Hi Rutuja,

which program/software are you referring to?

Modal analysis is basically a search for eigenvalues (co-diagonalisation of the matrices M and K). The problem to solve basically is to find U and f such as

M.U.f+K.U=0 (1)

When you perform a modal analysis, you find eigenvalues (the frequencies f), and eigenmodes associated to these frequencies (the deformed shapes U). 

Now consider multiplying U by any real number k, if U satisfies equation (1), then kU does too. Therefore, the amplitude of the deformation has no meaning at all. It is often scaled, either with the infinity norm (max value of the displacement set to 1m for example), or euclidean norm.

I hope it answers your question,

Best regards,

Romain Mesnil

To add to Romain's answer, the deformation is relative i.e. with respect to a stiffer part how much will be the relative movement of less stiffer part. Relative not absolute.

Good evening , I recommend you to look into the matrix method called Stodolla Vianello , it is very easy and gives you the lateral displacements of a building and you can take them to the third mode of vibration. if not deformation can be calculated as the division of the spectral angular acceleration between the level frecuancia

 hi guys i need to know what is the importance of the deformation and how is it calculated or related to the frequencies!

modal analysis is the heart beat of the structure.The frequency of the structure depend upon mass and stiffness .Higher the frequency lower the the period means yoir structure is stiff will be having less global reaponse.Despite of this lower frequency ,higher the natural period means flexible is your structure will be having high global response.The response is a relative term and this theory holds in elastic range.i hope i have cleared your point

Hi, 

The modal shape represent the way a structure can deflect. Modal shape for lowest frequency indicates the lower energy state. That is, if you provide very little input to a system it will deflect as mode shape 1. If you continue increasing energy input it will show two, three or next modal shape depending on the energy. The higher modal shapes require very high energy state which a structure or system may not face in its entire life. Therefore, we are worried about the first few modes of a system. 

Another importance of modal shape: When measuring response of a system we need to know modal shape. If you place censors at the point where u=0, you will not get any response although you are providing vibration to the system. 

I think this answers your question. If you need further clarification, please let me know. 

Thanks. 

Yes Mohiuddin  has answered  correctly.The significance is  how the structure will deflect with addition of energy starting from First mode which is fundamental frquency of Vibration.

Mode shapes provide most prominent deflection contributors for generalized (non specific) loading.

Calculation of modal analysis is based on what software you are using, if in ANSYS or ABAQUS or any structural code. However, the deformation calculation will help you with information on how the structure will deflect. Basically, the first mode in the modal frequencies is the most important mode, and is mostly considered in designs