Analysis of flexural natural vibrations of thin‐walled box beams using higher order beam theory

Abstract

Summary In order to study the influence of high‐order shear deformations and shear lag on the dynamic characteristics of thin‐walled box beams (TWBBs), this paper takes the Hamilton principle as a basis to consider multiple factors such as high‐order shear deformations, shear lag, and cross section rotary inertia of the TWBBs. The vibration differential equations and natural boundary conditions of TWBBs are deduced. On the basis of eight examples of TWBBs with different boundary conditions and span–width ratios, analytical results of this paper are compared with those of the ANSYS finite element method. Both results are in good agreement with each other, and the validity of the calculation method is verified. The effects of higher order shear deformations and shear lag on natural vibration characteristics of TWBBs are analyzed. And some meaningful conclusions are drawn: This theory shows the capability to accurately describe both higher order deformations and shear lag; when the span–width ratio is small, neglecting higher order web deformations will produce a large calculation error; under the action of shear lag, the natural vibration frequency of TWBBs decreases greatly, which cannot be neglected; and both the high‐order shear deformations and shear lag effect increase with increasing mode order and increase with decreasing span–width ratio.

Shear Lag Effects on Pedestrian-Induced Vibration and TMD-Based Vibration Control of Footbridges

“…Zhou et al [34] theoretically investigated the dynamic characteristics of steel-concrete composite box beams considering the SLE and slip by introducing self-balancing of axial forces in a longitudinal warping function of beam section. Jiang et al [35] studied the influence of high-order shear deformations and SLE on the dynamic characteristics of thin-walled box beams by using highorder beam theory. They concluded that the SLE increase with the increasing of mode order or the decreasing of span-width ratio.…”

“…Cai et al [36] derived the approximate solution of the first order Shear lag effects on pedestrian-induced vibration and TMD-based vibration control of footbridges vertical bending frequency for the simply supported curved thin-walled box girder considering the SLE. It has been reported that the SLE significantly affect the stiffness of the structures [35][36].…”

“…Recently, Zhang et al [39] investigated the SLE and accordion effect on dynamic characteristics of composite box girder bridge with corrugated steel web by proposing an analytical method. The aforementioned studies [35][36][37][38][39] indicate that the natural frequencies of the structures might be reasonably altered due to the SLE. However, the existing studies [33][34][35][36][37][38][39] on the dynamic responses of thin-walled box girder considering the SLE were mainly focused on the natural vibration characteristics or free vibration responses.…”

“…The aforementioned studies [35][36][37][38][39] indicate that the natural frequencies of the structures might be reasonably altered due to the SLE. However, the existing studies [33][34][35][36][37][38][39] on the dynamic responses of thin-walled box girder considering the SLE were mainly focused on the natural vibration characteristics or free vibration responses. To the best knowledge of the authors, however, there are very few studies related to SLE focusing on the forced vibrations of thin-walled box girder, not to mention the corresponding vibration control measures.…”

Mapping the relationship between the structural deformation of a simply supported beam bridge and rail deformation in high-speed railways

“…This study focused on a simply supported beam bridge on a high-speed railway, 23,24 analyzed the constraint effect of the rail in the subgrade section on both sides of the bridge, and derived the analytical expressions of the mapping relationship between the linear change of the beam and the deformation of the rail based on the principle of minimum potential energy. 25–27 Through calculation, the mapping deformation curve of the rail in the CRTS I unit slab ballastless track–bridge system induced by pier subsidence and beam faulting was investigated in detail. Further, the present results were compared to the corresponding finite element numerical calculation results for analyzing the main influencing factors of rail deformation.…”