Damping influence on the critical velocity and response characteristics of structurally pre-stressed beam subjected to traveling harmonic load
Volume 3, Issue 1, pp 18--28
http://dx.doi.org/10.22436/mns.03.01.03
Publication Date: August 02, 2019
Submission Date: October 16, 2017
Revision Date: April 02, 2018
Accteptance Date: April 06, 2018
-
1976
Downloads
-
3678
Views
Authors
B. Omolofe
- Department of Mathematical Sciences, School of Sciences, Federal University of Technology, P. M. B 704, Akure Ondo State, Nigeria.
T. O. Awodola
- Department of Mathematical Sciences, School of Sciences, Federal University of Technology, P. M. B 704, Akure Ondo State, Nigeria.
T. O. Adeloye
- Department of Mathematics, Faculty of Basic Sciences, Nigeria Maritime University, Okerenkoko, Delta State, Nigeria.
Abstract
In this present study, the response characteristics of a flexible member carrying harmonic moving load are investigated. The beam is assumed to be of uniform cross section and has simple support at both ends. The moving concentrated force is assumed to move with constant velocity type of motion. A versatile mathematical approximation technique often used in structural mechanics called assumed mode method is in first instance used to treat the fourth order partial differential equation governing the motion of the slender member to obtain a sequence of second order ordinary differential equations. Integral transform method is further used to treat this sequence of differential equations describing the motion of the beam-load system. Various results in plotted curves show that, the presence of the vital structural parameters such as the axial force \(N\), rotatory inertia correction factor \(r^0\), the foundation modulus \(F_0\), and the shear modulus \(G_0\), significantly enhances the stability of the beam when under the action of moving load. Dynamic effects of these parameters on the critical speed of the dynamical system are carefully studied. It is found that as the values of these parameters increase, the critical speed also increases. Thereby reducing the risk of resonance and thus the safety of the occupant of this structural member is guaranteed.
Share and Cite
ISRP Style
B. Omolofe, T. O. Awodola, T. O. Adeloye, Damping influence on the critical velocity and response characteristics of structurally pre-stressed beam subjected to traveling harmonic load, Mathematics in Natural Science, 3 (2018), no. 1, 18--28
AMA Style
Omolofe B., Awodola T. O., Adeloye T. O., Damping influence on the critical velocity and response characteristics of structurally pre-stressed beam subjected to traveling harmonic load. Math. Nat. Sci. (2018); 3(1):18--28
Chicago/Turabian Style
Omolofe, B., Awodola, T. O., Adeloye, T. O.. "Damping influence on the critical velocity and response characteristics of structurally pre-stressed beam subjected to traveling harmonic load." Mathematics in Natural Science, 3, no. 1 (2018): 18--28
Keywords
- Response characteristics
- flexural member
- harmonic load
- critical speed
- resonance
- foundation stiffness
- assumed mode
- concentrated force
MSC
References
-
[1]
M. Abu-Hilal, H. Zibdeh, Vibration analysis of beams with general boundary conditions traversed by a moving force, J. Sound Vibration, 229 (2000), 377--388
-
[2]
G. G. Adams, Critical speeds and the response of a tensioned beam on an elastic foundation to repetitive moving loads, Int. J. Mech. Sci., 37 (1995), 773--781
-
[3]
Y. Araar, B. Radjel, Delection Analysis of Clamped Rectangular Plates of Variable Thickness on Elastic Foundation by the Galerkin Method, Res. J. Appl. Services, 2 (2007), 1077--1082
-
[4]
T. O. Awodola, Variable velocity influence on the vibration of simply supported bernoulli-euler beam under exponentially varying magnitude moving load, J. Math. Stat., 3 (2007), 228--232
-
[5]
T. O Awodola, B. Omolofe, Response to concentrated moving masses of elastically supported rectangular plates resting on winkler elastic foundation, J. Theoretical Appl. Mech., 44 (2014), 65--90
-
[6]
R. S. Ayre, L. S. Jacobsen, C. S. Hsu, Transverse vibration of one-and of two-span beams under the action of a moving mass load, Proceedings of the first U. S. National Congress of Applied Mechanics, 1951 (1951), 81--90
-
[7]
C. Bilello, L. A. Bergman, Vibration of damaged beams under a moving mass: Theory and experimental validation, J. Sound Vibration, 274 (2004), 567--582
-
[8]
J. Clastornic, M. Eisenberger, D. Z. Yankelevsky, M. A. Adin, Beams on Variable Winkler Elastic Foundation, J. Appl. Mech., 53 (1986), 925--928
-
[9]
E. Esmailzadeh, M. Ghorashi, Vibration analysis of beams traversed by moving masses, Intern. J. Engin., 8 (1995), 213--220
-
[10]
E. Esmailzadeh, M. Ghorashi, Vibration analysis of beams traversed by uniform partially distributed moving masses, J. Sound Vibration, 184 (1995), 9--17
-
[11]
L. Frýba, Vibration of solids and structures under moving loads, Springer Science \& Business Media, Groningen (1972)
-
[12]
