Natural Vibration Frequency Analysis for a PC Continuous Box-Girder Bridge with Corrugated Steel Web Based on the Dynamic Stiffness Matrix

Abstract

In order to reasonably analyze the influence of shear deformation of corrugated steel web on the natural vibration frequency of PC continuous box-girder bridge with corrugated steel webs, first, the element stiffness matrix of PC box-girder bridge with corrugated steel webs is derived by using the energy variation principle. Second, according to the derived element stiffness matrix, the solution program for calculating the natural frequency of multispan uniform cross-section PC continuous box-girder bridge with corrugated steel webs considering the influence of steel web shearing effect is compiled by MATLAB software. The correctness of the natural vibration frequencies calculated by the MATLAB software is verified by the measured frequency of the constructed bridge and the calculated value by ANSYS 3D finite-element (FE) method. Finally, the influence parameters of the bending vibration frequency of the abovementioned bridge are analyzed. The result shows that (1) the natural frequencies calculated by the proposed program are in good agreement with the measured and FE values of the built bridges. The calculation program has higher precision, the difference of the first 5-order natural frequencies is within 6.01% and 7.32%. (2) The shear defomation effect of corrugated steel webs has great influence on the natural frequency of the subject bridge, while the modification of the shear modulus of corrugated steel webs and the type of corrugated steel webs has little influence on the bending vibration frequency of the bridge, the difference of the first 5-order bending vibration frequencies is within 1.07% and 0.55%, which can be ignored. (3) The dynamic analysis of the subject bridge considering the shear deformation effect can be easily incorporated into the matrix displacement system of the common framed structure, which avoids the complexity of the establishment and solution of the ANSYS FE model. It provides a reference for the calculation and analysis of the bending vibration frequency of the bridge type.