A multi-scale uncertainty analysis method based on the Hermite–Chebyshev polynomials for dynamic responses of FRP composite structures with hybrid uncertainties

Multi-scale hybrid uncertainties in material properties of FRP composites stemming from their manufacturing processes present significant challenges for dynamic analysis and reliability assessment. This paper proposes a multi-scale uncertainty surrogate model based on Hermite–Chebyshev polynomials. The relationship between micro- and macro-scale material properties is established using the Mori–Tanaka method. To demonstrate the efficacy of the proposed method, case studies are conducted on both a FRP wide-flange I-beam structure and a FRP truss bridge. Results indicate that this method accurately determines the probability density functions and cumulative distribution functions of natural frequencies and mode shapes. Notably, the method efficiently computes the upper and lower bounds of dynamic failure probability of FRP truss bridge with high numerical efficiency.