If all sources are removed from a frequency-domain equation, its solution becomes zero for all but a discrete set of angular frequencies ω, where the solution has a well-defined shape but undefined magnitude. These solutions are known as eigenmodes and the corresponding frequencies as eigenfrequencies.

The eigenmodes and eigenfrequencies have many interesting mathematical properties, but also direct physical significance because they identify the resonance frequency (or frequencies) of the structure. When approaching a resonance frequency in a harmonically-driven problem, a weaker and weaker source is needed to maintain a given response level. At the actual eigenfrequency, the time-harmonic problem loses the uniqueness of the solution for a nonzero excitation.

Select the Eigenfrequency study type () when you are interested in the resonance frequencies of the acoustic domain or the structure, whether you want to exploit them, as in a musical instrument, or avoid them, as in a reactive muffler or inside a hifi speaker system. To an engineer, the distribution of eigenfrequencies and the shape of eigenmodes can also give a good first impression about the behavior of a system.

An eigenfrequency analysis solves for the eigenfrequencies and the shape of the eigenmodes. When performing an eigenfrequency analysis, specify whether to look at the mathematically more fundamental eigenvalue λ (available as the variable lambda) or the eigenfrequency f which is more commonly used in an acoustics context:

In certain circumstances the material properties and/or boundary conditions can be frequency dependent. This is the case if the model built with The Pressure Acoustics, Frequency Domain Interface contains a Narrow Region Acoustics or a Poroacoustics equivalent fluid model. The same happens if, for example, the Impedance boundary condition is added: most of the options listed in Theory for the Boundary Impedance Models define the acoustic impedance as a function of frequency. Should the frequency dependence be nonlinear, this will lead to a nonlinear eigenvalue problem which is more complex and therefore often must be treated carefully.

The default Transform point value used in the Acoustics interfaces is 100 Hz. If the eigenfrequencies of interest lie in kHz or MHz range, the default value of the linearization point may not ensure an accurate solution of a nonlinear eigenvalue problem – depending on its nonlinear properties. In this case, it is a good practice to move the linearization point closer to the range of desired eigenfrequencies. For example, it can be the mean of the range. The other option is to define the Transform point as a parameter, for example TP, add a Parametric Sweep over this parameter to the Study, and search for one eigenfrequency around TP. This approach will be more accurate if the model exhibits strong nonlinear behavior within the range of desired eigenfrequencies, so that having a constant linearization point in not enough.