Wave Mode Control of Cantilever Slab Structure of T-Beam Bridge with Large Aspect Ratio

Tingting Liu,Guojin Chen,Zhigang Yan,Chuanping Zhou,Nan Zhang

doi:10.1155/2021/6544058

Tingting Liu, Guojin Chen + Show 3 more

Open Access

https://doi.org/10.1155/2021/6544058

Copy DOI

Abstract

The cantilever plate structure in a T-beam bridge with a large aspect ratio will cause vibration under the influence of environmental disturbance and self-stress, resulting in fatigue damage of the plate structure. Wave control based on elastic wave theory is an effective method to suppress the vibration of the cantilever plate structure in a beam bridge. Based on the classical thin plate theory and the wave control method, the active vibration control of the T-shaped cantilever plate with a large aspect ratio in the beam bridge is studied in this paper. The wave mode control strategy of structural vibration is analyzed and studied, the controller is designed, the vibration mode function of the cantilever plate is established, and the control force/sensor feedback wave control is implemented for the structure. The dynamic response of the cantilever plate before and after applying wave control force is analyzed through numerical examples. The results show that the response of the structure is intense before control, but after wave control, the structure increases damping, absorbs the energy carried by the elastic wave in the structure, weakens the sharp response, and changes the natural frequency of the structure to a certain extent.

Highlights

Halkyard studied the feedback adaptive control of bending vibration of beam structure by the wave control method [7]
In this paper, based on the research of the abovementioned documents, a large number of cantilever plate structures existing in the girder bridge structure are controlled by the sliding film variable structure control method which is different from the conventional control method
Based on the classical thin plate theory and the wave control method, the active vibration control of T-cantilever plate with a large aspect ratio in beam bridge is studied in this paper. e wave mode control strategy of structural vibration is analyzed and studied. e controller is designed to control the force/sensor feedback wave of the structure

Summary

Cantilever plate h x b y a z

Central rigid body Figure 1: Model of the cantilever plate. B Wr,sq(x, y, t)dxdy. Considering the boundary conditions at both ends of the cantilever Euler Bernoulli beam, it can be obtained that cos k0ia􏼁 · cosh k0ia􏼁 + 1 0. + ai􏼂sin h k0ix􏼁 − sin k0ix􏼁􏼃, where a is the length in the x-direction, k0i (ρhω2/D)1/4 is the elastic wave number in the classical plate; ai − cosh(k0ia) + cos(k0ia)/sinh(k0ia) + sin(k0ia), this coefficient is determined according to the boundary conditions at both ends of the cantilever Euler Bernoulli beam. + bi􏽨sinh 􏼐k0jy􏼑 + sin 􏼐k0jy􏼑􏽩, where b is the length in the y-direction, k0j (ρhω2/D)1/4 is the elastic wave number in the classical plate; bj − cosh(k0jb) − cos(k0jb)/sinh(k0jb) − sin(k0jb), this coefficient is determined according to the boundary conditions of Euler Bernoulli beams with free ends. 􏼢 i 􏼣a+ +􏼢 − i 1 􏼣􏼢 r1 􏼣a+ 􏼢 i − 1 􏼣􏼢 t1 􏼣a+ +􏼢 H H 􏼣􏼢 t1 􏼣a+

By solving this equation

Modal order

Findings

Conclusions