The following sections briefly describes the analysis types supported and multistage specific procedures:
The static analysis for the multistage procedure is similar to a standard static analysis. Multistage static analyses are valid for structural analyses as well as thermal analyses. Thermal analyses are only valid when using HI = 0 stages (multiharmonic is not supported). Note that thermal analyses using the radiosity solver method are not supported.
Multistage specific work such as stage preparation and application of loads is described in prior sections of this guide.
The following topics are discussed here:
Some static multistage analyses need to include multiple harmonics to accurately simulate the true physics of the system. Typical cyclic static structures use only harmonic index = 0 for a cyclic (HI = 0) load, but due to the different sector counts of stages, it may be necessary to add other contributing harmonics to generate more accurate modes and modal frequencies. For single and multiharmonic systems, only cyclically symmetric loading is supported, and loads must be applied only on HI=0.
Static loading in cyclic structures follows the harmonic index of the stage or stage clone. For example, consider a single physical stage. If one stage has a harmonic index of 0, all sectors of that stage will have the same applied load.
To maintain cyclically symmetric loading for multiharmonic groups with one or more stage clones, loads must be applied to only the HI = 0 stages. The following example demonstrates applying a rotational velocity to only HI = 0 stages.
Example 5.1: Command listing to apply a rotational velocity on a model with 2 stages
! Rotational velocity loading cmsel,s,_STAGE1_BASE_ELM ! Select base elements of first HI = 0 stage cmsel,a,_STAGE2_BASE_ELM ! Select base elements of additional HI = 0 stage cm,hi0_base_elm,elem cmomega,hi0_base_elm,,,50 ! Apply rotational velocity to component allsel,all
For multiharmonic cases that are the base step for a linear perturbation analysis, there may be multiple harmonic index = 0 stages (see Linear Perturbation Base Step). In this case, all HI = 0 stages must be loaded if the lead harmonic stage is loaded. However, if the load is applied to the lead harmonic base sector as a tabular load with NODE or ELEM primary variable, this load will be automatically copied to the harmonic index = 0 duplicate sector and all HI = 0 base and duplicate sectors of secondary harmonic stage clones during the solve. Only HI = 0 stages are permitted for a static base step that will be used for a linear perturbation analysis even if the downstream system is multiharmonic.
For multiharmonic static analyses that are not intended to be a base step for a linear perturbation analysis, stage harmonics other than 0 are permitted. In this case, loads may be applied to any stage harmonic, including those that are not HI = 0. These loads must be applied to each base and duplicate sector for any stages needed to create the desired load. However, if a load is applied to the lead harmonic base sector as a tabular load with MSHI as a primary variable, the loads will be automatically copied to the base and duplicate sectors of the appropriate stage to form a traveling wave (engine order) load. For details, see Harmonic Index-based Tabular Loads.
For tips on selecting possible stage clones to include in a multiharmonic system, see the links to a tutorial as well as tools to automate HI selection in Determining relevant harmonic indicies for modeling multiharmonic phenomena.
Note: Following a multistage analysis, a plot of the displacement (PLNSOL,U,SUM) at the interstage boundaries can be used to verify continuity and evaluate whether or not more harmonic stage clones need to be added to improve accuracy. For an example problem that details how to analyze possible displacement discontinuities at the interstage boundary, see Static Analysis of a 2-Stage Disk with Pinholes in the Mechanical Tutorials.
For a static analysis that is the base step for a downstream linear perturbation analysis, the only valid harmonic index is HI = 0. Use of another harmonic index will cause the updated matrices to become non-cyclic, invalidating the multistage assumptions.
If the linear perturbation base step is for a multiharmonic multistage analysis, you must create the same number of HI = 0 stage/stage clones for each physical stage. Furthermore, the number of stage and stage clones that must be created is equal to the maximum number of stage and stage clones for a given stage in the downstream linear perturbation analysis. For example, consider a 3 stage example. The stage and stage clones for the LP modal analysis are as follows:
Stage 1 : HI = 0, HI = 6
Stage 2 : HI = 0
Stage 3 : HI = 0, HI = 6, HI = 12
In this case, the maximum number of stage and stage clones is 3. The static base step must therefore have a stage and 2 stage clones for each physical stage as follows:
Stage 1: HI = 0, HI = 0, HI = 0
Stage 2: HI = 0, HI = 0, HI = 0
Stage 3: HI = 0, HI = 0, HI = 0
Including all these stage/stage clones ensures that the correct pre-stress state is calculated for each stage harmonic so that it can be used in the downstream linear perturbation analysis.
The modal analysis for the multistage procedure is similar to a standard modal analysis. Multistage specific work such as stage preparation and application of loads is described in prior sections of this guide.
The following sections describe some multistage modal specific procedural details:
For linear perturbation analyses without multiple harmonics, the procedure follows Figure 5.2: Process Flow for a Multistage (MS) Linear Perturbation Modal Analysis. In the static base step, there is one HI = 0 stage for each physical stage of system. After the system update (SOLVE, ELFORM), you can use MSOPT, MODIFY to change the harmonic indices to the desired modal harmonic indices. Then, the modal analysis can be solved.
