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

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.

Response characteristics of a beam‐mass system with general boundary conditions under compressive axial force and accelerating masses

“…Prominent among these studies are the works of Frybal who studied nonstationary response of a beam to a moving random force. Steel who worked on the finite beam with moving load, Timoshenko et al who investigated the case of a concentrated force moving with a constant velocity along a beam when neglecting damping forces, Kurihara and Shimogo who considered vibration of an elastic beam subjected to discrete loads, Wang and Chou who studied nonlinear vibration of Timoshenko beam due to moving force and the weight of the beam, Licari and Wilson who investigated the dynamic response of a beam subjected to moving force system, Florence who worked on the problem of traveling force on a Timoshenko beam, Belotserkovskiy who studied the oscillations of infinite periodic beams subjected to a moving concentrated force, Iwankiewicz and Sniady who worked on the vibration of a beam under random stream of moving forces, Omolofe and Oseni who scrutinized effects of damping and exponentially decaying foundation on the motions of finite thin beam subjected to traveling loads, Omolofe and Ogunyebi who studied dynamic characteristics of a rotating Timoshenko beam subjected to a variable magnitude load traveling at varying speed and Omolofe et al who considered damping influence on the critical velocity and response characteristics of structurally prestressed beam subjected to traveling harmonic load to mention a few.…”