Static and Free Vibration Analysis of Composite Straight Beams on the Pasternak Foundation

The objective of this study is to investigate the static and free vibration analysis of the cross-ply laminated straight beams on a two-parameter foundation, namely Pasternak. The curved element formulation is based on Timoshenko beam theory including the shear influence and the rotary inertia. The degrees of freedom of the two nodded element are three translations, three rotations, two shear forces, one axial force, two bending moment and one torque (12 DOF). A parametric study is performed on the static and the natural frequencies of cross-ply laminated straight beams with various foundation parameters. Support conditions are simply supported, fixed-fixed and fixed-roller.

[1]  Shougen Zhao,et al.  Vibration and buckling analysis of double-functionally graded Timoshenko beam system on Winkler-Pasternak elastic foundation , 2017 .

[2]  N. Wattanasakulpong,et al.  Stability and free vibration of functionally graded sandwich beams resting on two-parameter elastic foundation , 2016 .

[3]  M. H. Omurtag,et al.  Dynamic analysis of helicoidal bars with non-circular cross-sections via mixed FEM , 2016 .

[4]  Abbas Rastgoo,et al.  Free vibration of functionally graded spatial curved beams , 2011 .

[5]  C. Lim,et al.  A new analytic symplectic elasticity approach for beams resting on Pasternak elastic foundations , 2010 .

[6]  A. R. Vosoughi,et al.  DQM large amplitude vibration of composite beams on nonlinear elastic foundations with restrained edges , 2009 .

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

[8]  M. Kargarnovin,et al.  FREE VIBRATION ANALYSIS OF CROSS-PLY LAYERED COMPOSITE BEAMS WITH FINITE LENGTH ON ELASTIC FOUNDATION , 2008 .

[9]  Mohammad Taghi Ahmadian,et al.  Free Vibration Analysis of a Cross-Ply Laminated Composite Beam on Pasternak Foundation , 2007 .

[10]  P. Subramanian,et al.  Dynamic analysis of laminated composite beams using higher order theories and finite elements , 2006 .

[11]  Metin Aydogdu,et al.  Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method , 2005 .

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

[13]  Vebil Yıldırım,et al.  Effect of the longitudinal to transverse moduli ratio on the in-plane natural frequencies of symmetric cross-ply laminated beams by the stiffness method , 2000 .

[14]  Mehmet H. Omurtag,et al.  Stability Analysis of Composite-Plate Foundation Interaction by Mixed FEM , 2000 .

[15]  Vebil Yıldırım,et al.  Investigation of the rotary inertia and shear deformation effects on the out-of-plane bending and torsional natural frequencies of laminated beams , 2000 .

[16]  N. Naik.  Composite Beams on Elastic Foundations , 2000 .

[17]  M. Touratier,et al.  Nonlinear free flexural vibrations/post-buckling analysis of laminated orthotropic beams/columns on a two parameter elastic foundation , 1999 .

[18]  Erol Sancaktar,et al.  Free vibration analysis of symmetric cross-ply laminated composite beams with the help of the transfer matrix approach , 1999 .

[19]  V. Yildirim,et al.  Governing equations of initially twisted elastic space rods made of laminated composite materials , 1999 .

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

[21]  Xiaoqiao He,et al.  Exact Solutions for Timoshenko Beams on Elastic Foundations Using Green's Functions∗ , 1998 .

[22]  N. R. Naidu,et al.  Vibrations of initially stressed uniform beams on a two-parameter elastic foundation , 1995 .

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

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

[25]  K. Chandrashekhara,et al.  Analytical solutions to vibration of generally layered composite beams , 1992 .

[26]  Mehmet H. Omurtag,et al.  The mixed finite element solution of helical beams with variable cross-section under arbitrary loading , 1992 .

[27]  K. Chandrashekhara,et al.  Some observations on the modeling of laminated composite beams with general lay-ups , 1991 .

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

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

[30]  Mehmet H. Omurtag,et al.  The mixed finite element formulation for three-dimensional bars , 1991 .

[31]  K. Chandrashekhara,et al.  Free vibration of composite beams including rotary inertia and shear deformation , 1990 .

[32]  A. J. Valsangkar,et al.  Vibrations of beam‐columns on two‐parameter elastic foundations , 1988 .

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

[34]  J. Oden,et al.  Variational Methods in Theoretical Mechanics , 1976 .

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

[36]  Miklós Hetényi,et al.  Beams on Elastic Foundation: Theory with Applications in the Fields of Civil and Mechanical Engineering , 1946 .