The linear perturbation (LP) base step must be prepared according to Linear Perturbation Base Step. After the system has been updated (SOLVE,ELFORM), the unused stage clones should be deleted using MSOPT, DELE. The stages and stage clones that will be used in the LP modal analysis should be updated for the desired modal harmonic index using MSOPT, MODIFY. For details on this procedure, see Example: Multiharmonic Linear Perturbation Modal Analysis of a Simplified Model with 3 Axial Stages.
The harmonic response analysis for the multistage procedure is similar to a standard harmonic analysis. Two harmonic analysis methods are available, and the general guidelines for using those methods should be followed: full and mode-superposition harmonic analysis. General multistage-specific work such as stage preparation and application of loads is described in prior sections of this guide.
Specifics of a multistage harmonic analysis are discussed in the following sections:
Loading for a multistage harmonic response analysis follows the more general description of loading discussed in 4.3.2: Loads. You can apply various loads using the base and duplicate sector of each stage harmonic included in your multistage model. Since the harmonics contributing to the excitation and the response are not selected automatically, you must choose them as described in 3.1: Building the Model.
There are two ways to apply an engine order load (also known as a traveling wave):
manually apply the load to the base and duplicate sectors.
apply the load using an HI-based table, which eliminates the need to copy loads from the base sector to duplicate sectors or stage clones.
For an example problem that demonstrates both methods, see Linear Perturbation Harmonic Response Analysis of Two Stages.
You need to determine which harmonic is excited in order to apply an engine order load. For example, to manually apply an engine order 2 load to a physical stage with 6 sectors, you must apply the real load vector, F, to the base sector and the complex load vector, -i*F, where i is the unit imaginary number, to the duplicate sector of the HI = 2 stage clone.
When you apply a load to a given harmonic using an HI-based table that includes the multistage harmonic index (MSHI) as a primary variable, the load is automatically copied to the duplicate sector in a way that creates an engine order load (traveling wave). To apply a traveling wave in the reverse direction, specify a negative MSHI harmonic index number. Note that a positive value for MSHI will result in a backward traveling wave and a negative value for MSHI will result in a forward traveling wave. For a discussion and an illustration of the traveling wave sign convention, see Forcing Sign and Numbering Convention in the Theory Reference. For a detailed discussion on HI-based tables and an example snippet demonstrating how to create one and use it to apply an engine order load, see Harmonic Index-based Tabular Loads.
For a linear perturbation (LP) analysis without multiple harmonics, the procedure is similar to that of LP modal in the beginning steps (see Linear Perturbation Base Step). There is one HI = 0 stage for each physical stage of the system in the static base step. After regenerating the solution from the base analysis (SOLVE, ELFORM), change the harmonic indices to those desired for the harmonic response (MSOPT, MODIFY) and solve (SOLVE). The process is detailed in Figure 5.3: Process Flow for a Multistage (MS) Linear Perturbation Full Harmonic Response Analysis. For an example problem, see Linear Perturbation Harmonic Response Analysis of Two Stages.
Mode-superposition (MSUP) harmonic response analysis can be performed for multistage models. The beginning part of the procedure follows exactly the procedure for a multistage modal analysis. After a modal or LP modal analysis is performed, launch an MSUP harmonic response analysis using the modes from the modal analysis as a basis (HROPT,MSUP). Apply loads directly in the harmonic response solution or use a modal restart (ANTYPE,MODAL,REST) and issue the LVSCALE command in the harmonic response analysis. After completion of the MSUP harmonic response solution, perform the modal expansion first, followed by the multistage cyclic expansion. The procedure is detailed in Figure 5.4: Process Flow for a Multistage (MS) Linear Perturbation MSUP Harmonic Response Analysis. For an example problem, see Linear Perturbation Mode-superposition Harmonic Response Analysis of Two Stages.
Keep in mind the following tips and limitations:
Aerodamping is not supported.
Damping using MP,DMPR is prohibited.
Lumped mass formulation (LUMPM) is prohibited.
The following loads are not supported in the harmonic response solution part of the analysis, but may be applied as prestress loads:
The following tips and limitations apply only to multistage MSUP harmonic response analysis:
The only base analysis eigensolvers allowed for a MSUP harmonic response are: block Lanczos (MODOPT,LANB), PCG Lanczos (MODOPT,LANPCG) and subspace (MODOPT,SUBSP).
Be sure to extract all modes that may contribute to the harmonic response. As a general guideline, modes contributing to the harmonic response fall in the ½Ω - 2Ω range, where Ω is the harmonic frequency (HARFRQ) used in the subsequent harmonic solution.
When mode pairs are present, be sure to compute both modes of the pair in the modal analysis.
Mode selection (MODSELOPTION) is not supported.