Product Version: OptiStruct 2021.2 or above
Flutter Analysis Setup
Aeroelastic flutter is a dynamic instability of a structure associated with the interaction of aerodynamic, elastic, and inertial loads. Flutter analysis of aeroelastic systems involves determining the velocity of the system and the frequency of oscillation at which the system attains the state of flutter. In this phenomenon, the aerodynamic loads on a flexible body couple with its natural modes of vibration to produce oscillatory motions with increasing amplitude.
For the aforementioned flutter analysis, OptiStruct uses the modal approach where the structural-vibration modes in a selected frequency range are used as the degrees of freedom. K, KE, PK and PKNL methods are supported in OptiStruct flutter analysis. For details of different methods, please refer to OptiStruct help>User Guide>Aeroelastic Analysis>Dynamic Aeroelastic Analysis.
In order to setup the flutter analysis in OptiStruct, users need to setup both the structural and aeroelastic domain components. The following chart summarizes the flutter analysis workflow.
Figure1: Flutter analysis workflow
The subsequent sections will discuss the setup in both structural and aeroelastic domains.
Since OptiStruct is using modal approach for flutter analysis, structural domain setup of the analysis is similar to analysis that based on modal space, such as modal frequency response analysis, modal transient analysis and etc. An EIGRL or EIGRA card is used to define the range of interested frequencies. The frequency lower limit in the EIGRL or EIGRA card can be set to zero to include rigid body modes. The general guideline for the frequency upper limit is 2 times the frequency of the highest mode of interest. For K method, an EIGC card for complex eigenvalue analysis is defined instead. Damping can be defined using SDAMPING, TABDMP, PARAM, G and PARAM, KDAMP. For PK method, definition of PARAM, G and PARAM, KDAMP, -1 will not be considered.
In order to setup flutter analysis, an AERO card is first created to define the basic parameters for dynamic aeroelasticity. The input format of AERO is shown below. The ACSID refers to an aerodynamic coordinate system. The airflow is expected to be in the positive X-direction and the lift direction in the positive Z-direction of a rectangular coordinate system. By default, the ACSID points to the global system. The VELOCITY is used for recovery of aerodynamics force data and for calculating the reduced frequency (see section 2.5). For analysis that involves a range of velocities, any velocity in the range can be used in for the setup.
Figure 2: Card format of AERO
The REFC in the 4th field is the reference chord length of the primary control surface. It is used to calculate the reduced frequencies. For a taper wing, the reference chord could be obtained by dividing the projected wing area by the wingspan. The RHOREF in the 5th field is the reference air density at the sea level. The subsequent symmetry entities fields are typically left blank by default.
The AERO entry can be created by first accessing the Aeroelasticity Browser, as shown in Figure 3, then, right click on Controls to create the AERO entry, as shown in Figure 4.
Figure 3: Accessing the Aeroelasticity Browser
Figure 4: Creation of the AERO entry
The aerodynamic elements or panels are defined using CAERO1. The CAERO1 requires definition of 2 leading edges (4 corners) as it is shown in Figure 6. The aerodynamic panels and corner nodes numbers/IDs need to be sequential and unique. This arrangement is automatically executed while creating CAERO1 using the Panel Mesh under Aeroelasticity ribbon in HyperWorks 2021.2 (see Figure 7). The associated PAERO1 properties will be created accordingly. It is recommended to have at least 10 aerodynamic panels along the edge (chord direction) and the aspect ratio should be less than 3.
Figure 5: Card format of CAERO1
Figure 6: Element ID arrangement of Aerodynamic Panel
Figure 7: Panel Mesh under Aeroelasticity ribbon
In version 2022, DMI with WKK/WTFACT option can be used to define diagonal weight coefficient matrix for aerodynamic panels (see Figure 8 below). The aerodynamics loads will be adjusted by multiplying the aerodynamic forces by the weighting matrix. The order in the weighting coefficient array corresponds to the order of the box numbers in the CAERO1 cards (as shown in Figure 6). When multiple CAERO cards are present, the box numbers set of each CAERO1 is arranged in ascending order of the CAERO1 IDs.
Figure 8: Panel Mesh under Aeroelasticity ribbon
The card formats of DMI are shown in the Figure 9. The NAME field will be WKK or WTFACT for flutter analysis. For more details, please refer to OptiStruct help>Reference Guide>Input Data>Bulk Data Section>DMI
Figure 9: Card format of DMI
In flutter analysis, SPLINE entities are used to couple the structural and aeroelastic domain definition. The SPLINE1 defines a surface spline for interpolating motions and forces between defined structural grids and aerodynamics panels. The SPLINE2 is used to define a beam spline and SPLINE4 is used to define a curved surface. The card formats of SPLINE1/SPLINE2/SPLINE4 are shown in the Figure 10, 11 and 12. The CAERO field of SPLINE entities points to CAERO1 aerodynamic panels ID. For SPLINE1 and SPLINE2, the BOX1 and BOX2, ID1 and ID2 should point to the first and last id of aerodynamic panels of interest. For SPLINE4, an AELIST set that includes aerodynamic elements of interest can first be created and then referred by SPLINE4.
Figure 10: Card format of SPLINE1
Figure 11: Card format of SPLINE2
Figure 12: Card format of SPLINE4
The SETG field points to a selected set of structural grids/nodes. Note that typically only one surface of the structural nodes is sufficient for the flutter analysis as shown in Figure 13. It is also not recommended to select all structural nodes in the projected area of aerodynamic panels. Some examples of the structural nodes selection are shown in Figure 14. The DZ field is generally set to 0.0 and subsequent fields are left blank by default. The SPLINE entities can be defined using Spline under the Aeroelasticity ribbon in HyperWorks 2021.2 as shown in Figure 15.
