Transverse vibrations of prestressed continuous beams on rigid supports under the action of moving bodies

Abstract

The main objective of the paper is to investigate the dynamic response of the prestressed beams on rigid supports to moving concentrated loads. The governing equation of the transverse vibration of a prestressed continuous beam under the ununiformly distributed load is analytically formulated, taking into account the effect of the prestressing. The forced transverse vibration of the beam under the action of a large number of moving bodies has been investigated by using the method of substructures. In addition, the reaction forces at every rigid supports can be determined from the obtained differential equations. A comparison between the numerical results for the prestressed and the non-prestressed beam is presented to show the influence of the prestressing and the moving velocity of the bodies on the dynamic response of the beam. The calculating results are also examined and validated by experimental measurements at a large ferroconcrete bridge in Vietnam.

Transverse vibration of orthotropic rectangular plates under moving bodies

“…Using the mode superposition principle, a solution of equations (7) and (11) with the boundary conditions (12) and (13) is assumed in the form…”

“…The dynamical analysis of an orthotropic plate under the action of moving forces has attracted in [7,8,9]. The method of substructures and the Ritz method have been used for calculating transverse vibrations of a continuous beam on rigid and elastic supports under the action of moving bodies [10,11,12]. In this work, we use the method of substructures to derive transverse vibration equations of an orthotropic rectangular plate under the action of moving bodies.…”

Dynamic responses of prestressed bridge and vehicle through bridge–vehicle interaction analysis

“…Here D s can be readily obtained by assuming _ Q 0 ¼ € Q 0 ¼ ½0 NÂ1 and then solving Eq. (8). It should be noted that this approach is much easier and more straightforward than the existing method assuming a very slow vehicle speed and then solving the dynamic bridge-vehicle interaction response.…”

“…Kocaturk and Simsek [7] utilized the Lagrange equations to solve the dynamic response of a simply supported beam subjected to an eccentric compressive force and a concentrated moving harmonic force. Khang et al [8] investigated transverse vibrations of prestressed continuous beams under the action of moving bodies by using the method of substructure, which neglected the eccentricity of the prestress. Cai et al [9][10][11][12] particularly studied adopting dynamic impact factor for performance evaluation of bridges and researched effect of wind and bridge approach length on responses of bridge vehicle interaction.…”

On the Critial Velocity of a Vehicle Moving on the Bridge

“…Khi đó các phương trình mô tả dao động uốn của dầm có ứng suất trước chịu tác dụng của vật thể di động là một hệ hỗn hợp phương trình đạo hàm riêng và phương trình vi phân thường [7,8] ( )…”