An Efficient Polynomial Chaos Method for Stiffness Analysis of Air Spring Considering Uncertainties

Traditional methods for stiffness analysis of the air spring are based on deterministic assumption that the parameters are fixed. However, uncertainties have widely existed, and the mechanic property of the air spring is very sensitive to these uncertainties. To model the uncertainties in the air spring, the interval/random variables models are introduced. For response analysis of the interval/random variables models of the air spring system, a new unified orthogonal polynomial expansion method, named as sparse quadrature-based interval and random moment arbitrary polynomial chaos method (SQ-IRMAPC), is proposed. In SQ-IRMAPC, the response of the acoustic system related to both interval and random variables is approximated by the moment-based arbitrary orthogonal polynomial expansion. To efficiently calculate the coefficient of the interval and random orthogonal polynomial expansion, the sparse quadrature is introduced. The proposed SQ-IRMAPC was employed to analyze the mechanic performance of an air spring with interval and/or random variables, and its effectiveness has been demonstrated by fully comparing it with the most recently proposed orthogonal polynomial-based interval and random analysis method.

Switched Projective Synchronization of the Stochastic Newton-Leipnik System

The paper is involved with switched projective synchronization of two identical chaotic systems with random parameter using adaptive control method. Based on the orthogonal polynomial expansion of the Hilbert spaces, the Newton-Leipnik system with random parameter is transformed as the equivalent deterministic system. At last, an adaptive controller can be designed by the Lyapunov stability theorem for achieving switched projective synchronization of the equivalent deterministic system with different initial values. Corresponding numerical simulations are performed to verify the effectiveness of presented schemes for synchronizing the stochastic Newton-Leipnik system.

Seismic Response Analysis of Reinforced Concrete Frame Structures Considering the Variation of Parameters

The orthogonal polynomial expansion method expression of stochastic structure was deduced. Then, based on orthogonal polynomial expansion method, taking a 20-storey reinforced concrete frame structure as an example, the impact of the randomness of structural parameters on time history response was researched. Meanwhile, in order to verify the correctness of analysis program, the calculation results of orthogonal polynomial expansion method were compared with the Monte-Carlo method which based on Newmark integral. The results show that it can get relatively accurate results when the number of terms of the orthogonal polynomial is 5. Structural mass and stiffness have a greater impact on the structural dynamic response. And the greater number of random parameters, the greater the impact on structural dynamic response.