Relationship Between Static Wind Load And The Modal Frequency Of Bending Vibration For Suspension Bridge

The wind-induced vibrations have a key influence on the instability and c ollapse of long-span suspension [Bridges.Generally,the aerostatic l oad may change the vibrational frequencies of suspension bridge,and then change the dynamical response of the structure.In the relevant literatures on the study of air static instability,the static wind load instability mechanism is mainly studied in a linear or nonlinear method.And the calculation software based on the linear and nonlinear theory is compiled to discuss the static and dynamical properties under the aerodynamic.For the instability and dynamic characteristics,there are less theoretical studies of suspension bridges under static wind loads.The present paper proposes an analytical method to calculate the modal frequencies under the aerostatic load for the long-span suspension bridges.First,the vertical bending vibrational partial differ ential equation with integral terms are discretized into the nonlinear inhomogeneous ordinary differential equations through the Galerkin method.Then,through coordinate transformation,a set of nonlinear homogeneous ordinary differential equations is obt ained by eliminating the inhomogeneous terms,and the displacements of the bridge under the static air load is obtained through letting the homogeneous terms equaling to zero.Finally,the relationship between the aerostatic load and the modal frequencies are obtained through the linear part of the homogeneous nonlinear equations.In addition,to verify the effectiveness of the method,Runyang Yangtze River Highway Bridge is used as an example to compare the theoretical results with the finite element results.Under static wind loads with different directions,the effects of some material and geometrical parameters on modal frequency are discussed in detail.These parameters are the main cable sag,main cable elastic modulus,unit bridge length mass and beam stiffness.The results show that the displacement of the suspension bridge under the upward static wind load is greater than the displacement with the same downward static wind load.The upward static wind load weakens the structural rigidity of the suspension bridge.At the same time,with the decrease of the sag and stiffness of the main cable and the increase of the mass of the unit bridge length,the upward static wind load significantly reduces the frequency of the low-order mode of the suspension bri dge,and the downward static wind load significantly increases the suspension bridge’s frequencies of the low-order modes.