Pokud čtete tento článek, pravděpodobně vás bude zajímat provedení dynamické analýzy v programu RFEM 6. If you are already familiar with the program, you may know that several add-ons are available to you depending on the purpose of the analysis. In any case, the Modal Analysis add-on is the one you cannot leave out, as it performs the natural vibration analysis for member, surface, and solid models, and is therefore a prerequisite for all other dynamic add-ons.
The add-on can be used to determine and analyze natural vibration parameters such as natural frequencies, mode shapes, modal masses, and effective modal mass factors. Všechny potřebné vstupní hodnoty se přebírají přímo z programu RFEM/RSTAB. The results from this add-on can further be used for vibration design and further dynamic analysis (for example, loading by a response spectrum).
This text focuses on one of the above aspects; namely, the determination of the mode shapes. It shows you how to adjust the modal analysis settings and how to choose between the different methods for determining the number of eigenmodes. For this purpose, the model in Image 1 is used.
Nastavení pro modální analýzu
Data entry for modal analysis is done in the Load Cases and Combinations window, as shown in Image 2. Please note that this is only possible if the Modal Analysis add-on is activated in the "Base Data" beforehand. The first step is to create a load case with Modal Analysis as the analysis type and import masses directly from the desired load cases or load combinations. Then the modal analysis settings can be further defined in the Modal Analysis Settings window. There, you can define parameters for the mass matrix and the eigenvalue method, as you will see later. This text will show you the difference between the three available methods for determining the number of eigenmodes to consider.
Option 1: User-Defined Number of Modes to Be Determined
The first option is to manually specify the number of eigenmodes to be calculated (Image 3). The number of available eigenmodes depends on the degree of freedom (that is, the number of free mass points multiplied by the number of directions in which the masses act). It is possible to define up to 9,999 mode shapes in the program. In this example, the number of the smallest eigenmodes to be calculated is manually set to 12. This way, the eigenmode parameters for 12 eigenmodes are calculated and the results are displayed as shown in Image 4. The Results navigator can be used to navigate through the individual modes.
Option 2: Automatic Determination of Number of Modes to Reach Effective Modal Mass Factors
The program can now automatically determine how many eigenvalues need to be calculated to reach a certain value of the effective modal mass factor. This value can be customized in the settings, as shown in Image 5. In this example, the value is set to 90%. Note, however, that this option is only available in combination with the “Root of a characteristic polynomial” as a method for solving the eigenvalue problem.
This way, the program calculates all eigenvalues until the percentage of effective modal masses in both of the horizontal (that is, X and Y) directions is greater than 90% (or in other words, the value that has been set for the effective modal mass factor) of the total mass. In this example, you can see in the Results table in Image 6 that 10 modes are required to meet this requirement. If you check the effective modal mass factors, you can see that the sums of both fmeX and fmeY are greater than 90%.
Option 3: Automatic Determination of Number of Modes to Reach Maximum Natural Frequency
The third option for determining the number of modes to consider is "Automatic, to reach maximum natural frequency" (Image 7). Compared to the previous option, where you were asked to enter a value for the effective modal mass factor, you can now enter a value for the maximum natural frequency to be reached. Similarly to the second option, the program will determine as many modes as necessary until the specified natural frequency is reached (Image 8).
Slova závěrem
Three methods are available to determine the number of modes in the modal analysis. The first is to manually specify the number of mode shapes to be calculated. Please note that you should determine this number carefully. To do this, it is useful first to analyze the smallest mode shapes of the model and estimate the importance of each mode shape using the effective modal mass factors. Unlike this option, the second and third options allow you to let the program automatically determine the number of eigenmodes to consider, based on certain parameter values to be reached. One option is to specify a value for the effective modal mass factor, while the other is to specify a value for the maximum natural frequency to be achieved. In both cases, the program calculates all the eigenvalues until the specified value (of the effective modal mass factor or the maximum natural frequency, depending on the option selected) is reached.
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