timoshenko beam using differential transform", Int. J. Mech. Sci., 48, 1323-1331. crossref(new window)

Jun, L., Hongxing, H. and Rongying, H. (2008), "Dynamic stiffness analysis for free vibrations of axially loaded laminated composite beams", Comput. Struct., 84, 87-98. crossref(new window)

Lal, R. and Ahlawat, N. (2015), "Axisymmetric vibrations and buckling analysis of functionally graded circular plates via differential transform method", Eur. J. Mech. A/Solid., 52, 85-94. crossref(new window)

Lee, U., Kim, J. and Oh, H. (2004), "Spectral analysis for the transverse vibration of an axially moving Timoshenko beam", J. Sound Vib., 271, 685-703. crossref(new window)

Levinson, M. (1981), "A new rectangular beam theory", J. Sound Vib., 74, 81-87. crossref(new window)

Nefovska-Danilovic, M. and Petronijevic, M. (2015), "In-plane free vibration and response analysis of isotropic rectengular plates using the dynamic stiffness method", Comput. Struct., 152, 82-95. crossref(new window)

Ozkaya, E. and Oz, H.R. (2002), "Determination of natural frequencies and stability regions of axially moving beams using artificial neural networks method", J. Sound Vib., 252, 782-789. crossref(new window)

Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51, 745-752. crossref(new window)

Reddy, J.N., Wang, C.M. and Lee, K.H. (1997), "Relationships between bending solutions of classical and shear deformation beam theories", Int. J. Solid. Struct., 34, 3373-3384. crossref(new window)

Semnani, S.J., Attarnejad, R. and Firouzjaei, R.K. (2013), "Free vibration analysis of variable thickness thin plates by two-dimensional differential transform method", Acta Mechanica, 224, 1643-1658. crossref(new window)

Soldatos, K.P. and Sophocleous, C. (2001), "On shear deformable beam theories: The frequency and normal mode equations of the homogenous orthotropic Bickford beam", J. Sound Vib., 242, 215-245. crossref(new window)

Su, H. and Banerjee, J.R. (2015), "Development of dynamic stiffness method for free vibration of functionally graded Timoshenko beams", Computers and Structures, 147, 107-116. crossref(new window)

Wattanasakulpong, N. and Charoensuk, J. (2015), "Vibration characteristics of stepped beams made of FGM using differential transformation method", Meccanica, 50, 1089-1101. crossref(new window)

Wickert, J.A. and Mote, C.D. (1989), "On the energetics of axially moving continua", J. Acoust. Soc. Am., 85, 1365-1368. crossref(new window)

Yan, Q.Y., Ding, H. and Chen, L.Q. (2014), "Periodic responses and chaotic behaviors of an axially accelerating viscoelastic Timoshenko beam", Nonlin. Dyn., 78, 1577-1591. crossref(new window)

Yesilce, Y. and Catal, S. (2009), "Free vibration of axially loaded Reddy-Bickford beam on elastic soil using the differential transform method", Struct. Eng. Mech., 31, 453-476. crossref(new window)

Yesilce, Y. (2010), "Differential transform method for free vibration analysis of a moving beam", Struct. Eng. Mech., 35, 645-658. crossref(new window)

Yesilce, Y. (2011), "Free vibrations of a Reddy-Bickford multi-span beam carrying multiple spring-mass systems", Shock Vib., 18, 709-726. crossref(new window)

Yesilce, Y. (2013), "Determination of natural frequencies and mode shapes of axially moving Timoshenko beams with different boundary conditions using differential transform method", Adv. Vib. Eng., 12, 89-108.

Yesilce, Y. (2015), "Differential transform method and numerical assembly technique for free vibration analysis of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and rotary inertias", Struct. Eng. Mech., 53, 537-573. crossref(new window)

Zhou, J.K. (1968), Differential transformation and its applications for electrical circuits, Huazhong University Press, Wuhan, China.