Vibration analysis of beams with non-local foundations using the finite element method

International Journal for Numerical Methods in Engineering

Volumn 71, Issue 11, 2007, Pages 1365-1386

  Friswell, M I ^a   Adhikari, S ^a   Lei, Y ^b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b NATIONAL UNIVERSITY OF DEFENSE TECHNOLOGY   (China)

Author keywords

Beams; Finite element analysis; Non local foundation

Indexed keywords

BOUNDARY CONDITIONS; DAMPING; DYNAMIC ANALYSIS; EIGENVALUES AND EIGENFUNCTIONS; ELASTICITY; FINITE ELEMENT METHOD; FOUNDATIONS; INTEGRAL EQUATIONS; INTERPOLATION; STIFFNESS MATRIX; STRUCTURAL ANALYSIS; VIBRATION ANALYSIS;

CONVOLUTION INTEGRAL; NON-LOCAL FOUNDATION;

BEAMS AND GIRDERS;

BEAMS AND GIRDERS; BOUNDARY CONDITIONS; DAMPING; DYNAMIC ANALYSIS; EIGENVALUES AND EIGENFUNCTIONS; ELASTICITY; FINITE ELEMENT METHOD; FOUNDATIONS; INTEGRAL EQUATIONS; INTERPOLATION; STIFFNESS MATRIX; STRUCTURAL ANALYSIS; VIBRATION ANALYSIS;

EID: 34548548562     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2003     Document Type: Article

References (39)

1. Yankelevsky DZ, Eisenberger M. Analysis of beam column on elastic foundation. Computers and Structures 1986; 23:351-356.
2. Thambiratnam D, Zhuge Y. Free vibration analysis of beams on elastic foundation. Computers and Structures 1996; 60: 971-980.
3. Sun L. A closed form solution of a Bernoulli-Euler beam on a viscoelastic foundation under harmonic line loads. Journal of Sound and Vibration 2001; 242: 619-627.
4. Kim SM. Vibration and stability of axial loaded beams on elastic foundation under moving harmonic loads. Engineering Structures 2004; 26:95-105.
5. Fryba L. Vibration of Solids and Structures under Moving Loads (3rd edn). Thomas Telford: London, 1999.
6. de Rosa MA, Maurizi MJ. Three approaches for the axial vibrations of bars on modified Winkler soil with nonclassical boundary conditions. Journal of Sound and Vibration 2000; 231:1257-1269.
7. Kim SM. Buckling and vibration of a plate on elastic foundation subjected to in-plane compression and moving loads. International Journal of Solids and Structures 2004; 41:5647-5661.
8. Paliwal DN, Pandey RK, Nath T. Free vibrations of circular cylindrical shell on Winkler and Pasternak foundations. International Journal of Pressure Vessels and Piping 1996; 69:79-89.
9. Yokoyama T. Vibration analysis of Timoshenko beam-columns on two-parameter elastic foundations. Computers and Structures 1996; 61:995-1007.
10. Eisenberger M. Vibration frequencies for beams on variable one- and two-parameter elastic foundations. Journal of Sound and Vibration 1994; 176:577-584.
11. Chen WQ, Lu CF, Bian ZG. A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation. Applied Mathematical Modelling 2004; 28:877-890.
12. Chen CN. Solution of beam on elastic foundation by DQEM. Journal of Engineering Mechanics 1998; 124: 1381-1384.
13. Chen CN. Vibration of prismatic beam on an elastic foundation by the differential quadrature element method. Computers and Structures 2000; 77:1-9.
14. de Rosa MA, Maurizi MJ. The influence of concentrated masses and Pasternak soil on the free vibration of Euler beams - exact solution. Journal of Sound and Vibration 1998; 212:573-581.
15. Avramidis IE, Morfidis K. Bending of beams on three-parameter elastic foundation. International Journal of Solids and Structures 2006; 43: 357-375.
16. Ayvaz Y, Ozqan K. Application of modified Vlasov model to free vibration analysis of beams resting on elastic foundations. Journal of Sound and Vibration 2002; 255:111-127.
17. Atanackovic TM, Stankovic B. Stability of an elastic rod on a fractional derivative type of foundation. Journal of Sound and Vibration 2004; 277:149-161.
18. Fenander A. A fractional derivative railpad model included in a railway track model. Journal of Sound and Vibration 1998; 212:889-903.
19. Kerr AD. A study of a new foundation model. Acta Mechanica 1965; 1:135-147.
20. Flugge W. Viscoelasticity (2nd edn). Springer: Berlin, 1975.
21. Polizzotto C. Non-local elasticity and related variational principles. International Journal of Solids and Structures 2001; 38:7359-7380.
22. Eringen AC. Theory of nonlocal elasticity and some applications. Res Mechanica 1987; 21:313-342.
23. Pisno AA, Fuschi P. Closed form solution for non-local elastics bar in tension. International Journal of Solids and Structures 2003; 40:13-23.
24. Nowinski JL. On the non-local aspects of stress in a viscoelastic medium. International Journal of Non-linear Mechanics 1986; 21:439-446.
25. Ahmadi G. Linear theory of nonlocal viscoelasticity. International Journal of Non-linear Mechanics 1975; 10:253-258.
26. Adhikari S, Lei Y, Friswell MI. Modal analysis of non-viscously damped beams. Journal of Applied Mechanics 2006, in press.
27. Yang B, Tan CA. Transfer functions of one-dimensional distributed parameter systems. Journal of Applied Mechanics 1992; 59(4):1009-1014.
28. Lei Y, Friswell MI, Adhikari S. A Galerkin method for distributed systems with non-local damping. International Journal of Solids and Structures 2006; 43:3381-3400.
29. Banks HT, Inman DJ. On damping mechanisms in beams. Transactions of ASME, Journal of Applied Mechanics 1991; 58:716-723.
30. Bagley RL, Torvik PJ. Fractional calculus in the transient analysis of viscoelastically damped structures. AIAA Journal 1985; 23:918-925.
31. Kim TW, Kim JH. Eigensensitivity based optimal distribution of a viscoelastic damping layer for a flexible beam. Journal of Sound and Vibration 2004; 273:201-218.
32. Golla DF, Hughes PC. Dynamics of viscoelastic structures - a time domain finite element formulation. Transactions of ASME, Journal of Applied Mechanics 1985; 52:897-906.
33. McTavish DJ, Hughes PC. Modeling of linear viscoelastic space structures. Transactions of ASME, Journal of Vibration and Acoustics 1993; 115:103-110.
34. Friswell MI, Inman DJ, Lam MJ. On the realisation of GHM models in viscoelasticity. Journal of Intelligent Material Systems and Structures 1997; 8(11):986-993.
35. Inman DJ. Engineering Vibration. Prentice-Hall: Englewood Cliffs, NJ, 2003.
36. Adhikari S. Dynamics of non-viscously damped linear systems. ASCE Journal of Engineering Mechanics 2002; 128(3):328-339.
37. Wagner N, Adhikari S. Symmetric state-space formulation for a class of non-viscously damped systems. AIAA Journal 2003; 41(5):951-956.
38. Lai YC, Ting BY, Lee WS, Becker WR. Dynamic response of beams on elastic foundation. Journal of Structural Engineering 1992; 118:853-858.
39. Timoshenko S, Young DH, Weaver W. Vibration Problems in Engineering (4th edn). Wiley: New York, 1974.