Power mode shapes for early damage detection in linear structures Adviser ： Jeng-Tzong Chen Professor Reporter: Sui-Wei Chen

Sheng-En Fang Department of Structural Mechanics,Technical University of Madrid,Madrid 28006,Spain Ricardo Perera Department of Civil Engineering,Central South University,Changsha,Hunan Province ,PR China

Abstract Establishing non-modal-based damage indices for non-destructive damage detection purposes, using the statistical properties of signals is a worthwhile topic and so far little literature related to this aspect can be found. 建立非模態的損傷指數，達到檢測非破壞性目的，並利用 統計特性 （均方根 RMS ） ，迄今很少文獻關於這方面研究. In addition, two extended parameters initially named as power mode shape curvature and power flexibility are derived using power mode shapes. 兩個參數命名為 PMSC 和 PF ，來建立 PMS 模式.

Satisfactory predictions are given for both single and multiple damage situations, and minor damage inducing few changes in the structural dynamic properties can also be detected, which is meaningful and important for early damage detection. 不論單一和多重破壞情況，或是少數輕微損壞的變化，這 個模式都能有令人滿意的結果，這是有意義且重要的對檢 測初期建築物損壞. A further experimental study on real structures is an important prerequisite before the practical application. 對近代的研究和實務分析結構都是不可或缺的.

Introduction Non-destructive 近十年被廣泛的研究 Modal parameters 選取方式一般是採用 spectrum estimation of signals Non-modal parameters 採用 statistical 的 root mean squares(RMS) 來分析，減少 measurement noise influence 尤其是 random noise 並能找出少數局部損害。

Das and Dey It was found that the displacement PSD is sensitive to the damage especially when the damage approaches the center of the simply supported beam. Cacciola et al nonlinear cantilever beam skewness coefficient

Yang et al cross correlation function amplitude vectors(CorVs) damage location index →aircraft panel → structural health monitoring(SHM) New concept of power mode shape The PMS utilizes the RMS values calculated directly from the PSDs of objective signals and is found to have a similar shape to the conventional mode shape.

New concept of power mode shape PMS is used to derive two extended parameters power mode shape curvature(PMSC)and power flexibility(PF) → damage localization indices

Power mode shapes Power spectral density analysis time lag τ=0 autocorrelation function Ryi( τ) mean square value(MSV) Ψ 2 yi

Feasibility analysis of the PMS concept

not complicate modal

Damage localization indices based on PMSs PMSC PF

Case

PMSC Approximately point out the possible damaged elements PF Predicts two of the three damaged elements

Conclusions Two damage localization indices based on a novel concept of power mode shapes are proposed in this paper. PMSC 和 PF 是兩個很新的概念去建立 PMS The proposed indices are designed for linear and lightly damped structures and were found to be capable of locating minor damage in different numerical and experimental cases. 對 linear and lightly damped structures 能夠找出微小損壞不 管是在數值或試驗性案件

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