Modal Analysis Results

In a static analysis there is a unique set of displacement results. By contrast, in a modal analysis the displacements are mode shapes and so can be scaled by any constant and still represent a solution of the eigenproblem. Some method is required to decide on the scaling of the results and in GSA the results are scaled so that the maximum translational displacement at any node in the mode is 1m. (If there are no translation the results are scaled so that the maximum rotation at any node in 1 rad.)

Once the scaling for the modes is fixed there are a number of other results specific to modal analysis. These are described below.

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 (), modal stiffness () and modal mass () are related as follows:

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.

Buckling Analysis

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

• Load factor
• Modal stiffness
• Modal geometric stiffness

These terms are defined in the GSA Theory Manual section.

The load factor (), modal stiffness () and modal geometric stiffness () are related as follows:

Note that load factors may be positive or negative. Negative load factors are not a cause for concern, however if the loads leading to a negative load factor can be reversed the factor will become positive.