1)  modal perturbation method

1.
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.

2.
An approximate approach based on the direct modal perturbation method is suggested for analyzing the complex modal characteristics of non-proportional damping structure systems.

2)  mode perturbation method

1.
The mode perturbation method is applied to deduce the approximation analysis technique for dynamic characteristics of the prestressed beam.

2.
The mode perturbation method is used to establish an approximate analysis technique for the modal characteristics of the prestressed beam in lateral vibrations.

3.
In this method,the mode perturbation method is applied.

3)  mode perturbation

1.
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.

4)  modal perturbation

1.
This paper discussed a method of modal perturbation to analyze the characteristics of free vibration of Timoshenko cantilever beams.

2.
Considering the effect of reinforcement, the method, which may be called the method of modal perturbation, is put forward.

3.
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.

5)  direct modal perturbation method

1.
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.

6)  Complex Modal Matrix Perturbation Method

 奇异摄动法singular perturbation method   求含有小参数微分方程在整个区域上一致有效渐近解的近似方法。它是1892年由H.庞加莱倡导的。对于无限域含长期项的问题，可对自变量作变换，即采用M.J.莱特希尔提出的变形坐标法；对于最高阶导数项含小参数的边界层型问题，则采用L.普朗特从物理直觉提出的匹配渐近展开法，即将内解与外解按匹配条件对接起来的方法。20世纪50～60年代，这一方法得到了充分发展，其中包括P.A.斯特罗克以及J.D.科尔和J.凯沃基安的多重尺度法，H.克雷洛夫、H.H.博戈留博夫和U.A.米特罗波利斯基的平均法，G.B.威瑟姆的变分法，并形成应用数学的一门新的学科分支 。中国和华裔学者对奇异摄动法的发展作出了杰出的贡献，如郭永怀对变形坐标法的推广被钱学森称为PLK法、钱伟长的合成展开法、林家翘的解析特征线法等。奇异摄动法是从事理论研究的重要数学工具之一，对于弱非线性问题的分析甚为有效。该法在基础和应用研究中已被广泛应用于微分方程、轨道力学、非线性振动、固体力学、流体力学、大气动力学、动力海洋学、声学、光学、等离子体物理学、量子力学等领域。