M. H. Ghayesh, S. E. Khadem, Rotatory inertia and temperature effects on non-linear vibration, steady-state response and stability of an axially moving beam with time-dependent velocity, Int. J. Mech. Sci., 50 (2008), 389--404
-
[13]
T. R. Hamada, Dynamic analysis of a beam under a moving force: a double laplace transform solution, J. Sound Vibration, 74 (1981), 221--233
-
[14]
M. H. Hsu, Vibration characteristics of rectangular plates resting on elastic foundations and carrying any number of sprung masses, Int. J. Appl. Sci. Eng., 4 (2006), 83--89
-
[15]
T. C. Huang, V. N. Shah, Elastic system moving on an elastically supported beam, J. Vibration Acoustics Stress Reliab. Design, 106 (1984), 292--297
-
[16]
Y. H. Lin, Comments on vibration analysis of beams traversed by uniform partially distributed moving masses, J. Sound Vibration, 199 (1997), 697--700
-
[17]
A. V. Metrikine, S. N. Verichev, J. Blaauwendraad, Stability of a two-mass oscillator moving on a beam supported by a visco-elastic half-space, Int. J. Solid Structures, 42 (2005), 1187--1207
-
[18]
G. Muscolino, A. Palmeri, Response of beams resting on viscoelastically damped foundation to moving oscillators, Int. J. Solid Srtuctures, 44 (2007), 1317--1336
-
[19]
D. K. Nguyen, Free vibration of prestressed Timoshenko beams resting on elastic foundation, Vietnam J. Mech., 29 (2007), 1--12
-
[20]
M. Olsson, On the fundamental moving load problem, J. Sound Vibration, 145 (1991), 299--307
-
[21]
B. Omolofe, Deflection profile analysis of beams on two-parameter elastic subgrade, Latin Amer. J. Solid Structures, 10 (2013), 263--282
-
[22]
B. Omolofe, A. Adedowole, Response characteristics of non-uniform beam with time-dependent boundary conditions and under the actions of travelling distributed masses, J. Appl. Math. Comput. Mech., 16 (2017), 77--99
-
[23]
B. Omolofe, T. O. Adeloye, Behavioral study of finite beam resting on elastic foundation and subjected to travelling distributed masses, Latin Amer. J. Solids Structures, 14 (2017), 312--334
-
[24]
B. Omolofe, S. N. Ogunyebi, Transverse vibrations of elastic thin beam resting on variable elastic foundations and subjected to traveling distributed forces, Pacific J. Sci. Tech., 10 (2009), 112--119
-
[25]
M. Ouchenane, R. Lassoued, K. Ouchenane, Vibration analysis of bridges structures under the influence of moving loads, (a conference proceeding), 3rd International conference on integrity, reliability and failure, Porto/Portugal, 2009 (2009), 20--24
-
[26]
A. V. Presterev, L. A. Bergman, An improved series expansion of the solution to the moving oscillator problem, J. Vib. Acoust., 122 (2000), 54--61
-
[27]
A. V. Presterev, L. A. Bergman, C. A. Tan, T.-C. Tsao, B. Yang, On the asymptotics of the solution of the moving oscillator problem, J. Sound Vibration, 260 (2003), 519--536
-
[28]
G. V. Rao, Linear dynamics of an elastic beam under moving loads, J. Vib. Acoust., 122 (2000), 281--289
-
[29]
B. J. Ryu, Dynamic analysis of a beam subjected to a concentrated moving mass, Master Thesis (Yonsei University), Seoul (1983)
-
[30]
S. Sadiku, H. H. E. Leipholz, On the dynamics of elastic systems with moving concentrated masses, Ing. Arch., 57 (1987), 223--242
-
[31]
D. Stăncioiu, H. Ouyang, J. E. Mottershead, Vibration of a beam excited by a moving oscillator considering separation and reattachment, J. Sound Vibration, 310 (2008), 1128--1140
-
[32]
M. M. Stanišić, J. A. Euler, S. T. Montgomery, On a theory concerning the dynamical behaviour of structures carrying moving masses, Ing. Arch., 43 (1974), 295--305
-
[33]
M. M. Stanišić, J. C. Hardin, On the response of beams to an arbitrary number of concentrated moving masses, J. Franklin Ins., 287 (1969), 115--123
-
[34]
G. G. Strokes, Discussion of a differential equation relating to the breaking of railway bridges, Transactions of the Cambridge Philosophical Society, 85 (1849), 707--735
-
[35]
D. Thambiratnam, Y. Zhuge, Dynamic analysis of beams on an elastic foundation subjected to moving loads, J. Sound Vibration, 198 (1996), 149--169
-
[36]
S. P. Timoshenko, On the transverse vibrations of bars of uniform cross-section, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 43 (1922), 125--131
-
[37]
Y. M. Wang, The dynamical analysis of a finite inextensible beam with an attached accelerating mass, Int. J. Solid Structures, 35 (1998), 831--854
-
[38]
R. T. Wang, T. H. Chou, Nonlinear vibration of timoshenko beam due to a moving force and the weight of beam, J. Sound Vibration, 218 (1998), 117--131
-
[39]
J. J. Wu, Vibration analyses of a portal frame under the action of a moving distributed mass using moving mass element, Int. J. Num. meth. Engin., 62 (2005), 2028--2052
-
[40]
J. Ying, C. F. Lu, W. Q. Chen, Two-dimensional elasticity solutions for functionally graded beams resting onelastic foundations, Composite Structures, 84 (2008), 209--219
-
[41]
D. M. Yoshida, W. Weaver, Finite element analysis of beams and plates with moving loads, Int. Associat. Bridge Structural Eng., 31 (1971), 179--195