Based on this and by introducing Green s function,dynamic compatible equation and corresponding boundary conditions are transformed into a equivalent integral equation and using perturbation variational method to dynamic equilibrium equation and taking static load as the parameter,the characteristic relation between the least natural .

The equations are solved by using the perturbating variation method, so the second\|order approximate characteristic relation between nonlinear natural frequency and amplitude is obtained.

Matrix perturbation methods for eigenvalue analysis of vibration of compressible fluid-solid;

A perturbation method for weakly damped systems repeated eigenvalues;

An analytical solution to tunnels with over-under-excavated surface based on perturbation method;

Theoretical derivation and analyses of the problem of the acoustic multipole logging have been conducted in the case that the principal symmetric axis of the transversely isotropic elastic solid is perpendicular to the borehole axis with the perturbation method.

The Navier-Stokes equation about the fluid between two cylinders was expanded with the perturbation method.

By combining the interval finite element(FEM) analysis with perturbation method and optimization technique, the interval parameter perturbation method and interval parameter optimization method were presented to solve the equations of interval FEM.