Response characteristics of non-uniform beam with time-dependent boundary conditions and under the actions of travelling distributed masses

• Autorzy: Omolofe B. , Adedowole A.

Identyfikatory

DOI

10.17512/jamcm.2017.2.07

• Języki publikacji: EN

Abstrakty

EN

In this paper, dynamic response of non-prismatic elastic beam resting on elastic foundation and subjected to moving distributed masses is investigated. To obtain the solution of the fourth order partial differential equations with singular and variable coefficients governing the motion of the structural member, an elegant mathematical procedure involving the Mindlin and Goodman's technique, the generalized Galerkin method and the asymptotic Struble's technique with the series representation of the Heaviside function. Various results obtained from the analysis of the closed form solutions are presented in plotted curves and fully discussed.

Słowa kluczowe

EN

resonance; time dependent; foundation modulus; distributed masses; uniform beam; truble’s method; Galerkin equation; beam displacement

PL

rezonans; równanie Galerkina; przemieszczenie belki; masy rozproszone; jednolita belka

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2017
• Tom: Vol. 16, nr 2
• Strony: 77--99
• Opis fizyczny: Bibliogr. 34 poz., rys.

Twórcy

autor

Omolofe B.

• Department of Mathematical Sciences, School of Sciences Federal University of Technology, PMB 704, Akure, Ondo State, Nigeria

autor

Adedowole A.

• Department of Mathematical Sciences, Faculty of Sciences Adekunle Ajasin University, Akungba-Akoko, Ondo State Nigeria

