Chapter 13 Mass Scaling of Mode Shapes Based on the Effect of Traffic on Bridges: A Numerical Study M. Sheibani, A.H. Hadjian-Shahri, and A.K. Ghorbani-Tanha Abstract In order to derive mass normalized mode shapes from Operational Modal Analysis (OMA) techniques, additional experiments have to be conducted in the interest of scaling the determined mode shapes. Various investigations have been carried out based on the deterministic perturbed mass matrix, also known as the mass change method. However, the conventional form of this method requires a number of rather costly and sometimes impractical experiments on the structure. In this article, it is intended to use traffic as a stochastic source of mass change to calculate mass scaling factors. Adequate traffic stream on bridges can affect the Eigen properties of the structure efficiently. The vehicles on the bridge are only considered to affect the mass properties, and vehicle-bridge interaction is neglected. A simplified structural model of a bridge is considered and the traffic is modeled as lognormal distribution. Nodal masses induced by the vehicles are converted to time histories to avoid difficulties based on the moving mass problem. Consequently, a method is proposed to produce the modified mass matrix which can be used in the scaling factor equations. Finally, scaling factors of mode shapes are proposed by comparing the unperturbed structure and the perturbed mass matrix structure. Keywords Mass change strategy • Mode shape scaling • Traffic induced • Lognormal distribution • Modified mass matrix 13.1 Introduction Operational Modal Analysis (OMA) techniques have been widely used during the recent decades and have nearly made Experimental Modal Analysis (EMA) obsolete. The advantages of OMA, such as elimination of the need for heavy shakers and the ability to perform tests without interruption of normal structure service, have made this method a reliable substitution for the EMA technique. However, certain drawbacks exist in every approach of OMA. As these methods consider the input force to be the unknown ambient noise, there is not a direct method available to normalize the extracted mode shapes and additional steps need to be taken [1]. Mass scaled modes are essential in numerous applications of modal analysis such as structural response simulation, damage detection, health monitoring applications, model updating, etc. [2, 3]. Several methods have been proposed to overcome this issue and they all share the notion that a controlled perturbation to the dynamics of the structure is the key element in obtaining scale factors of the mode shapes. The most promising methods have been found to be mass change techniques, in which known masses are added to the structure and the tests are performed before and after the addition of masses. The scale factors, consequently, can then be calculated by comparing the results. Parloo et al. proposed a sensitivity based method for obtaining scale factors of each mode shape. Mass change method was first introduced and validated by comparing the scale factors derived from forced vibration test, with those from repeated in-operation test considering different locations of the added mass [4]. Parloo et al. further evaluated the normalization method by employing it in a full-scale bridge test. Heavy concrete blocks were added to specific locations of the bridge in order to provide sufficient frequency shifts that are desired for the mass change method [5]. Brinker and Andersen further studied the method and derived a formula based on the equation of motion to estimate the scale factors [6]. Other studies investigated the best mass change setups and sources of error [2, 7]. Aenlle et al. offered optimized strategies regarding the method and studied the best mass ratios, optimized locations and uncertainties relating the method. It was shown that the best mass change scenarios were those which induced uniform mass changes to the entire structure and consequently prevented alteration of the mode shapes. Furthermore, the ratios of added masses to the entire structure were recommended to be high M. Sheibani ( ) • A.H. Hadjian-Shahri • A.K. Ghorbani-Tanha School of Civil Engineering, College of Engineering, University of Tehran, P.O. Box: 11155-4563, Tehran, Iran e-mail: mr.sheibani@ut.ac.ir © The Society for Experimental Mechanics, Inc. 2017 J. Caicedo, S. Pakzad (eds.), Dynamics of Civil Structures, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-54777-0_13 95
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