Four harmonic analysis methods are available: full, frequency-sweep via Variational Technology, frequency-sweep via Krylov, and mode-superposition. The memory requirements for the reduced methods that are meant for speed (Krylov, VT and MSUP) are similar, based mainly on the use of the sparse direct solver in the first computation step.
If the model has local nonlinearities, such as nonlinear springs (COMBIN39), the harmonic balance method can be used to obtain the multiharmonic steady-state solution (see the Harmonic Balance Method Analysis Guide).
A more computationally intensive method than solving the problem in the frequency domain consists of solving it in the time domain by performing a transient dynamic analysis with the harmonic loads specified as time-history loading functions (Applying Loads Using Tabular Input in the Basic Analysis Guide). For more information, see Transient Dynamic Analysis.
Note: For the auto (HROPT,AUTO), full (HROPT,FULL), frequency-sweep (HROPT,VT), and Krylov (HROPT,KRYLOV) methods, you can activate the frequency domain decomposition algorithm (DDOPTION,FREQ), which divides the specified frequency range into domains that are solved simultaneously. This feature uses distributed-memory parallel (DMP) processing and typically speeds up the harmonic analysis solution. The frequency domain decomposition method requires a lot of memory to run effectively.
The following topics summarize the four methods:
The full method (HROPT,FULL) is the easiest method for performing a harmonic analysis. It uses the full system matrices to calculate the harmonic response (no matrix reduction). The matrices may be symmetric or unsymmetric. The advantages of the full method are:
It is easy to use because you don't have choose mode shapes.
It uses full matrices, so no mass matrix approximation is involved.
It accommodates unsymmetric matrices, which are typical of applications such as acoustics and bearing problems.
It calculates all displacements and stresses in a single pass.
It accepts all types of loads: nodal forces, imposed (nonzero) displacements, and element loads (pressures and temperatures).
It supports frequency-dependent material (TB) and frequency-dependent element characteristics (such as COMBIN14 real constants).
A disadvantage is that this method is computationally expensive, particularly when you use the sparse solver. However, when you use the PCG solver, JCG solver or the ICCG solver, the full method can be more efficient in some 3D cases where the model is bulky and well-conditioned.
The frequency-sweep method (HROPT,VT) uses the underlying Variational Technology method, providing a high performance solution for forced-frequency simulations in structural analyses.
The frequency-sweep method is similar to the full method in that it uses the full system matrices to compute the harmonic response. Instead of using the full system matrices to calculate the results at the last requested frequency, however, the VT method calculates the harmonic solution at the middle of the requested frequency range, then interpolates the system matrices and loading on the entire frequency range to approximate the results across the range.
General Advantages:
No need to choose mode shapes.
Uses full matrices, so no mass approximation is involved.
Accommodates unsymmetric matrices, which are typical of applications such as acoustics and bearing problems.
Calculates all displacements and stresses in a single pass.
Accepts all types of loads: nodal forces, imposed (nonzero) displacements, and element loads (pressures and temperatures).
Advantages over the full method:
Support for structural analyses with frequency-dependent material properties.
Possible 2X to 5X performance improvement, depending on the model and hardware involved.
Possible 2X to 10X performance improvement for parameter changes.
Before a frequency-sweep harmonic analysis re-solve, you can:
Modify, add, or remove loads. (Constraints cannot change, although you can modify their values.)
Change materials and material properties.
Change section data and real constants.
Change geometry, although the mesh connectivity must remain the same (that is, mesh morphing).
Disadvantages:
Only the sparse solver is supported, which may be computationally demanding for larger problem sizes.
When requesting only a few frequency points, it is typically less efficient than the full method.
By default (HROPT,AUTO), the program automatically selects the most efficient method of these two: the full method (FULL) or the frequency sweep (VT) method.
In general, the frequency-sweep method is selected for most models except for the following situations where the full method is preferred:
When you use the
FREQARRoption of the HARFRQ command to specify frequencies to be evaluated during post-processing.When you use the WRFULL command to perform the assembly of the global matrices without solving.
Acoustic analyses that use an incident wave source.
The model contains MPC184 elements.
Loads or material properties are defined using table arrays or tabular functions.
When the stiffness, mass, and damping matrices are frequency-dependent (in most cases).
Models that include both viscous and hysteretic damping properties.
When the number of frequencies specified for postprocessing (NSUBST) is small (≤ 15). The efficiency of the frequency sweep method increases with respect to the number of frequency points you want to postprocess.
The frequency-sweep harmonic analysis based on the Krylov method provides a high performance solution for forced-frequency simulations in acoustic analyses. It can provide quick, estimated results compared to the Full method.
Both the full and the Krylov methods use the full system matrices to compute the harmonic response, but they differ as follows. For the full method, the full system matrices are used at every frequency point in the frequency range. Instead, the frequency-sweep Krylov method performs the following steps to approximate the results across the frequency range:
Builds a Krylov subspace set of vectors at a given frequency value (typically at the middle of the requested frequency range), and reduces the system matrices and loading on the entire frequency range.
Expands the results back to compute the harmonic response.
Note: The links above show details of these steps in customizable macros. The Krylov method can be implemented in a harmonic analysis by either Mechanical APDL commands or Customizable macros. For more details, see Frequency-Sweep Harmonic Analysis via the Krylov Method.
The first operation to build the subspace is more computationally expensive than solving at just one frequency with the full method, but the computations to solve the reduced system matrices throughout the frequency range are greatly accelerated compared to the full method. For this reason, the efficiency gain of the Krylov method over the full method becomes significant when solving for many frequency values.
General Advantages:
No need to choose mode shapes.
Uses full matrices, so no mass approximation is involved.
Accepts all types of loads: nodal forces, imposed (nonzero) displacements, and element loads.
Advantages over the full method:
Possible 2X to 10X performance improvement, depending on the model and hardware involved.
Disadvantages:
Less accurate than the full method since the Krylov method is meant to provide a fast approximate solution. Although there are steps to make it more accurate, they involve a computational cost and increased memory requirements.
Does not support unsymmetric matrices.
Only supports single-field structural or acoustic applications.
Only the sparse solver is supported, which may be computationally demanding for larger problem sizes.
When requesting only a few frequency points, it is typically less efficient than the full method.
The mode-superposition method (HROPT,MSUP) sums factored mode shapes (eigenvectors) from a modal analysis to calculate the structure's response. Its advantages are:
It is faster and less computationally intensive than the full and frequency-sweep methods for many problems.
Element loads applied in the preceding modal analysis can be applied in the harmonic analysis via the LVSCALE command.
It enables solutions to be clustered about the structure's natural frequencies. This results in a smoother, more accurate tracing of the response curve.
Prestress effects can be included.
It accepts modal damping (damping ratio as a function of frequency).
The calculation of the element results in a mode-superposition harmonic analysis for large models (large number of modes and/or large number of degrees of freedoms) and possibly having a large number of frequency points can be time consuming. The most effective method is to combine the modal element results directly during the expansion pass (MXPAND,ALL,,,YES,,YES). For details, see Option: Number of Modes to Expand (MXPAND).
All methods are subject to common restrictions:
All loads must be sinusoidally time-varying.
All loads must have the same frequency.
Nonlinearities are not permitted.
Transient effects are not calculated.
You can overcome any of these restrictions by performing a transient dynamic analysis with harmonic loads expressed as time-history loading functions.