Damping Effects on the Transverse Motions of Axially-loaded Beams Carrying Uniform Distributed Load

Oluwatoyin Kehinde Ogunbamike

Abstract

In this study, the dynamic analysis of a clamped-clamped Rayleigh beam under moving distributed loads is investigated. The solution technique is based on the generalized finite integral transform and a modification of the Struble’s asymptotic technique.  Analytical solutions and numerical analysis showed that higher values of axial force, damping due to strain resistance and rotatory inertia reduce the response amplitudes of the beam. It is observed that the influence of structural parameters such as axial force, mass ratio and viscous damping  have significant effects on the transverse motion and the critical velocity of the elastic structure carrying moving distributed load. Furthermore, it is also found that for the same natural frequency, the critical velocity for the moving distributed mass problem is smaller than that of moving distributed force problem. Hence resonance conditions for the moving distributed mass problem are reached prior to those of moving distributed force problem. Finally, the accuracy of the solutions obtained is numerically validated by comparison studies with other available cases in literature.

Keywords

Axial force; Clamped-clamped beam; Critical velocity; Resonance; Viscous damping.

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References

E. Esmailzadeh and M. Ghorashi, Vibration analysis of beams traversed by uniform partially distributed masses, Journal of Sound and Vibration, 184, 1995, 9-175.

J. J. Wu, Vibration analysis of a portal frame under the action of moving distributed masses using moving mass element, International Journal of Numerical Methods in Engineering, 62, 2005, 2028-2052.

E. J. Sapountzakis and G. C. Tsiatas, Elastic flexural buckling analysis of composite beams of variable cross-section by boundary element method, Engineering Structures, 29, 2007, 675-681.

H. A. Isede and J. A. Gbadeyan, On the dynamic analysis of a tapered Timoshenko beam under a uniform partially distributed moving load, Journal of Nigerian Mathematical Society, 32, 2013, 109-141.

O. K. Ogunbamike, Seismic analysis of simply supported damped Rayleigh beams on elastic foundation, Asian Research Journal of Mathematics, 16(11), 2020, 31-47.

L. Fryba, Non-stationary response of a beam to a moving random force, Journal of Sound and Vibration, 46, 1976, 323-338.

S. T. Oni and T. O. Awodola, Dynamic response under a moving load of an elastically supported non-prismatic Bernoulli-Euler beam on variable elastic foundation, Latin American Journal of Solids and Structures, 7, 2010, 3-20.

R. T. Wang and T. H. Chou, Non-linear vibration of Timoshenko beam due to a moving force and the weight of beam, Journal of Sound and Vibration, 218, 1998, 117-131.

L. Sun and F. Luo, Steady-state dynamic response of a Bernoulli-Euler beam on a viscoelastic foundation subject to a platoon of moving dynamic loads, ASME Journal of Vibration and Acoustics, 130, 2008, 051002.

G. Muscolino and A. Palmeri, Response of beams resting on viscoelastically damped foundation to moving oscillators, International Journal of Solids and Structures, 44(5), 2007, 1317-1336.

A. N. Krylov, Mathematical collection of papers of the academy of sciences, 61, Pittsburgh, 1905.

J. T. Kenny, Steady state vibrations of beams on an elastic foundation for a moving load, Journal of Applied Mechanics, 76, 1954, 359-364.

C. R. Steele, The finite beam with moving loads, Journal of Applied Mechanics, 34, 1967, 111-118.

V. V. Bolotin, The dynamic stability of elastic system, San Francisco: Holden-day, 139-141, 1964.

R. T. Wang, Comparative study of free vibration of multi-span beams between analytical solution and finite element transfer matrix computation, Journal of the Chinese Society of Mechanical Engineers, 14(6), 1993, 599-604.

L. Fryba, Vibration of Solids and Structures under Moving Loads. Groningen, Noordhoff, 1972.

S. Sadiku and H. H. E. Leipholz, On the dynamics of elastic systems with moving concentrated masses, Ing. Arhciv, 57, 1981, 223-242.

