10.1371/journal.pone.0215773.g001 Jianwei Liu Jianwei Liu Dejian Li Dejian Li Peng Yu Peng Yu Beam element considering constraint torsion. Public Library of Science 2019 mass damper parameters steel-box girder bridge freedom vehicle model pattern search algorithm 7 degrees vibration reduction integer programming method freedom curved-beam element model ergodic search method variably-accelerated pattern search algorithm road surface condition Den Hartog formula Final TMD parameter optimization values TMD design parameters frequency equivalent method 2019-04-23 17:35:30 Figure https://plos.figshare.com/articles/figure/Beam_element_considering_constraint_torsion_/8028257 <p><i>k</i> is the torsion center. <i>c</i> is mass center. <i>X</i> is bridge center curve coordinate calculated according to the unit arc length. <i>Y</i> is the radial coordinate. <i>Z</i> is the vertical coordinate.</p>