To run harmonic analysis, define the structure and load cases as linear static analysis. All load types available in the linear static analysis can also be defined in the harmonic analysis (including thermal loads, imposed displacements and others). The loads are interpreted as excitation force amplitudes, acting in the same phase as the user defined pulsation, frequency or period.
Displacement, internal force and reaction amplitudes are the results of the harmonic analysis.
For harmonic analysis cases, the nodal loads and mass matrix types are defined similarly to modal analysis.
The equation of motion being solved in the harmonic analysis is presented as follows (assuming structure damping is neglected):
(K - ω * ω * M) * Q = F
where:
w - excitation pulsation,
F - amplitudes of excitation forces acting with pulsation w: F(t) = F * sin(ωt).
The solution to this equation assumes that the displacement response is also harmonic and can be described as: Q(t) = Q * sin(ωt).
All forces F defined in the same load case act with the same pulsation w and are always in the same phase. If the structure is loaded with groups or forces acting with various pulsations, separate load cases should be defined (for each group). However, combination of obtained results should not be considered as those results do not have a physical interpretation due to different pulsations and phases.
It is possible to combine the results (with physical interpretation) of a single harmonic analysis case with any number of cases of other analysis types.
Harmonic Analysis without Damping
The extreme values of harmonic responses such as displacements, reactions, forces, moments, stresses, occur at the same time, without any time phase shift. These extreme values are available as results.
Harmonic Analysis with Non-Zero Damping
The extreme values of harmonic responses such as displacements, reactions, forces, moments, stresses, occur at a different moment in time, with non-zero time phase shifts. These time phase shifts can differ depending on a result component.
From 2019 release on:
- For this type of analysis, you obtain the results for 360 different time phase shifts (each 1 degree or 1/360 of the harmonic vibration period). This is due to the fact that, for example, the maximum UX displacement at a specific node can occur at a different moment in time (with a different time phase shift) with respect to the maximum UY displacement at this node. The maximum values are not reached simultaneously.
- The harmonic analysis load cases with non-zero damping are composed load cases including 360 components. To be precise, there are 361 components - the first component with a 0 phase angle is repeated as the last component with a 360 degree phase angle. You can access these components in the same way as the results of time history analysis. See Case component. You can also convert single components to simple load cases.