S. T. Oni, Flexural vibrations under moving loads of isotropic rectangular plates on a Winkler elastic foundation, Journal of the Nigerian Society of Engineers, 35(1), 2000, 40-41.

J. A. Gbadeyan and S. T. Oni, Dynamic behaviour of beams and rectangular plates under moving loads, Journal of Sound and Vibration, 182(5), 1995, 667-695.

H. P. Lee and T. Y. Ng, Transverse vibration of a plate moving over multiple points supports, Applied Acoustics, 47(4), 1996, 291-301.

E. Savin, Dynamic Amplification factor and response spectrum for the evaluation of vibrations of beams under successive moving loads, Journal of Sound and Vibration, 248(2), 2001, 267-288.

G. V. Rao, Linear dynamics of an elastic beam under moving loads, Journal of Vibration and Acoustics, 122(3), 2000, 281-289.

F. J. Shaker, Effect of axial load on mode shapes and frequencies of beams, NASA TN D-8109, NASA, Washington, DC, USA, 1975.

A. Bokaian, Natural frequencies of beams under compressive axial loads, Journal of Sound and Vibration, 126(1), 1988, 49–65.

S. Kukla and B. Skalmierski, The effect of axial loads on transverse vibrations of an Euler-Bernoulli beam, Journal of Theoretical and Applied Mechanics, 31(2), 1993, 413-430.

J. M. Tolorunsagba, Transverse vibrations of axially tensioned uniform beam subjected to harmonic moving loads and resting on variable foundation, Journal of the Nigerian Association of Mathematical Physics, 16, 2010, 133-140.

D. Adair, A. Ibrayev, A. Tazabekova and J. R. Kim, Free vibration with large amplitude of axially loaded beams on an elastic foundation using the Adomian modified decomposition method, Shock and Vibration, 2019, ID 3405075.

G. R. Bhashyam and G. Prathap, Galerkin finite element method for non-linear beam vibrations, Journal of Sound and Vibration, 72, 1980, 191–203.

E. Özkaya, M. Pakdemirli, and H. R. Öz, Non-linear vibrations of a beam-mass system under different boundary conditions, Journal of Sound and Vibration, 199, 1997, 679–696.

S. T. Oni and B. Omolofe, Dynamic response of prestress Rayleigh beam resting on elastic foundation and subjected to masses travelling at varying velocity, Journal of Vibration and Acoustics, 133(4), 2011, 041005.

P. Fritzkowski, Transverse vibrations of a beam under an axial load: minimal model of a triangular frame, Arch Appl Mech, 87, 2017, 881-892.

B. Bozyigit, Y. Yesilce and S. Catal, Free Vibration of axial-loaded beams resting on viscoelastic foundation using Adomian decomposition method and differential transformation, Engineering Science and Technology, an international Journal, 21, 2018, 1181-1193.

L. O. Sigueira, R. L. Cortez and S. S. Hoefel, Vibration analysis of an axial-loaded Euler-Bernoulli beam on two-parameter foundation, 25th ABCM International congress of Mechanical Engineering, Uberlandia, Brazil, 2019, 1-4.

S. T. Oni, Flexural motions of uniform beam under the actions of a concentrated mass travelling with variable velocity, Abacus Journal of Mathematical Association of Nigeria, 31(2), 2004, 79-93.

S. T. Oni and O. K. Ogunbamike, Convergence of closed form solutions of the initial-boundary value moving mass problem of rectangular plate resting on Pasternak foundations, Journal of the Nigerian Association of Mathematical Physics, 18, 2011, 83-90.

T. O. Awodola and S. T. Oni, Dynamic response to moving masses of rectangular plates with general boundary conditions and resting on variable Winkler foundation, Latin American Journal of Solids and Structures, 10, 2013, 301-322.

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