Bibliografia

• [1] Timoshenko S., Young D.H., Weaver W., Vibration Problems in Engineering, 4th John Wiley Edition, New York 1964.
• [2] Fryba L., Vibrations of Solids and Structures under Moving Loads, Groningen, Noordhoff 1972.
• [3] Milormir M., Stanisic M.M., Hardin J.C., On the response of beams to an arbitrary number of concentrated moving masses, Journal of the Franklin Institute 1969, 287(2), 115-123.
• [4] Sadiku S., Leipholz H.H.E., On the dynamics of elastic systems with moving concentrated masses, Ing. Archiv. 1981, 57, 223-242.
• [5] Gbadeyan J.A., Oni S.T., Dynamic behaviour of beams and rectangular plates under moving loads, Journal of Sound and Vibration 1995, 182(5), 677-695.
• [6] Kargarmovin M.H., Younesian D., Dynamics of Timoshenko beams on Pasternak foundation under moving load, Mechanics Research Communications 2004, 31, 713-723.
• [7] Awodola T.O., Oni S.T., Dynamic behaviour under moving concentrated masses of simply supported rectangular plates resting on variable Winkler elastic foundation, Latin America Journal of Solid and Structures 2011, 8(4), 373-392.
• [8] Ali R.D., Mahdi B., Hassan G., Mesbah S., Boundary Element Method applied to the bending analysis of thin functionally graded plates, Latin America Journal of Solid and Structures 2013, 10(3), 549-570.
• [9] Shahin N.A., Mbakisya O., Simply supported beam response on elastic foundation carrying repeated rolling concentrated loads, Journal of Engineering Science and Technology 2010, 5(1), 52-66.
• [10] Ghugal Y.M., Sayyad A.S., Free vibration of thick orthotropic plates using trigonometric shear deformation theory, Latin America Journal of solid and structure 2011, 8, 229-243.
• [11] Zolkiewski S., Vibrations of beams with a variable cross-section fixed on rotational rigid disks, Latin American Journal of Solids and Structures 2013, 10, 39-57.
• [12] Hsu J.C., Lai H.Y., Chen C.K., Free vibration of non-uniform Euler-Bernoulli beams with general elastically end constraints using Adomian modified decomposition method, Journal of Sound and Vibration 2008, 318, 965-981.
• [13] Saravi M., Hermaan M., Ebarahimi K.H., The comparison of homotopy perturbation method with finite difference method for determination of maximum beam deflection, Journal of Theoretical and Applied Physics 2013, 7, 8.
• [14] Li R., Zhong Y., Li M.L., Analytic bending solutions of free rectangular thin plates resting on elastic foundations by a new symplectic superposition method, Proceedings of the Royal Society A 2013, 46, 468-474.
• [15] Nikkhoo A., Rofooei F.R., Parametric study of the dynamic response of thin rectangular plates traversed by a moving mass, Acta Mechanica 2012, 223(1), 15-27.
• [16] Zarfam R., Khaloo A.R., Nikkhoo A., On the response spectrum of Euler-Bernoulli beams with a moving mass and horizontal support excitation, Mechanics Research Communications 2013, 47, 77-83.
• [17] Stanisic M.M., Hardin J.C., Lou Y.C., On the response of the plate to a multi-masses moving system, Acta Mechanical 1968, 5, 37-53.
• [18] Oni S.T., Adedowole A., Influence of prestress on the response to moving loads of rectangular plates incorporating rotatory inertia correction factor, Journal of the Nigerian Association of Mathematical Physics 2008, 13, 127-140.
• [19] Oni S.T., On the dynamic response of elastic structures to moving multi-mass systems, PhD Thesis, University of Ilorin, Ilorin, Nigeria 1991.
• [20] Oni S.T., Awodola T.O., Dynamic response to moving concentrated masses of uniform Rayleigh beams resting on variable Winkler elastic foundation, Journal of the Nigerian Association of Mathematical Physics 2005, 9, 151-162.
• [21] Omer C., Aitung Y., Large deflection static analysis of rectangular plates on two parameter elastic foundations, International Journal of Science and Technology 2005, 1(1), 43-50.
• [22] Adams G.G., Critical speed and the response of a tensioned beam on an elastic foundation to repetitive moving loads, International Journal of Mechanical Sciences 1995, 7, 773-781.
• [23] Savin E., Dynamics amplification factor and response spectrum for the evaluation of Vibrations of beams under successive moving loads, Journal of Sound and vibrations 2001, 248(2), 267- 288.
• [24] Jia-Jang W., Vibration analysis of a portal frame under the action of a moving distributed mass using moving element, International Journal for Numerical Methods in Engineering 2006, 66, 2028-2052.
• [25] Kenny J., Steady state vibrations of a beam on an elastic foundation for a moving load, Journal of Applied Mechanics 1954, 76, 359-364.
• [26] Shahidi M., Bayat M., Pakar I., Abdollahzadeh G., On the solution of free non-linear vibration of beams, International Journal of Physical Science 2011, 6(7), 1628-1634.
• [27] Zolkiewski S., Damped vibrations problem of beams fixed on the rotational disk, International Journal of Bifurcation and Chaos 2011, 21(10), 3033-3041.
• [28] Zolkiewski S., Numerical application for dynamical analysis of rod and beam systems in transportation, Solid State Phenomena 2010, 164, 343-348.
• [29] Zarfam R., Khaloo A.R., Nikkhoo A., On the response spectrum of Euler-Bernoulli beams with a moving mass and horizontal support excitation, Mechanics Research Communications 2013, 47, 77-83.
• [30] Kolousek V., Civil Engeering Structures subjected to Dynamic Loads, SVTL, Bratislava (in Slovak) 1967.
• [31] Oni S.T., Omolofe B., Dynamic behaviour of non-uniform bernoulli-euler beams subjected to concentrated loads travelling at varying velocities, Journal of the Nigerian Association of Mathematical Physics 2005, 9, 79-102.
• [32] Ogunyebi S.N., Dynamical analysis of finite prestressed Bernoulli-Euler beam with general boundary conditions under travelling distributed loads, M.Sc. Dissertation, Federal University of Technology, Akure, Nigeria, 2006.
• [33] Oni S.T., Ogunyebi S.N., Dynamical analysis of a prestressed elastic beam with general boundary conditions under the action of uniform distributed masses, Journal of the Nigerian Association of Mathematical Physics 2008, 12, 87-102.
• [34] Mindlin R.D., Goodman L.E., Beam vibration with time-dependent boundary condition, J. Appl. Mech. 1950, 17, 377-380.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).