Nonlinear vibration analysis of longitudinal-transverse coupled beam

The coupling phenomenon of longitudinal and transverse vibration is representative in boost rocket. Taking longitudinal and transverse vibration coupling into account by using the second order term of longitudinal strain, the governing differential equations of Rayleigh beam was derived through Hamilton variational principle, and the finite element method was employed to explore the behaviors of this nonlinear coupling system. As for the inherent frequency of the corresponding linear system and the dynamic responses of nonlinear longitudinal and transverse coupling system, the obtained results were in agreement with those of NASTRAN, which validated the correctness of present method and results. According to characteristics of the viberation governing equations and the results of finite element method, the analyses focused on the time-variable property of nonlinear system frequency, the amplitude-frequency characteristic of nonlinear dynamical responses, the mutual effects of the longitudinal and transverse vibration and resonant phenomenon when the combinations of frequencies of exciting forces are closer to the frequency of the nonlinear system. The results of present study lie the theoretical foundation for the practical application of the present method.