Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Dynamics of Timoshenko Beam on Nonlinear Soil


Affiliations
1 Department of English, Faculty of Engineering, Cairo University
2 Department of Mathematics, Faculty of Engineering, Cairo University
3 Department of Physics, Faculty of Engineering, Cairo University
     

   Subscribe/Renew Journal


The main objective of this publication is to derive the characteristic differential equations for two-dimensional (2D) Timoshenko beam with simply supported ends subjected to distributed dynamic load and resting on one parameter nonlinear soil. A numerical solution using Adomian decomposition method is carried out to obtain the deflection shape of the beam. A Parametric analyses of are carried out and influences of all varying parameters on the beam responses are investigated. The model includes the simultaneous effects (or couplings) of bending and shear deformations, translational and rotational inertias of all masses considered.

Keywords

Nonlinear Soil, Timoshenko, Adomian Decomposition Method
Subscription Login to verify subscription
User
Notifications
Font Size


  • J. Dario Aristizabal-Ochoa1. (2004) “Timoshenko Beam-Column with Generalized End Conditions and Nonclassical Modes of Vibration of Shear Beams” J. Engineering Mechanics. ASCE, 1151-1159
  • Abbas, B. A. H. (1984) “Vibration of Timoshenko beams with elastically restrained ends. ” J. Sound Vib. 97, 541–548.
  • Blevins R. D. (1979). Formulas for natural frequency and mode shape, Chap. 8, Van Nostrand-Reinhold, New York, 171–175.
  • Cheng, F. Y., and Pantelides, C. P. (1988). “Dynamic Timoshenko beam– columns on elastic Media.” J. Struct. Eng., 114(7), 1524–1550.
  • Cheng, F. Y., and Tseng, W-H. (1973). “Dynamic matrix of Timoshenko beam columns.” J. Struct. Div. ASCE, 99(3), 527–549.
  • Clough, R. W., and Penzien, J. (1993). Dynamics of structures, 2nd Ed., Chap. 26, McGraw-Hill, New York, 628–628.
  • Aristizábal-Ochoa, J. Dario. (1983). “Cracking and shear effects on structuralwalls.” J. Struct. Eng., 109(5), 1267–1277.
  • Geist, B., and McLauglin, J. R. (1997). “Double eigenvalues for the uniform Timoshenko beam.” Appl. Math. Lett., 10(3), 129–134.
  • Goodman, L. E., and Sutherland, J. G. (1951). “Discussion of natural frequencies of continuous beams of uniform span length.” J. Appl. Mech., 18, 217–218.
  • Hurty, W. C., and Rubenstein, J. C. (1964). “On the effect of rotatory inertia and shear in beam vibration.” J. Franklin Inst., 278, 124–132.
  • Kausel, E. (2002). “Nonclassical modes of unrestrained shear beams.” J. Eng. Mech., 128(6), 663–667.
  • Thomson, W. T. (1972). Theory of vibration with applications, Chap. 8, Prentice-Hall, Englewoods Cliff, N.J., 275–276.
  • Weaver, W., Timoshenko, S. P., and Young, D. H. (1990). Vibration problems in engineering, 5th Ed., Chap. 5, Wiley Interscience, New York, 433–460
  • Zhou, D., and Cheung, Y. K. (2001). “Vibrations of tapered Timoshenko beams in terms of static Timoshenko beam functions.” J. Appl. Mech., 68, 656–602.
  • George Adomian.(1993) “Solving Frontier problems of physics :the decomposition method”.
  • Shaher Momani, Muhammad Aslam Noor.(2007) “Numerical comparison of methods for solving a special fourth-order boundary value problem”.” J. Appl. Mech., 191, 218–224

Abstract Views: 271

PDF Views: 0




  • Dynamics of Timoshenko Beam on Nonlinear Soil

Abstract Views: 271  |  PDF Views: 0

Authors

M. Taha
Department of English, Faculty of Engineering, Cairo University
A. Omar
Department of Mathematics, Faculty of Engineering, Cairo University
M. Nassar
Department of Physics, Faculty of Engineering, Cairo University

Abstract


The main objective of this publication is to derive the characteristic differential equations for two-dimensional (2D) Timoshenko beam with simply supported ends subjected to distributed dynamic load and resting on one parameter nonlinear soil. A numerical solution using Adomian decomposition method is carried out to obtain the deflection shape of the beam. A Parametric analyses of are carried out and influences of all varying parameters on the beam responses are investigated. The model includes the simultaneous effects (or couplings) of bending and shear deformations, translational and rotational inertias of all masses considered.

Keywords


Nonlinear Soil, Timoshenko, Adomian Decomposition Method

References