Maximization of the First Eigenfrequencies | ||||
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It is important to consider more than the first natural eigenfrequency as illustrated in the above figure (b) when increasing the natural frequencies using optimization. At least the next two first natural frequencies should be considered in the optimization.
All natural eigenfrequencies requested in the FE model are applied in the optimization if ALL option is applied in the LC_SET parameter.
During the optimization, the various natural frequencies are automatically weighted by their distance from the lowest natural frequency, i.e., when the other natural frequencies approach the first natural frequency during the optimization, the more they will be weighted. Generally, the first natural frequency is always maximized.
The design response is defined using the Kreisselmaier-Steinhauser formulation.
Any number of natural frequencies in the design response can be specified using the DRESP command.
Formulation of the Optimization Problem
The optimization task is to maximize the lowest modal eigenfrequencies with a volume constraint of 100%.
Model:  |
f=20.4Hz:  |
f=22.1Hz:  |
f=25.8Hz:  |
f=26.4Hz:  |
f=30.6Hz:  |
f=35.0Hz:  |
In the above figure you can see the model and the first six modal eigenfrequencies.
Result and Convergence
The following figure shows the objective function (maximize eigenfrequencies):
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The constraint (Mass) is shown in the following figure:
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The gradient of three eigenfrequencies over 15 iterations and the mass constraint are illustrated in the above figure. The constraint is fullfilled.
In this example, all calculated natural frequencies are considered for the objective function using the Kreisselmaier-Steinhauser formulation, and the definition is as follows:
DRESP ID_NAME = all_lowest_eigenfrequencies DEF_TYPE = SYSTEM TYPE = DYN_FREQ_KREISSEL LC_SET = MODAL, ALL, ALL END_ OBJ_FUNC ID_NAME = maximize_eigenfrequencies DRESP = all_lowest_eigenfrequencies TARGET = MAX END_
If one has requested 10 eigenfrequencies in the finite element input model but only the first 5 eigenfrequencies are to be used in the optimization definition, then the design response for 5 eigenfrequencies is defined as follows:
DRESP ID_NAME = all_lowest_eigenfrequencies_1_5 DEF_TYPE = SYSTEM TYPE = DYN_FREQ_KREISSEL LC_SET = MODAL, ALL, 1-5 END_ OBJ_FUNC ID_NAME = maximize_eigenfrequencies_1_5 DRESP = all_lowest_eigenfrequencies_1_5 TARGET = MAX END_