In order to solve the bending vibration response of multi-span shaft with the elastic support boundary condition, a dynamic model of the Rayleigh continuous shaft was established based on the second Lagrange equation, and the partial differential equations were transformed into the ordinary differential ones by using Galerkin's method. A polynomial fitting method for the mode shape function of multi-span shaft was proposed, the mode shape values of the finite section of the shaft were calculated by means of transfer matrix method, and the mode shape functions and their higher order derivatives were fitted by polynomial. The helicopter tail drive shaft for example, fitting functions of three order mode shapes and their higher-order derivatives were substituted into dynamic equations, and the bending vibration response of the tail drive shaft under eccentric excitation was calculated by mode superposition method. The study results revealed that the method has good convergence and reliability.
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