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Isogeometric analysis is an efficient method to accurately represent geometry and obtain accurate solutions, and can be utilized for dynamic analysis of flexible multibody systems. In this paper, l 1 norm based dynamic analysis of flexible multibody system modeled with trimmed isogeometry is presented, in which, (1) the exact shape deformation of regular NURBS element after trimming is characterized by geometric transformation, (2) the l 1 norm optimization is employed to select the predominant modal shapes for accurate dynamic analysis under rapidly changed loads, and (3) motion equations are sampled by considering the acceleration of control variables influence on control variables variation to obtain stable dynamic results. Finally, the presented approach is validated with three examples. The dynamic response results show that the trimmed isogeometric analysis can be employed to achieve considerable accuracy. As the continuity between NURBS elements increases from C0 to C1, the degree of freedom is reduced by 75%, and the computational time of l 1 norm based dynamic analysis is about 35% of the full order modal shapes method. Furthermore, the proposed sampling method can be utilized to reduce the 33% sampling number compared with the Latin Hypercube sampling method. • The trimmed NURBS element deformation is characterized by geometric transformation. • The l 1 norm optimization is employed to select the predominant modal shapes. • Motion equations are sampled by considering the of control variables acceleration. [ABSTRACT FROM AUTHOR]

• The dynamic responses are approximated by the sparse polynomial chaos expansion. • The multilevel sampling based resampling strategy is applied to weaken the RIP. • The generalized coordinates are used to evaluate the coherence of mechanical system. The polynomial chaos is widely used in uncertainty analysis of the mechanical system, in which, the samplings hugely affect the efficiency and accuracy. In this paper, a multilevel sampling based sparse polynomial chaos approach is presented for efficient uncertain analysis of the mechanical system, in which, 1) the dynamic responses are approximated with sparse polynomial chaos expansion which enables the sampling number to be much less than that of the polynomial terms, and the number of deterministic systems would be reduced, 2) the multilevel sampling based resampling strategy is applied to weaken the Restricted Isometry Property condition for sparse polynomial chaos expansion based equations solving, and in addition, 3) such multilevel sampling based on evaluating system coherence with generalized coordinates acceleration is used to reduce the motion equations with deterministic parameters for obtaining the dynamic responses accurately and efficiently. Finally, the presented approach is validated with three examples. The results are shown that the sparse polynomial chaos can be utilized to calculate the mean and standard deviation with 1E-5 and 1E-2 accuracy. The sparse polynomial chaos based on multilevel sampling can be used to reduce the sampling size by 25% compared with the Latin Hypercube sampling. Compared with coherence optimal sampling, the convergence of the proposed sampling method is more stable as the sampling size is increased. Lastly, multilevel sampling also can be used to reduce the deterministic motion equations by 20% to obtain 1E-5 accuracy dynamic responses compared with the Latin Hypercube sampling. [ABSTRACT FROM AUTHOR]