Harmonic analysis is a technique used to determine the steady-state response of a linear structure to loads that vary sinusoidally (harmonically) with time. The objective is to calculate the structure's response at several frequencies and obtain a graph of some response quantity (usually displacements) versus frequency. "Peak" responses are then identified on the graph and stresses reviewed at those resonance frequencies.
This analysis technique calculates only the steady-state, forced vibrations of a structure. The transient vibrations, which occur when the load is applied, are not accounted for in a harmonic analysis. (See Figure 4.1: Harmonic Systems.)
Figure 4.1: Harmonic Systems
Typical harmonic system. Fo and Ω are known. uo and Φ are unknown (a). Transient and steady-state dynamic response of a structural system (b).
Harmonic analysis is a linear analysis in most cases. Geometric nonlinearities are usually ignored, even if they are defined. However, the following specificities are supported:
Unsymmetric system matrices such as those encountered in a fluid-structure interaction (FSI) problem. For more information, see the Acoustic Analysis Guide and the Coupled-Field Analysis Guide.
Local element-based nonlinearities (see the Harmonic Balance Method Analysis Guide).
Material nonlinearities, such as plasticity, are not supported. The following material specificities are supported:
Frequency-dependent properties such as elastic material or damping properties (data table TB). See Predefined Field Variables in the Material Reference.
Linear harmonic analysis can also be performed on a prestressed structure, assuming the harmonic stresses are much smaller than the preload ones. An example is the simulation of a violin string. See Prestressed Full-Harmonic Analysis Using the PSTRES Command (Legacy Procedure) and Linear Perturbation Analysis for more information on prestressed harmonic analyses.