Study On Random Vibration Analysis For Coupled Vehicle-Track Systems With Uncertain Parameters

Generally, the dynamic analysis of practical engineering is affected by a lot of uncertain factors, which are classified roughly into two aspects:the first type of uncertainty can be called mechanical property's uncertainty of system due to the dispersion of material properties and the precision of processing technology and so on; another type of uncertainty may come from inherent randomness of external environment loads, such as gust, earthquake, wave and road surface roughness. In order to assess precisely the dynamic behavior of real structure, the effect of the two uncertainties above mentioned on structural dynamics behavior must be considered simultaneously, as often it is called double random vibration analysis. However, it is more challenging than the dynamics analysis, in which single random factor is included only. As the core of the thesis, the dynamic analysis of the coupled vehicle-track systems with parameter uncertainties under random track irregularity is investigated, which is taken as the starting point to study the double random vibration. Pseudo excitation method (PEM) is developed to analyze the stochastic system above mentioned. By combining pseudo excitation method with polynomial chaos expansion theory, adaptive regression algorithm and modified perturbation method, a series of effective analysis methods are established. The main research carried out includes the following contexts:1. Developing pseudo excitation method to random vibration analysis of stochastic linear system, the dynamics model of coupled vehicle-track system undergoing double random vibration is established and the sensitivity method of responses with respected to uncertain parameters is derived. Take in to account the geometric and mechanical characteristics of the coupled vehicle-track system, by virtue of the spatial periodicity of track, the dynamics system model can be built by transfer matrix method under the Symplectic geometric space to reduce the degrees of freedom of the coupled vehicle-track system considerably. The uncertainties that exist in structural model of the coupled vehicle-track system are transformed into a sequence of independent random variables. The track irregularity is characterized as random process and pseudo excitation is constructed using the power spectral density of the random process. The motion equation of pseudo response with uncertain parameters is used as a fundamental equation, then sensitivities of power spectral density with respect to uncertain parameters are derived analytically, in which important stochastic parameters can be selected conveniently.2. The polynomial chaos/generalized polynomial chaos-pseudo excitation method (PC/gPC-PEM) is proposed to solve the double random vibration of coupled vehicle-track system in the frame of stochastic Galerkin procedure. Firstly, the pseudo responses are expanded using polynomial chaos in the probability space of stochastic parameters. For Gaussian random variables the pseudo responses are expand in the space spanned by Wiener-Hermite polynomial chaos; for non-Gaussion random variables, however, the base function is selected according to their probability density function, accordingly it is called generalized polynomial chaos expansion. Secondly, the governing equations to solve the responses are derived using the orthogonality of the base function of polynomial chaos expansion based on stochastic Galerkin method and the expansion coefficients of the polynomial chaos are solved efficiently in the frequency domain. Finally, the mean and variance of the response's power spectral density can be assessed from the polynomial chaos expansion with the known coefficients of the pseudo responses. The proposed method provides good convergency, and it can acquire stable solutions even though for the case with large variation of random variables.3. An adaptive regression algorithm for double random vibration is proposed to overcome the difficulty encountered in the solution process when the number of the base function increases dramatically with the increases of the dimension of random variables and the order of polynomial chaos. In order to assess the base functions coefficients of polynomial chaos more effectively, the important base functions are extracted according to a criterion based on the increment of the modified error statistic of degrees of freedom considered. Furthermore, the inherited Latin hypercube sampling method is combined to produce the adaptive regression algorithm with good accuracy and efficiency. The algorithm is a non-intrusive method and is easy to implement. In addition, for given precision the adaptive base function algorithm reserves only the base function with significant coefficient and it avoids effectively'curse of dimensionality'. Because of the high sparsity of the base functions, the requirement of sample size is reduced considerably in the regression algorithm and it will converge at a faster rate than previous ones with complete combination polynomial base functions. The proposed method is used in the solution of double random vibration of coupled vehicle-track system, and then the reliability of the quality riding comfortable index is evaluated.4. Based on the modified perturbation method, a fast algorithm for riding comfort assessment of coupled vehicle-track systems with uncertain parameters under track irregularity is proposed. The mean values and standard deviations associated with riding comfort are expanded using Taylor series and they can be considered as a fundamental formula as a starting point for theoretical analysis. The standard deviations of the random parameters are assumed to be small and it can be substituted into different combination of standard deviations according to random variable type, then the riding comfort index of deterministic system is simulated and its mean values and standard deviations are assessed using the different order formulas. The modified perturbation method does not need to derive the recursive equations and the derivatives of the random matrix. It possesses the advantages of high accuracy and low complexity for the case with small variances. Consider a vehicle coupled with the track as an example of the three dimensional rigid-flexible body mixed model with the parameter's uncertainties existing in the suspension system, the random vibration analysis and riding comfort simulation is carried out in the frequency domain. The distribution and probability characteristics of riding comfort are investigated. The proposed method is used efficiently, which does not need integral and simulation of random samples and need only harmonic analysis at discrete frequency points.