Engineering Transactions, 70, 1, pp. 77–93, 2022
10.24423/EngTrans.1254.20220314

Analytical Investigation of a Beam on Elastic Foundation with Nonsymmetrical Properties

Iwona Małgorzata WSTAWSKA
Poznan University of Technology
Poland

Krzysztof MAGNUCKI
Łukasiewicz Research Network – Rail Vehicles Institute “TABOR”
Poland

Piotr KĘDZIA
Poznan University of Technology
Poland

The subject of presented analytical and numerical investigation is the stability of  an axially compressed beam on an elastic foundation. The shape function of the foundation was assumed. The formula was supplemented with the offset parameter. The critical values of loads were calculated and presented as a function of geometric and mechanical properties of the beam and nonsymmetrical properties of the elastic foundation. The highest values of critical loads can be obtained for the highest values of shape parameter and the lowest values of amplitudes of shape function. The values of critical loads increase with the increase of the value of the offset parameter.

Keywords: homogeneous beam; elastic foundation; critical load; nonsymmetrical properties
Full Text: PDF

References

Shi L., Sun H., Pan X., Geng X., Cai Y., A theoretical investigation on characteristic frequencies of ground vibrations induced by elevated high speed train, Engineering Geology, 252: 14–26, 2019, doi: 10.1016/j.enggeo.2019.02.014 .

Zhang Y., Murphy K.D., Jumping instabilities in the post-buckling of a beam on a partial nonlinear foundation, Acta Mechanica Solida Sinica, 26(5): 500–513, 2013, doi: 10.1016/S0894-9166(13)60045-2.

Palacio-Betancur A., Aristizabal-Ochoa J.D., Statics, stability and vibration of non-prismatic linear beam-columns with semirigid connections on elastic foundation, Engineering Structures, 181: 89–94, 2019, doi: 10.1016/j.engstruct.2018.12.002.

Matsunaga H., Vibration and buckling of deep beam-columns on two-parameter elastic foundations, Journal of Sound and Vibration, 228(2): 359–376, 1999, doi: 10.1006/jsvi.1999.2415.

Li S.R., Batra R.C., Thermal buckling and postbuckling of Euler-Bernoulli beams supported on nonlinear elastic foundations, AIAA Journal, 45(3): 712–720, 2007, doi: 10.2514/1.24720.

Zhang H., Wang C.M., Ruocco E., Challamel N., Hencky bar-chain model for buckling and vibration analyses of non-uniform beams on variable elastic foundation, Engineering Structures, 126: 252–263, 2016, doi: 10.1016/j.engstruct.2016.07.062.

Deng H., Chen K., Cheng W., Zhao S., Vibration and buckling analysis of double-functionally graded Timoshenko beam system on Winkler-Pasternak elastic foundation, Composite Structures, 160: 152–168, 2017, doi: 10.1016/j.compstruct.2016.10.027.

Robinson M.T.A., Adali S., Buckling of nonuniform and axially functionally graded nonlocal Timoshenko nanobeams on Winkler-Pasternak foundation, Composite Structures, 206: 95–103, 2018, doi: 10.1016/j.compstruct.2018.07.046.

Challamel N., Meftah S.A., Bernard F., Buckling of elastic beams on non-local foundation: A revisiting of Reissner model, Mechanics Research Communications, 37(5): 472–475, 2010, doi: 10.1016/j.mechrescom.2010.05.007.

Eltaher M.A., Mohamed N., Mohamed S.A., Seddek L.F., Periodic and nonperiodic modes of postbuckling and nonlinear vibration of beams attached to nonlinear foundations, Applied Mathematical Modelling, 75: 414–445, 2019, doi: 10.1016/j.apm.2019.05.026.

Bora ́k L., Marcia ́n P., Beam on elastic foundation using modified Betti’s theorem, International Journal of Mechanical Sciences, 88: 17–24, 2014, doi: 10.1016/j.ijmecsci.2014.06.014.

Aslami M., Akimov P.A., Analytical solution for beams with multipoint boundary conditions on two-parameter elastic foundations, Archives of Civil and Mechanical Engineering, 16(4): 668–677, 2016, doi: 10.1016/j.acme.2016.04.005.

Avramidis I.E., Morfidis K., Bending of beams on three-parameter elastic foundation, International Journal of Solids and Structures, 43(2): 357–375, 2006, doi: 10.1016/j.ijsolstr.2005.03.033.

Morfidis K., Exact matrices for beams on three-parameter elastic foundation, Computers & Structures, 80(15–16): 1243–1256, 2007, doi: 10.1016/j.compstruc.2006.11.030.

Sato M., Kanie S., Mikami T., Mathematical analogy of a beam on elastic supports as a beam on elastic foundation, Applied Mathematical Modelling, 32(5): 688–699, 2008, doi: 10.1016/j.apm.2007.02.002.

Binesh S.M., Analysis of beam on elastic foundation using the radial point interpolation method, Scientia Iranica, 19(3): 403–409, 2012, doi: 10.1016/j.scient.2012.04.003.

Karamanlidis D., Prakash V., Exact transfer and stiffness matrices for a beam/column resting on a two-parameter foundation, Computer Methods in Applied Mechanics and Engineering, 72(1): 77–89, 1989, doi: 10.1016/0045-7825(89)90122-9.

Morfidis K., Avramidis I.E., Formulation of a generalized beam element on a two-parameter elastic foundation with semi-rigid connections and rigid offsets, Computers & Structures, 80(25): 1919–1934, 2002, doi: 10.1016/S0045-7949(02)00226-2.

Yu D., Wen J., Shen H., Xiao Y., Wen X., Propagation of flexural wave in periodic beam on elastic foundations, Physics Letters A, 376(4): 626–630, 2012, doi: 10.1016/j.physleta.2011.11.056.

Wang L., Ma J., Peng J., Li L., Large amplitude vibration and parametric instability of inextensional beams on the elastic foundation, International Journal of Mechanical Sciences, 67: 1–9, 2013, doi: 10.1016/j.ijmecsci.2012.12.002.

Wstawska I., Magnucki K., Kędzia P., Approximate estimation of stability of homogeneous beam on elastic foundation, Engineering Transactions, 67(3): 429–440, 2019, doi: 10.24423/EngTrans.979.20190404.




DOI: 10.24423/EngTrans.1254.20220314

Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland