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过载是火箭的真实环境.考虑纵向过载环境,根据Hamilton变分原理,得到了欧拉梁变系数横向自由振动微分方程,证明了该变系数系统存在满足刚度和质量正交条件的本征解,揭示了纵向过载环境下欧拉梁本征函数的非对称性.用本征向量叠加方法和改进欧拉中点直接积分算法求解了该变系数系统的动态响应,二者结果的一致性说明该理论推导的正确性和方法的可行性.
Overloading is the real environment of the rocket.According to the Hamiltonian variational principle, the transverse free vibration of the variable coefficient of Eulerian beam is obtained by considering the longitudinal overload conditions, and it is proved that there exists an eigenvector satisfying the orthogonal condition of stiffness and mass, The asymmetry of Euler beam eigenfunctions under longitudinal overload is revealed.The dynamic response of the system with variable coefficients is solved by using the eigenvector superposition method and the improved Euler midpoint direct integration algorithm.The consistency of the results indicates that the theoretical derivation The correctness and feasibility of the method.