Static and free vibration analysis of straight and circular beams on elastic foundation

Abstract Static and free vibration analyses of straight and circular beams on elastic foundation are investigated. The Timoshenko beam theory is adopted in the derivation of the governing equation. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method. The static and free vibration analyses of beams on elastic foundation are analyzed through various examples.

[1]  M. A. De Rosa,et al.  THE INFLUENCE OF CONCENTRATED MASSES AND PASTERNAK SOIL ON THE FREE VIBRATIONS OF EULER BEAMS—EXACT SOLUTION , 1998 .

[2]  Yusuf Ayvaz,et al.  APPLICATION OF MODIFIED VLASOV MODEL TO FREE VIBRATION ANALYSIS OF BEAMS RESTING ON ELASTIC FOUNDATIONS , 2002 .

[3]  V. Haktanir,et al.  Statical analysis of elastically and continuously supported helicoidal structures by the transfer and stiffness matrix methods , 1993 .

[4]  Ji Wang.  Vibration of stepped beams on elastic foundations , 1991 .

[5]  Steven C. Chapra,et al.  Numerical Methods for Engineers , 1986 .

[6]  Faruk Firat Calim,et al.  Free and forced vibrations of non-uniform composite beams , 2009 .

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

[8]  Chaofeng Lü,et al.  Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations , 2008 .

[9]  Faruk Firat Calim.  Dynamic analysis of composite coil springs of arbitrary shape , 2009 .

[10]  A. Y. Aköz,et al.  The mixed finite element solution of circular beam on elastic foundation , 1996 .

[11]  W. F. Brannen,et al.  Natural frequencies for out-of-plane vibrations of curved beams on elastic foundations , 1982 .

[12]  N. Tutuncu,et al.  Forced vibration of composite cylindrical helical rods , 2005 .

[13]  R. M. Redheffer,et al.  Mathematics of Physics and Modern Engineering , 1958 .

[14]  Quasi-static and dynamic response of viscoelastic helical rods , 2004 .

[15]  Chaofeng Lü,et al.  A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation , 2004 .

[16]  Faruk Firat Calim.  Forced vibration of helical rods of arbitrary shape , 2009 .

[17]  M. S. Issa,et al.  Natural frequencies of continuous curved beams on Winkler-type foundation , 1988 .

[18]  Faruk Firat Calim,et al.  Dynamic analysis of beams on viscoelastic foundation , 2009 .

[19]  Forced Vibration of Cylindrical Helical Rods Subjected to Impulsive Loads , 2003 .

[20]  Sondipon Adhikari,et al.  Vibration analysis of beams with non‐local foundations using the finite element method , 2007 .

[21]  Moshe Eisenberger,et al.  Vibration Frequencies For Beams On Variable One- And Two-parameter Elastic Foundations , 1994 .

[22]  D. Sengupta,et al.  Horizontally curved isoparametric beam element with or without elastic foundation including effect of shear deformation , 1988 .