A Method to Determine Main Direction of a Curved Bridge’s Mode Shape

Abstract

Due to the special construction feature, the mode shape of a curved bridge has “flexure—torsion” coupling situation. In order to determine whether the main direction of the mode shape is flexure or torsion, each mode shape was divided into four sub directions which are vertical bending, pure torsion, transverse bending and longitudinal shift respectively. Accordingly, the energy of each mode was also subdivided into four directions. The ratios between the energy of sub direction and the total energy of a mode were denoted by four direction parameters. Theoretical derivation for the direction parameters was given based on the energy conversation principle of each mode of undamped system. The derivation result reveals that four formulas of the direction parameters are only related to structural mass, sectional geometric characteristics and mode vectors. Finally, the method of determining the main sub direction of mode shape of a curve bridge was given according to the values of the four parameters, and how to use the method was presented too by a instance.