1.    The definition of modal analysis: The physical coordinates of vibration integro-differential equations are transformed into modal coordinates, and the equations are decoupled into a set of independent equations described by modal coordinates and modal parameters, so as to obtain the modal parameters of the system. The transformation matrix of coordinate transformation is modal matrix, and each column is modal mode.

2.    The use of modal analysis: The goal of modal analysis is to identify the modal parameters of the system, which provides the basis for the analysis of vibration characteristics, the diagnosis and forecast of vibration faults and the optimization of structural dynamic characteristics. The application of modal analysis technology can be summarized as follows:

1) Evaluating the dynamic characteristics of existing system structure;
2) Prediction and optimization of structural dynamic characteristics in the design of new product;
3) Faults diagnosis and forecast of system structure;
4) Control the radiated noise of the structure;
5) Identify the loads of system;
Modal analysis is a modern method to study the dynamic characteristics of structures. It is the application of system identification method in the field of engineering vibration. Modal is the inherent vibration characteristic of mechanical structure, and Each modal has specific natural frequency, damping ratio and modal shape. These parameters can be obtained by calculating or testing analysis, during which modal analysis happens. Normally, modal analysis refers to testing modal analysis. Vibration modal is the inherent and integral characteristic of elastic structure. If the characteristics of the main modal of the structure in a certain frequency range which is easy to be affected are found out by the modal analysis method, it is possible to predict the actual vibration response of the structure under the action of various external or internal vibration sources in this frequency range. Therefore it is the important method of dynamic design of structure and fault diagnosis.
The vibration of machines, buildings, aerospace vehicles, ships, automobiles, etc. varies in various forms and instantaneously. Modal analysis provides an effective way to study the vibration of various actual structure. 
Four basic procedures in modal analysis are listed below:
1) Acquisition of dynamic data and analysis of frequency response function or pulse response function;
2) Build up mathematical model to describe state and characteristics of the structure, and the model is the basis of parameter identification;
3) Parameter identification can be divided into frequency-domain method, time-domain method and mix-domain method according to the different identification domain. And it’s not the case that the more complex the method is, the more reliable the result is.
4) The modal parameter model of the structure is obtained, which is a group of natural frequency, modal damping and the corresponding modal shapes.

3.    Structure dynamic modify and sensitivity analysis

Structure dynamic modify (SDM) has two meanings, one is how will the dynamic characteristics change if some modification about design is applied to machine, and the other is what kind of modification should be applied to the design of machine if modification to some parameters is required. These two meanings are the two different side of SDM.

The signal from the signal source is ranked in the order of frequency, and make it a function of frequency, and observe its law of change. It is called frequency spectrum analysis. Using Fourier series or Fourier transform, we can transform time domain signal into frequency domain signal, which is called frequency description or spectrum analysis.


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