Modal analysis

Linear Analysis, FRF - Modal analysis

Modal analysis is the study of the dynamic properties of systems in the frequency domain. The goal of modal analysis in mechanics is to determine the natural mode shapes and frequencies of an object or structure during free vibration. The types of equations which arise from modal analysis are those seen in eigensystems. The physical interpretation of the eigenvalues and eigenvectors which come from solving the system are that they represent the frequencies and corresponding mode shapes. Sometimes, the only desired modes are the lowest frequencies because they can be the most prominent modes at which the object will vibrate, dominating all the higher frequency modes.

To perform modal analysis of the equivalent linear system which is obtained at a linearization time, select the FRF - Modal analysis item in the Linear Analysis menu.

Figure 28: FRF - Modal analysis item in the toolbar

This opens a dedicated window that contains a set of tools to analyze the dynamics of your system in the frequency domain.

Figure 29: FRF - Modal analysis tools

The result visualization are displayed according to the linearization time and the result set selected from the drop-down lists.

The global update button in the toolbar or the update after simulation option allows to refresh the drop-down lists with the latest available simulation results.

There are three main parts:

• Eigenvalues The eigenvalues of a state space model represents the natural frequencies, also know as eigenfrequency, of a physical system. The analysis of these specific frequencies allows to predict the resonance phenomenon of the system occurring at the natural frequency, as well as the amplitude of the oscillation thanks to the damping ratio.

• Top contributing states The top contributing states table lists the top 5 state variables of the model that govern the selected current eigenvalue. They are determined by the modal participation factors that are calculated from the eigenvectors and that measure the interaction between the eigenvalues and the state variables.

• Frequency response function The frequency diagrams allows you to analyze the frequency response of the equivalent linear system. The frequency response function describes the relationship between the inputs (control variables) and the outputs (observer variables) of a system in the frequency domain.