The Vibration Analysis Of Defective Bridge Support

Highway bridge dynamics is an important topic of the development of modern roads and bridges, especially in the recent earthquakes, so many bridges were damaged or even collapse, of course, the main reasons are structural fortification issues, bridge work with defects, etc. Bridge supports which have long been considered a weak link of the overall seismic performance of the bridge are important components that connect the superstructure and substructure of the bridge, and its damage will directly affects the safety of the beam and pier. Therefore, the research on the vibration analysis of bridges with defective supports has certain engineering significance.This paper considers the damage of elastic modulus and cross sectional area, through the derivation of basic relations of spring damage, the defective support is simplified to spring supporting model, and involved the concept of damage factor, we can get the relationship of spring stiffness before and after injury: k-k(1-DA)(1-DE).We did vibration analysis of cantilever Beam Bridge, continuous beam bridge and arch bridge with the combination of damage mechanics and the basic principles of bridge dynamics. In this paper, the specific work and achievements are:1. On the basis of bending vibration equation of elementary beam, we introduce the concept of injury, and get the mode function and natural frequency equation of single span cantilever with the condition of the vertical stiffness defects and horizontal stiffness defects; and use the conversion matrix method, we get the mode function and natural frequency equation of multi-span cantilever beam fixed at both ends and one end fixed, the other end free, but there is a defective support in the middle of the beam; obtained the displacement response of cantilever bridge with support has a vertical defective stiffness under the moving mass.2. Use the Laplace transform and inverse transform, under normal circumstances, we got the mode function and natural frequency equation of continuous beam with rigid hinged at both ends and there is a defective support in the middle of the beam, got the mode function,natural frequency equation when considering the axial force and the buckling load characteristic equation when elastic buckling; got the influence of the degree of support damage to the natural frequency of continuous beam by calculating; discussed the dynamic characteristics of bridge with different supports. Use the orthogonal modes; we got the displacement response equation of the continuous beam bridge with defective supports in the harmonic excitation.3. We also deduced the balance equation of plane bending of arch bridge with horizontal defective stiffness supports; consider the natural vibration of the bridge, then use Matlab we can got the curve of arch thrust and injury factor. Curve shows that:with the injury increased, the level of thrust value decreased faster. We got the affect of horizontal defective stiffness supports to the displacement response of arch bridge under harmonic force, deduced the dynamic response of arch bridge with defective supports under uniform velocity biaxial moving vehicle load.