## 1 Introduction  
Fibre reinforced composite material and structures are extensively used in diverse engineering applications such as aircraft, rockets, ships, wind turbines, buildings, etc. Due to complexity in material microstructure and manufacture process, composite structure often shows undesirably large uncertainty in its mechanical performance, such as structure deflection [1, 2], load capacity [3, 4], buckling behaviour [5, 6] and dynamic response [7]. Therefore, structure design in stochastic or probabilistic approaches is especially important for composite structures [8]. Since engineering composite structures are commonly required to have natural frequencies away from the operating value to avoid structure resonance, stochastic natural frequency of composite structures has received increased attention in recent years. [PERSON] and [PERSON] [9] adopted stochastic finite element method (SFEM) to investigate stochastic natural frequency of composite cantilever beams. [PERSON] et al. [10, 11] derived natural frequency statistics of composite plates by an RS-HDMR approach and later used a surrogate model. [PERSON] et al. [12] investigated stochastic free vibration behaviour of laminated composite plates using polynomial correlated function expansion and also response surface method (RSM). [PERSON] et al. [13] presented a neural network-based second order reliability method to obtain probabilistic natural frequency of composite plates. [PERSON] et al. [14] investigated stochastic variability of natural frequencies of laminated plates by modal stability procedure probabilistic approach. [PERSON] et al. [15] provided a free vibration analysis of composite cylindrical panels with random material properties by first-order perturbation technique, and similar study is shown in [16]but for composite conical shell structure. It is noticed that these current studies are based on meso-scale (ply-scale) uncertainty such as uncertainty in ply elastic properties, ply orientation, ply density and thickness, and these meso-scale random variables are considered to be independent with one another. It is known that uncertainty of ply properties is essentially caused by stochastic variation of micro-scale (constituent-scale) parameters such as properties of fibre/matrix, fibre volume ratio, micro-structure, void, etc. [17]. Although probabilistic analysis based on meso-scale uncertainty takes less computation effort, uncertainty consideration started from micro-scale would provide insight into propagation of uncertainty across different scales [18] and also possible coupling between meso-scale random variables [19; 20; 21; 22; 23; 24]. Still, it seems that little work has been reported about achieving comprehensive understanding on stochastic natural frequency of composite structures by considering uncertainty at different scales. [PERSON] et al. [25] showed difference in natural frequency statistics of composite plates derived from different scale uncertainty, but the uncertainties at different scales are somehow not connected. Therefore, it would be valuable to conduct comprehensive comparison on achieving natural frequency statistics of composite structures from meso-scale and micro-scale uncertainty, and any difference on the results would provide good indication or enlightenment to achieve complete description over uncertainty at different scales. This study provides natural frequency analysis of typical composite structures based on micro-scale and meso-scale uncertainty. Meso-scale statistics are derived from micro-scale uncertainty by a combination of Monte-Carlo simulation and micromechanical model, and especially statistical correlation between meso-scale random variables is discussed. Response surface method (RSM) based on finite element modeling is employed to obtain approximate natural frequency of structures with complex shape or boundary condition. Statistics of natural frequencies of laminate plate and cylindrical shell are derived by a combination of Monte-Carlo simulation and the RSM.