By means of the accurate dynamic condensating method,bicompactible conditions and variable frequency transformation a characteristic equation with stiffness and mqss matrix containing eigen parameter is obtained. In the solution of the natural frequencies of the whole structure, the functional relationship between the eigenvalue and eigenvalue parameter is dealt with and the chebyshev interpolation polynomial is used to approach the non linear function. Then the natural frequencies of each mode are obtained by using the Newton method to solve the non-linear equations.