Eigenfrequency Study
An eigenfrequency study solves for the natural frequencies and the corresponding mode shapes. It is also possible to compute the eigenfrequencies for a problem that is not fully constrained. This sometimes is referred to as free-free modes. In practice, the natural frequencies of the rigid-body modes are not computed as exactly zero, but can appear as small numbers, which can even be negative or complex valued. If the rigid-body modes are present in the model, then it is important to use a nonzero value in the Search for eigenfrequencies around field in the settings for the Eigenfrequency study step. The value should reflect the order of the magnitude of the first important nonzero eigenfrequency.
In the COMSOL Multiphysics Reference Manual:
•
Eigenvalue Solver
•
Studies and Solvers
•
Derived Values, Evaluation Groups, and Tables
In the Structural Mechanics Module User’s Guide:
•
Eigenfrequency Analysis
In rotordynamics, an eigenfrequency analysis is the most commonly used study type. It is used to determine the critical speed of the rotor. This type of analysis can be performed in the following scenarios:
•
To determine the stable operating ranges and critical speeds of the rotor. In this case, an eigenfrequency analysis is repeated multiple times by performing a sweep over the rotor’s angular speed to determine the resonance conditions of the rotor. An angular speed at which the rotor experiences a resonance is called a critical speed. A very important result of such an analysis is a plot of the variation of the natural frequency of the rotor versus the angular speed of the rotor, called a Campbell diagram.
•
To check if the assembly operates safely for a given operational speed. Sometimes, the operational angular velocity of a rotor is predetermined. In this case, the main interest lies in studying the behavior of the rotor at the given operational speed. You can then perform the eigenfrequency analysis at a given spin speed to check that none of the eigenfrequencies is close to it.
Prestressed Analysis
In a loaded structure the frequencies may be shifted due to stress stiffening. A rotor modeled with a Solid Rotor or Solid Rotor, Fixed Frame interface is always prestressed due to the frame acceleration forces. Therefore, it is extremely important to perform a prestressed analysis in these interfaces to get the correct natural frequencies.
Another scenario where a prestressed analysis is important is in modeling a nonlinear bearing behavior. Both fluid-film bearings and roller bearings have a nonlinear force displacement relationship. Thus, a prestressed analysis can be used to determine the natural frequencies of a rotor-bearing system about the static equilibrium position of the rotor. Roller bearings are also preloaded sometimes. A prestressed analysis also helps in using the linearized coefficients for a roller bearing about its preloaded state.