Symmetrically loaded beam on a two-parameter tensionless foundation

Static response of an elastic beam on a two-parameter tensionless foundation is investigated by assuming that the beam is symmetrically subjected to a uniformly distributed load and concentrated edge loads. Governing equations of the problem are obtained and solved by pointing out that a concentrated edge foundation reaction in addition to a continuous foundation reaction along the beam axis in the case of complete contact and a discontinuity in the foundation reactions in the case of partial contact come into being as a direct result of the two-parameter foundation model. The numerical solution of the complete contact problem is straightforward. However, it is shown that the problem displays a highly non-linear character when the beam lifts off from the foundation. Numerical treatment of the governing equations is accomplished by adopting an iterative process to establish the contact length. Results are presented in figures to demonstrate the linear and non-linear behavior of the beam-foundation system for various values of the parameters of the problem comparatively.

[1]  G. Rao.  Large-amplitude free vibrations of uniform beams on Pasternak foundation , 2003 .

[2]  I. Coskun,et al.  The response of a finite beam on a tensionless Pasternak foundation subjected to a harmonic load , 2003 .

[3]  George G. Adams,et al.  Beam on tensionless elastic foundation , 1987 .

[4]  Michael W. O'Neill,et al.  Beam on Generalized Two‐Parameter Foundation , 1985 .

[5]  R. A. Westmann,et al.  BEAM ON TENSIONLESS FOUNDATION , 1967 .

[6]  Fuat Demir,et al.  Circular rigid beam on a tensionless two-parameter elastic foundation , 2005 .

[7]  Mircea Radeş.  Steady-state response of a finite beam on a Pasternak-type foundation , 1970 .

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

[9]  Z. Celep,et al.  In-plane vibrations of circular rings on a tensionless foundation , 1990 .

[10]  Takashi Yokoyama,et al.  Vibrations of timoshenko beam‐columns on two‐parameter elastic foundations , 1991 .

[11]  M. B. Rosales,et al.  A variant of Rayleigh's method applied to Timoshenko beams embedded in a Winkler-Pasternak medium , 1988 .

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

[14]  Kevin D. Murphy,et al.  Response of a finite beam in contact with a tensionless foundation under symmetric and asymmetric loading , 2004 .

[15]  M. A. De Rosa,et al.  Free vibrations of Timoshenko beams on two-parameter elastic foundation , 1995 .

[16]  G. Onu,et al.  Shear Effect in Beam Finite Element on Two-Parameter Elastic Foundation , 2000 .

[17]  Hui-Shen Shen,et al.  Nonlinear bending behavior of Reissner-Mindlin plates with free edges resting on tensionless elastic foundations , 2004 .

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

[19]  Hiroyuki Matsunaga,et al.  Vibration and Buckling of Deep Beam-Columns on Two-Parameter Elastic Foundations , 1999 .

[20]  J. E. Stephens,et al.  Natural frequencies of Timoshenko beams on pasternak foundations , 1977 .

[21]  Arnold D. Kerr,et al.  On the derivation of well posed boundary value problems in structural mechanics , 1976 .

[22]  Angelo Masi,et al.  Free vibrations of foundation beams on two-parameter elastic soil , 1993 .

[23]  Z. Celep.  Dynamic Response of a Circular Beam on a Wieghardt‐Type Elastic Foundation , 1984 .

[24]  A. G. Razaqpur,et al.  Exact analysis of beams on two-parameter elastic foundations , 1991 .

[25]  S. Çatal.  Analysis of free vibration of beam on elastic soil using differential transform method , 2006 .

[26]  Kadir Güler.  Circular Elastic Plate Resting on Tensionless Pasternak Foundation , 2004 .

[27]  A. Mallik,et al.  Steady-state response of an elastically supported infinite beam to a moving load , 2006 .

[28]  Nikolaos I. Ioakimidis.  BEAMS ON TENSIONLESS ELASTIC FOUNDATION: APPROXIMATE QUANTIFIER ELIMINATION WITH CHEBYSHEV SERIES , 1996 .

[29]  Martti Mikkola,et al.  A beam on a wieghardt-type elastic foundation , 1967 .

[30]  Polat Gülkan,et al.  An exact finite element for a beam on a two-parameter elastic foundation: a revisit , 1999 .

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

[32]  Marta B. Rosales,et al.  A further study about the behaviour of foundation piles and beams in a Winkler–Pasternak soil , 2002 .

[33]  G. K. N. Murthy.  Buckling of beams supported by Pasternak foundation. , 1973 .

[34]  T. E. Smith.  Buckling of a beam on a Wieghardt-type elastic foundation , 1969 .

[35]  Ioannis Avramidis,et al.  Formulation of a generalized beam element on a two-parameter elastic foundation with semi-rigid connections and rigid offsets , 2002 .

[36]  Arnold D. Kerr,et al.  Beams on a two-dimensional pasternak base subjected to loads that cause lift-off , 1991 .

[37]  T. M. Wang,et al.  Vibrations of continuous Timoshenko beams on Winkler-Pasternak foundations , 1978 .

[38]  M. El-Mously.  Fundamental frequencies of Timoshenko beams mounted on Pasternak foundation , 1999 .

[39]  M. Eisenberger,et al.  Finite beams on infinite two-parameter elastic foundations , 1992 .