NON-LINEAR VIBRATIONS OF A BEAM RESTING ON A TENSIONLESS WINKLER FOUNDATION

The forced vibrations of an elastic beam resting on a non-linear tensionless Winkler foundation subjected to a concentrated dynamic load at its centre are described in this paper. The problem is a non-linear one because of the tensionless character of the foundation and the non-linear term in the foundation model. A non-linear governing differential equation for the forced vibrations of the beam is derived in matrix form by employing the Galerkin method. The free vibration mode functions of the completely free beam are adopted as the co-ordinate functions of the displacement function of the beam. Firstly, the static solution is obtained and the contact length is determined. This is then used as an initial configuration of the forced vibrations. The results which represent the static and dynamic responses of the beam for linear and non-linear cases are presented in the Figures.

[1]  Z. Celep,et al.  Circular Plate on Tensionless Winkler Fundation , 1988 .

[2]  George G. Adams,et al.  A Steadily Moving Load on an Elastic Beam Resting on a Tensionless Winkler Foundation , 1979 .

[3]  Anil K. Chopra,et al.  Simplified Earthquake Analysis of Structures with Foundation Uplift , 1985 .

[4]  Anil K. Chopra,et al.  Earthquake response of structures with partial uplift on winkler foundation , 1984 .

[5]  Y. Weitsman,et al.  Onset of separation between a beam and a tensionless elastic foundation under a moving load , 1971 .

[6]  Z. Celep,et al.  Forced vibrations of a beam on a tensionless foundation , 1989 .

[7]  Anil K. Chopra,et al.  Simplified Earthquake Analysis of Multistory Structures With Foundation Uplift , 1985 .

[8]  P. C. Dumir,et al.  Non-linear vibration of orthotropic thin rectangular plates on elastic foundations , 1988 .

[9]  G. Venkateswara Rao,et al.  Effect Of A Non-linear Elastic Foundation On The Mode Shapes In Stability And Vibration Problems Of Uniform Columns/beams , 1993 .

[10]  Arnold D. Kerr,et al.  Elastic and Viscoelastic Foundation Models , 1964 .

[11]  Z. Celep,et al.  Axisymmetric Vibrations of Circular Plates on Tensionless Elastic Foundations , 1990 .

[12]  I. Coskun,et al.  Non-Linear Vibrations of a Beam on AN Elastic Foundation , 1999 .

[13]  Moshe Eisenberger,et al.  Analysis of beams on nonlinear winkler foundation , 1989 .

[14]  Kadir Güler,et al.  Static and dynamic responses of a circular plate on a tensionless elastic foundation , 1995 .

[15]  P. T. Blotter,et al.  Non-Linear Vibration Analysis Of Arbitrarily Laminated Thin Rectangular Plates On Elastic Foundations , 1993 .

[16]  P. C. Dumir,et al.  Non-linear axisymmetric vibration of orthotropic thin circular plates on elastic foundations , 1985 .

[17]  J. Smaill.  Large deflection response of annular plates on Pasternak foundations , 1991 .

[18]  N. S. V. Kameswara Rao,et al.  Onset of Separation Between a Beam and Tensionless Foundation Due to Moving Loads , 1974 .

[19]  A. Selvadurai,et al.  Flexure of beams resting on hyperbolic elastic foundations , 1985 .

[20]  Z. Celep,et al.  Rectangular Plates Resting on Tensionless Elastic Foundation , 1988 .

[21]  Fred W. Beaufait,et al.  Analysis of elastic beams on nonlinear foundations , 1980 .

[22]  Y. Weitsman,et al.  On Foundations That React in Compression Only , 1970 .