Modal analysis results: Dynamic analysis

The motivation for a modal dynamic analysis is to characterise the dynamic response of a structure in discrete modes. Along with the mode shape (the eigenvectors) are the load factors (the natural frequencies). The “Global Results – Buckling Details” reports the following data:

• Frequency
• Modal mass
• Modal stiffness
• Total mass and inertia of structure
• Centre of mass
• Effective mass and inertia
• Participation factors

These terms are defined in the GSA Theory Manual.

The natural frequencies ($f$), modal stiffness ($k$) and modal mass ($m$) are related as follows:

$$f = \frac{1}{2\pi}\sqrt\frac{k}{m}$$

The effective masses can be used to check that sufficient modes have been chosen to capture the dynamic behaviour of the structure. In the limit the sum of the effective masses for each of the global direction should approach the total mass of the structure.