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This study's objective is an irrationally nonlinear oscillating system, whose bifurcations and consequent multi-stability under the circumstances of single potential well and double potential wells are investigated in detail to further reveal the mechanism of the transition of resonance and its utilization. First, static bifurcations of its nondimensional system are discussed. It is found that variations of two structural parameters can induce different numbers and natures of potential wells. Next, the cases of mono-potential wells and double wells are explored. The forms and stabilities of the resonant responses within each potential well and the inter-well resonant responses are discussed via different theoretical methods. The results show that the natural frequencies and trends of frequency responses in the cases of mono- and double-potential wells are totally different; as a result of the saddle-node bifurcations of resonant solutions, raising the excitation level or frequency can lead to the coexistence of bistable responses within each well and cause an inter-well periodic response. Moreover, in addition to verifying the accuracy of the theoretical prediction, numerical results considering the disturbance of initial conditions are presented to detect complicated dynamical behaviors such as jump between coexisting resonant responses, intra-well period-two responses and chaos. The results herein provide a theoretical foundation for designing and utilizing the multi-stable behaviors of irrationally nonlinear oscillators. [ABSTRACT FROM AUTHOR]

Based on the urban railway transportation vehicle wheel,three kinds of typical wheel plate（ straight plate,single S plate and double S plate） were set up. The study presents the calculation method of structure load and thermal load of the urban railway transportation vehicle wheel,and focuses on the thermal-mechanical coupling performance of the three types of wheel plate under different abrasion,the characteristic of the thermal-mechanical coupling stress is obtained under the thermal-mechanical coupling condition. The results show that three kinds of urban railway wheels are all satisfied with the requirements of fatigue strength; and the double S plate wheel has a better anti-fatigue performance than straight plate and single S plate wheel in the coupling field.