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

Abstract

KEYWORDS frequency loci veering, local weak coupling, mode localization, quasiperiodically supported beam, support damage 1 | INTRODUCTION Natural frequencies and vibration modes are essential dynamic characteristics of a structure, which have been widely used in structural health monitoring or damage detection. 1-11 A variety of modal analysis and extraction methods have been proposed in the past decades. [12][13][14][15][16][17][18][19] The extracted low-order vibration modes from a complex structure in general have higher accuracy than high-order vibration modes. However, structural high-order vibration modes are more sensitive to local damage than low-order modes, and thus the reliability of modal-based damage detection is influenced by the sensitivity and accuracy of extracted modal properties. The use of low-order vibration modes such as the fundamental mode is a more effective method for structural damage detection.Many engineering structures have geometric and physical periodicity, for example, continuous girder viaducts and bridges with periodically spaced supports (supports are equally spaced and have identical stiffness). The dynamic characteristics of periodic structures have been studied extensively. [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] The periodically supported beam consists of multiple spans, and the adjacent spans share the same displacement and angular rotation at the joint support due to continuity. For small support stiffness, the continuity of displacement and angular rotation indicates a strong coupling of the periodically supported beam between adjacent spans. On the contrary, for large support stiffness, the support displacement of the beam, for example, in the fundamental vibration mode is close to zero, and then the beam between spans has coupling only in angular rotation, which is the so-called local weak coupling. The periodically supported beam is a local weak coupling beam when the support stiffness is higher than a certain value. 39,40 Nevertheless, the periodically supported beam with local weak coupling leads to a quasiperiodically supported beam if the stiffness in one or a few supports is weakened due to damage. When the support stiffness is lowered to be smaller than a critical value, the fundamental natural frequency of the quasiperiodically supported beam manifests frequency loci veering, and its fundamental vibration mode exhibits modal jump. The modal jump yields a noticeable increase of absolute displacement of the fundamental vibration mode around the stiffness-reduced support, which is the so-called mode localization. 40 The dynamic characteristics such as fundamental mode localization of the quasiperiodically supported beam with local weak coupling rely directly on the support stiffness, and the mode localization is around the stiffness-reduced support. These outstanding dynamic characteristics of quasiperiodically supported structures have the potential to be applied for detecting and locating support damage based on the fundamen...

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