Abstract
Structure material properties are heterogeneous in nature and would be characterized with different statistics at different length scales due to the spatially averaging effects. This work develops a framework for the modal analysis of beam structures with random field models at multiple scales. In this framework, the random field theory is adopted to model heterogeneous material properties, and the cross‐correlations between material properties are explicitly considered. The modal parameters of a structure are then evaluated using the finite element (FE) method with the simulated heterogeneous material properties taken as input. With the aid of Monte Carlo simulation, the modal parameters are analyzed in a probabilistic manner. In addition, to accommodate the necessity of different mesh sizes in FE models, an approach of evaluating random field parameters and generating random field material properties at different length scales is developed. The performance of the proposed framework is demonstrated through the modal analysis of a simply supported beam, where the formulation of the multiscale random field approach is validated and the effects of heterogeneous material properties on modal parameters are analyzed. Parametric studies on the random field parameters, including the coefficient of variation and the scale of fluctuation, are also conducted to further investigate the relations between the random field parameters at different scales.
Highlights
To evaluate the sustainability of structures is a long-lasting problem in civil engineering community [1,2,3]
Structures are often subjected to dynamic loads, such as winds, waves, earthquakes, traffic, and human activities, which could gradually deteriorate the life-long sustainability of a structure. e force magnitudes or directions of dynamic loads keep varying with time, leading structures to exhibit complex mechanical behaviours
Modal analysis aims at determining the modal parameters of a structure and has become an essential task for a wide range of applications, such as serviceability analysis [6], vibration control [7, 8], load estimation [9], structural damage identification [10, 11], and structural health monitoring [12, 13]
Summary
To evaluate the sustainability of structures (e.g., buildings and bridges) is a long-lasting problem in civil engineering community [1,2,3]. In the random variable approach, the material properties of a structure are modelled as a set of random variables that are independent with each other (i.e., without any correlation). When applying the random field approach to simulate a heterogeneous structure, it is important to recognize that the statistics of a material property are determined upon elements with a specific size, i.e., the size of testing samples during site investigation. An approach of evaluating random field parameters and generating random field material properties at different scales is developed to accommodate the necessity of different mesh sizes in the FE-based structural modal analysis. Assuming that the random field parameters (e.g., mean, standard deviation, and correlation) of a material property are given at the fine scale, the statistics of this
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