In this paper, a method is developed, which may be called the method of mode perturbation, to analyze the characteristics of vibration of complicated beams.

First, the modal perturbation method based on Ritz vectors is applied to solve the dynamic characteristics of Timoshenko deep beam including the effects of shear deformation and rotational inertia.

An approximate approach based on the direct modal perturbation method is suggested for analyzing the complex modal characteristics of non-proportional damping structure systems.

The mode perturbation method is applied to deduce the approximation analysis technique for dynamic characteristics of the prestressed beam.

The mode perturbation method is used to establish an approximate analysis technique for the modal characteristics of the prestressed beam in lateral vibrations.

In this method,the mode perturbation method is applied.

This paper discussed a method of modal perturbation to analyze the characteristics of free vibration of Timoshenko cantilever beams.

Considering the effect of reinforcement, the method, which may be called the method of modal perturbation, is put forward.

A method of modal perturbation,based on Ritz vector,is developed for solving the modal characteristics of Timoshenko beam including the second effects of shear deformation and rotational inertia.

Based on the principal of direct modal perturbation method,a simplified semi-analytical technique for the modal characteristics of the short shear wall with small openings was developed.