Mode localization characteristics of damaged quasiperiodically supported beam structures with local weak coupling.

Summary Some kinds of structures such as continuous girder viaducts and bridges have periodically spaced supports, and their support damage can potentially be detected using the change in extraordinary dynamic characteristics pertinent to quasiperiodic structure dynamics. In this study, the dynamic characteristics of quasiperiodically multisupported beam structures with local weak coupling are explored by using analytical and numerical methods. The eigenvalue equation and analytical expression of characteristic response of the spaced supported beam are first derived using the Galerkin method. For the periodic beam with four supports in particular, the analytical expressions for calculating natural frequencies and vibration modes are obtained. The fundamental frequency loci veering and local weak coupling between spans of the periodic beam are demonstrated, and the critical value of support stiffness is determined. In the case of quasiperiodic beam with four supports, the frequency loci veering and fundamental modal jump are explicitly illustrated through tuning the support stiffness. The modal jump leads to mode localization around the stiffness‐reduced support, which can be used for determining the support damage. Subsequently, a periodically multisupported girder bridge model in consideration of support damage is addressed, where the stiffness reduction due to support damage induces the period detuning. The natural frequency equation and vibration mode expression of the quasiperiodic girder are elicited. Numerical results illustrate some extraordinary dynamic characteristics including the frequency loci veering and nonlinear reliance of the first natural frequency on support stiffness, the fundamental vibration mode alteration and modal jump, the fundamental mode localization, and noticeable change in absolute mode displacement, which can be used to determine the reduction in support stiffness or damage. The analysis method and results on the dynamic characteristics such as mode localization are greatly helpful for determining the support damage of periodically supported structures and identifying the damage location. [ABSTRACT FROM AUTHOR]