Eigen value problem / Solution? in modal analysis? 2

[9865395996]

I have two basic doubts.

First of all what is eigen value Problem / eigen value solution ?

Next is why this method is used for modal analysis? Is there any type of method can be used for modal analysis?

 

[BlasMolero]

Hello!,
Understanding these concepts is basic in FEA Dynamic Analysis (by the way, all are in the manuals of your favorite FEA code!!).

Reasons to Compute Normal Modes
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There are many reasons to compute the natural frequencies and mode shapes of a structure. One reason is to assess the dynamic interaction between a component and its supporting structure. For example, if a rotating machine, such as an air conditioner fan, is to be installed on the roof of a building, it is necessary to determine if the operating frequency of the rotating fan is close to one of the natural frequencies of the building. If the frequencies are close, the operation of the fan may lead to structural damage or failure.

Decisions regarding subsequent dynamic analyses (i.e., transient response, frequency response, response spectrum analysis, etc.) can be based on the results of a natural frequency analysis. The important modes can be evaluated and used to select the appropriate time or frequency step for integrating the equations of motion. Similarly, the results of the eigenvalue analysis-the natural frequencies and mode shapes-can be used in modal frequency and modal transient response analyses.

The results of the dynamic analyses are sometimes compared to the physical test results. A normal modes analysis can be used to guide the experiment. In the pretest planning stages, a normal modes analysis can be used to indicate the best location for the accelerometers. After the test, a normal modes analysis can be used as a means to correlate the test results to the analysis results.

Design changes can also be evaluated by using natural frequencies and normal modes. Does a particular design modification cause an increase in dynamic response?. Normal modes analysis can often provide an indication.

In summary, there are many reasons to compute the natural frequencies and mode shapes of a structure. All of these reasons are based on the fact that real eigenvalue analysis is the basis for many types of dynamic response analyses. Therefore, an overall understanding of normal modes analysis as well as knowledge of the natural frequencies and mode shapes for your particular structure is important for all types of dynamic analysis.


Eigenvalue Extraction Methods (I will explain the options I know using NX NASTRAN FEA solver)
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Seven methods of real eigenvalue extraction are provided in NX Nastran. These methods are numerical approaches to solving for natural frequencies and modes shapes. The reason for seven different numerical techniques is because no one method is the best for all problems. While most of the methods can be applied to all problems, the choice is often based on the efficiency of the solution process.

The methods of eigenvalue extraction belong to one or both of the following two groups:

• Transformation methods
• Tracking methods

In the transformation method, the eigenvalue equation is first transformed into a special form from which eigenvalues may easily be extracted. In the tracking method, the eigenvalues are extracted one at a time using an iterative procedure. The recommended real eigenvalue extraction method in NX Nastran is the Lanczos method. The Lanczos method combines the best characteristics of both the tracking and transformation methods. For most models the Lanczos method is the best method to use.

Two of the real eigenvalue extraction methods available in NX Nastran are transformation methods:

• Householder method
• Modified Householder method

The real eigenvalue extraction method available in NX Nastran is classified as tracking methods:

• Sturm modified inverse power method


COMPARISON OF METHODS
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Since NX Nastran provides a variety of real eigensolution methods, you must decide which is best for your application. The best method for a particular model depends on four factors: the size of the model (the total number of degrees-of-freedom as well as the number of dynamic degrees-of-freedom), the number of eigenvalues desired, the available real memory of your computer, and the conditioning of the mass matrix (whether there are massless degrees-of-freedom). In general, the Lanczos method is the most reliable and efficient, and is the recommended choice.

• For small, dense models whose matrices fit into memory, we recommend using the automatic method (automatic Householder ). The automatic Householder runs modified methods if the mass matrix is singular; however, it runs the unmodified methods, which isfaster, if the mass matrix is not singular. The automatic Householder method runs faster on computers with vector processing and also supports parallel processing computers. Note that most real world problems are not small and dense, unless you use reductive methods such as superelements.

• The Sturm modified inverse power method can be the best choice when the model is too large to fit into memory, only a few modes are needed, and a reasonable eigenvalue search range is specified. This method is also a backup method for the other methods and is used when a check of the other methods' results is needed.

• For medium to large models the Lanczos method is the recommended method. In addition to its reliability and efficiency, the Lanczos method supports sparse matrix methods that substantially increase its speed and reduce disk space requirements.

Hope this helps!!.
Best regards,
Blas.

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Blas Molero Hidalgo
Ingeniero Industrial
Director

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