Efficient Random Vibration Analysis And Optimization For Coupled Vehicle-Track Systems

Due to the outstanding energy and environmental issues and growing transportation needs, the development of high-speed and heavy haul technologies are becoming the main directions on railway development. This considerably increases the interaction between the vehicle and the track, the bridge, the ground, the catenary and the surrounding buildings, which has a direct impact on a range of issues of the train and the railway line, e.g. safety, ride comfort, fatigue, noise, etc. The track irregularity is known as the most important source of random excitation of the railway vehicle, hence the random vibration analysis of the coupled vehicle-track systems subjected to the track irregularity, especially the calculation of response power spectral densities (PSDs) plays a very important role in the dynamic analysis for railway transportation.However, the degrees of freedom (DOFs) of the track models are usually considerably large and the computational efficiencies of both the conventional frequency-domain and time-domain random vibration analysis methods are very low, which undoubtedly makes the random vibration analysis of the complicated coupled vehicle-track systems particularly challenging. As a result, only very simple models have previously been used and it is in urgent need to develop new theories and numerical methods.In order to meet the specific needs of practical engineering, some valuable exploration and research for random vibration analysis and optimization of coupled vehicle-track systems are performed in this thesis. The main work can be summarized as follows:1. Generalized symplectic random vibration analysis for infinite long chain-type structuresIn this thesis, the symplectic mathematical method is generalized for the first time to investigate the transient response of an infinitely long chain-type structure subjected to arbitrary loads. This method simply needs to establish the equation of motion of the loaded substructure. The dependent DOFs are firstly condensed into the independent ones according to the properties of the wave propagation constants. Consequently, the condensed equation of motion, whose coefficient matrices are functions of the wave number, is derived. Two solving forms, i.e. the discrete form and closed form, are then performed based on the dispersion relations of such structures and the basic assumptions of symplectic method to obtain the transient responses. The former form is established by desecrating the wave number evenly in the interval [0,2n), so that the corresponding propagation constants are derived. This enables the response of the infinitely periodic structure to be obtained by accumulating the pass-band frequency responses. The latter form is established by applying Fourier expansions to these coefficient matrices, so that the response vectors, the time and wave number variables are easily separated accordingly. Finally, the resulting equations are combined with PEM for stationary or non-stationary random response analysis.2. Pseudo-steady state approach for random vibration analysis of periodic time-dependent systemsA pseudo-steady state approach for random vibration analysis of periodic time-dependent systems is developed based on PEM, separation of variables and the Schur decomposition scheme. The periodically time-varying equation of motion of the coupled system subjected to pseudo-excitation is firstly established by transforming the stationary/non-stationary random excitation into deterministic pseudo-excitation using PEM, which is then rewritten as a first order linear differential equation group with periodic coefficients in state-space. Since the frequency-dependent terms are separated from the load vector to avoid repeated computations for different frequencies associated with the pseudo-excitations, the periodic state transition matrix and periodic load vector of the state-space equation of motion are then derived using a step-by-step integration scheme over only one period. Finally, based on the periodicity of the solution, the Schur decomposition scheme is performed to further transform the former pseudo response problem for this time-dependent system into a set of linear equations whose coefficient matrix is upper triangular. Thus the conventional periodically time-history analysis is transformed in to a pseudo-steady state response analysis and an improvement of the computational efficiency by above1-2orders of magnitude can be achieved as compared with the non-stationary PEM approach based on numerical integration method.3. Efficient random vibration analysis of coupled multi-body vehicle-track systemsThe random responses of the2-dimentional (2D) vertical and3-dimentional (3D) multi-body models of coupled vehicle-track systems subjected to three types of rail irregularities, i.e. the longitudinal level irregularity, alignment irregularity and the cross level irregularity are achieved using the PEM, the symplectic mathematical method, the symmetric condensation approach and the pseudo-steady state approach. PEM is firstly applied to convert the complicated random vibration analysis subjected to multi-sourse multi-point fully-coherent non-stationary random excitations into simple deterministic response analysis subjected to generalized single-point harmonic excitations by transforming the above three types of rail irregularities into corresponding harmonic pseudo-excitations. The symplectic method, the generalized symplectic method and the symmetric condensation approach are then applied to establish the equations of motion of2D/3D F-V/M-V models based on the concrete forms of pseudo-excitations and the characteristics of F-V/M-V models, which considerably reduces the computational DOFs of the coupled system. Finally, the pseudo-steady state approach is applied to transform the equations of motion of the M-V models into pseudo-steady state form so that the pseudo-responses of both the F-V and M-V models can be calculated by solving linear equations, after which the response PSDs and the standard deviations can be derived conveniently. Based on the calculation results, the F-V model and the M-V model are compared; the influences of vehicle velocity and class of track on system responses are discussed; the transmission mechanism of random vibration in the coupled system is also investigated.4. FEM-based random vibration analysis of coupled vehicle-track systemsIn this thesis, an accurate and efficient random vibration analysis of a well-meshed FE coupled vehicle-track system with hundreds of thousands of DOFs is performed on a ordinary personal computer for the first time based on the multi-body model approach. The vehicle components are modeled by Ansys software and then connected by the1st and2nd suspension system using their free modals. The track is modeled as a3D discrete-supported structure with three layers. PEM is firstly used to transform the four types of rail irregularities, i.e. the longitudinal level irregularity, alignment irregularity, the cross level irregularity and the gauge irregularity, into corresponding harmonic pseudo-excitations, which fundamentally solves the difficulties in the random vibration analysis of well-meshed FE model. Based on this, the equation of motion of the FE vehicle model and the low-DOFs symplectic equation of motion of the3D track model are coupled and then solved to derive the pseudo-response, after which the response PSD and the standard deviation of the coupled system can be derived conveniently. Finally, the elastic vibration mechanism of the vehicle is studied. Some standard deviation nephograms of vehicle components are also drawn, through which the overall random vibration behavior and vulnerable parts of these components can be viewed intuitively. This provides a powerful foundation for vehicle design and maintenance in practical engineering.5. FEM-based riding comfort optimization using a coupled vehicle-track systemBased on the above-mentioned FEM-based random vibration analysis of coupled vehicle-track systems, a riding comfort optimization approach on the suspension system of a domestic high-speed railway train is developed using a coupled FE body rigid-flexible hybrid vehicle-track model with millions of DOFs is achieved. The min-max optimization approach is utilized to improve the train riding comfort with related8parameters of the suspension structure adopted as design variables, in which54design points on the vehicle floor are chosen as estimation locations and the international standard ISO-2631is used to evaluate the riding comfort. The K-S function is applied to fit the objective function to make it smooth, differentiable and have superior integrity, which is then solved accurately and efficiently using the PEM, the symplectic method and the symmetric condensation approach. The1st and2nd order analytical sensitivities are derived by further developing these methods and so the difficulties in the optimization are fundamentally solved. The max weighted RMS acceleration among the54design points reduced by58.34%after optimization, the influences of vehicle velocities and class of track irregularity on optimization results are also discussed.