### MODES OF VIBRATION OF THE BEAMS UNDER THE INFLUENCE OF DISCONTINUITY IN FOUNDATION

**DOI Number**

**First page**

**Last page**

#### Abstract

#### Full Text:

PDF#### References

Wang T. M., Stephens J. E., 1977, Natural frequencies of Timoshenko beams on Pasternak foundations, Journal of Sound and Vibration, 5, pp. 149–155.

Sun L., 2001, A closed-form solution of a Bernoulli-Euler beam on a viscoelastic foundation under harmonic line loads, Journal of Sound and Vibration, 242, pp. 619–627.

Sapountzakis E. J., Kampitsis A. E., 2011, Nonlinear response of shear deformable beams on tensionless nonlinear viscoelastic foundation under moving loads, Journal of Sound and Vibration, 330, pp. 5410–5426.

Mamandi A., Kargarnovin M. H., Farsi S., 2012, Dynamic analysis of a simply supported beam resting on a nonlinear elastic foundation under compressive axial load using nonlinear normal modes techniques under three-to-one internal resonance condition, Nonlinear Dynamics, 70, pp. 1147–1172.

Chen J.-S., Chen Y.-K., 2011, Steady state and stability of a beam on a damped tensionless foundation under a moving load, International Journal of Non-Linear Mechanics, 46, pp. 180–185.

Kim S.-M., Cho Y.-H., 2006, Vibration and dynamic buckling of shear beam-columns on elastic foundation under moving harmonic loads, International Journal of Solids and Structures, 43, pp. 393–412.

Muscolino G., Palmeri A., 2007, Response of beams resting on viscoelastically damped foundation to moving oscillators, International Journal of Solids and Structures, 44, pp. 1317–1336.

Chang T.-P., Liu Y.-N., 1996, Dynamic finite element analysis of a nonlinear beam subjected to a moving load, International Journal of Solids and Structures, 33, pp. 1673–1688.

Malekzadeh P., Vosoughi A. R., 2009, DQM large amplitude vibration of composite beams on nonlinear elastic foundations with restrained edges, Communications in Nonlinear Science and Numerical Simulation, 14, pp. 906–915.

Demeio L., Lenci S., 2013, Nonlinear resonances of a semi-infinite cable on a nonlinear elastic foundation, Communications in Nonlinear Science and Numerical Simulation, 18, pp. 785–798.

Szabó B., Babuska I., 1991, Finite Element Analysis, John Wiley & Sons.

Ribeiro P., 2004, A p-version, first order shear deformation, finite element for geometrically non-linear vibration of curved beams, International Journal for Numerical Methods in Engineering, 61, pp. 2696-2715.

Ribeiro P., 2010, Free periodic vibrations of beams with large displacements and initial plastic strains, International Journal of Mechanical Sciences, 52, pp. 1407–1418.

Ribeiro P., 2001, Hierarchical finite element analyses of geometrically non-linear vibration of beams and plane frames, Journal of Sound and Vibration, 246, pp. 225-244.

Ribeiro P., 2004, Non-linear forced vibrations of thin/thick beams and plates by the finite element and shooting methods, Computers & Structures, 82, pp. 1413–1423.

Han W., Petyt M., 1996, Linear vibration analysis of laminated rectangular plates using the hierarchical finite element method, Part 1: free vibration analysis, Computers & Structures, 61, pp. 705-712.

Bardell N. S., 1989, The application of symbolic computing to the hierarchical finite element method, International Journal for Numerical Methods in Engineering, 28, pp. 1181-1204.

Bardell N. S., Langley R. S., Dunsdon J. M., Aglietti G. S., 1999, An h-p finite element vibration analysis of open conical sandwich panels and conical sandwich frusta, Journal of Sound and vibration, 226, pp. 345-377.

Ribeiro P., 2003, A hierarchical finite element for geometrically non-linear vibration of doubly curved, moderately thick isotropic shallow shells, International Journal for Numerical Methods in Engineering, 56, pp. 715-738.

Stoykov S., Ribeiro P., 2010, Nonlinear forced vibrations and static deformations of 3D beams with rectangular cross section: The influence of warping, shear deformation and longitudinal displacements, International Journal of Mechanical Sciences, 52, pp. 1505–1521.

Houmat A., 2005, Free vibration analysis of membranes using the h-p version of the finite element method, Journal of Sound and Vibration, 282, pp. 401-410.

Stojanović V., Ribeiro P., Stoykov S., 2013, Non-linear vibration of Timoshenko damaged beams by a new p-version finite element method, Computers & Structures, 120, pp. 107–119.

Petyt M., 1990, Introduction to Finite Element Vibration Analysis, Cambridge University Press, Cambridge.

Stojanović V., Kozić P., Janevski G., 2013, Exact closed-form solutions for the natural frequencies and stability of elastically connected multiple beam system using Timoshenko and high order shear deformation theory, Journal of Sound and Vibration, 332, pp. 563-576.

ANSYS, 2009, Workbench User’s Guide.

Kaneko T., 1975, On Timoshenko’s correction for shear in vibrating beams, Journal of Physics D, 8, pp. 1927–1936.

Hutchinson JR., 2001, Shear coefficients for Timoshenko beam theory, Journal of Applied Mechanics, 68, pp. 87–92.

Wolfe H., 1995, An experimental investigation of nonlinear behaviour of beams and plates excited to high levels of dynamic response, PhD thesis, University of Southampton.

Wang C. M., Reddy J. N. and Lee K. H., 2000, Shear deformable beams and plates, Elsevier, Relationships with Classical Solutions.

### Refbacks

- There are currently no refbacks.

ISSN: 0354-2025 (Print)

ISSN: 2335-0164 (Online)

COBISS.SR-ID 98732551

ZDB-ID: 2766459-4