# Damping influence on the critical velocity and response characteristics of structurally pre-stressed beam subjected to travelling harmonic load

Volume 4, Issue 1, pp 26--36 Publication Date: August 11, 2019       Article History
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### Authors

B. Omolofe - 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 increase. Thereby reducing the risk of resonance and thus the safety of the occupant of this structural member is guaranteed.

### Keywords

• Response characteristics
• flexural member
• harmonic load
• critical speed
• resonance
• foundation stiffness
• assumed mode
• concentrated force

•  47H10
•  54H25

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