Figure 13: Structural grid selection for SPLINE
Figure 14: Structural grid selection of SPLINE
Figure 15: Spline under Aeroelasticity
The MKAERO1/MKAERO2 entries allow the calculation of aerodynamic matrix at specified velocities and reduced frequencies in the flutter analysis. The MKAERO1/MKAERO2 cards definition are shown in Figure 16 and 17. The velocities are defined in term of Mach number, airstream speed over the speed of sound. Note that the flutter analysis in OptiStruct is intended for subsonic condition (Mach < 0.8). The reduced frequency is a dimension less parameter that defined by the following equation:
where REFC is the reference chord length defined in the AERO card. ω is the angular frequency of structural natural frequency f and V is the velocity of the air stream. The range of the Mach numbers and reduced frequencies can be determined using the range of flight envelope operating velocities and the frequencies of modes of interested.
While MKAERO1 is used, aerodynamic matrices will be computed using all combination of Mach number and reduced frequency pairs from the supplied velocity and reduced frequency list. This is different from MKAERO2, where aerodynamic matrices will be computed only using the provided set of velocity and reduced frequency pairs.
The MKAERO entities can be created in the Aeroelasticity browser by right click on Controls as shown in Figure 18.
Figure 16: Card format of MKAERO1
Figure 17: Card format of MKAERO2
Figure 18: Creation of MKAERO entities
The FLUTTER will be used to define the MACH numbers, density ratios, reduced frequencies or velocities for the flutter analysis. For flutter analysis that is using K and KE Method, FLUTTER will refer to lists of MACH numbers, density ratios and reduced frequencies. For flutter analysis that uses PK and PKNL Method, FLUTTER will refer to lists of MACH numbers, density ratios and velocities. Each density ratio corresponds to an altitude. With the reference density defined in the AERO card, each density ratio would provide information of different air densities at different altitudes. The velocities are that referred by FLUTTER are true air speeds. PARAM, VREF is normally used to convert the unit of FE model velocities to a commonly used unit, for example, knots.
The list of MACH numbers, density ratios, reduced frequencies and velocities are defined using FLFACT cards. As an example, for futter analysis using PK method, FLUTTER will refer to a MACH FLFACT, a density ratio FLFACT and a velocity FLFACT. The card formats of the FLFACT and FLUTTER are shown in Figures 19 and 20. The METHOD field of FLUTTER specifies which method to use in the flutter analysis. The DENS, MACH and RFREQ/VEL fields, each refer to a FLFACT. The NVALUE enables control on number of modes in the output. For example, if the EIGRL setup extracted 40 modes, NVALUE could be set to 20 to only look at results of the first 20 modes.
Figure 19: Card format of FLFACT
Figure 20: Card format of FLUTTER
Note that the lists of MACH numbers, reduced frequencies and velocities in FLFACT should be within the range defined by MKAERO. The FLFACT entities can be created in the Aeroelasticity browser by right clicking on Controls as shown in Figure 21. Similarly, the FLUTTER entry can be created in the Aeroelasticity browser by right clicking on Aero Loads as shown in Figure 22.
Figure 21: Creation of the FLFACT entry
Figure 22: Creation of FLUTTER entry
Once FLUTTER is defined, it can be referred by FMETHOD in an Aerodynamic Flutter subcase as shown in Figure 23. The EIGRL/EIGRA defined in structural domain can be referred by METHOD and SDAMPING can point to TABDMP1 for damping definition. If K method is used for the flutter analysis, CMETHOD and EIGC is used instead of METHOD and EIGRL/EIGRA. Note that when SPC is not referring to any constraints as shown in Figure 23, there will be rigid modes from the eigenvalue analysis. Hence, body freedom flutter due to coupling of rigid body modes and elastic modes should be expected. With the Aerodynamic Flutter subcase defined, the flutter analysis setup is completed and ready to run.
Figure 23: Creation of FLUTTER entry
Flutter analysis creates a .flt file (as shown in Figure 24) in addition to the typical OptiStruct output .out file. In the .flt file, each point corresponds to a mode. As a result, if the NVALUE in FLUTTER is set to 20, there will be 20 points for each MACH number and density ratio (altitude) combination. For example, if there are 3 entries in MACH FLFACT and 4 entries in density ratio FLFACT in the FLUTTER definition, there will be 3 x 4 = 12 combinations. Depending on the number of reduced frequencies or velocities defined in FLFACT of FLUTTER, within each point, there will be corresponding lines of damping and frequencies info.
Figure 24: Flutter analysis summary from .flt file
Flutter instability occurs when the damping changes from negative to positive. In the above example, flutter instability occurs at point 2 (mode 2) between velocities of 470 and 480.
Due to the sheer amount of data, the h3d animation is not output by default. While using K method, DISPLACEMENT(H3D) = ALL output request is needed. For PK or PKNL method, additional negative sign for the velocities in FLFACT definition is required. In the above example, if users want to see the flutter mode animation, in the velocity FLFACT of FLUTTER, users could enter -470 and -480 instead of 470 and 480 in addition to the DISPLACEMENT output request.
The V-g, damping vs. velocity and V-f, frequency vs. velocity, are the 2 most common plots used to post process the flutter analysis results. HyperWorks 2021.2 can read the .flt from the flutter analysis to create both plots. The Flutter Curve under Aeroelasticity ribbon (as shown in Figure 25) can read the .flt in the steps shown in Figure 26 to create V-g curves shown in Figure 27.
Figure 25: Accessing the Flutter Curve Utility
Figure 26: Steps to plot the V-g curve in the Flutter Curve utility
Figure 27: V-g plot
From the above figure, it can be observed that point 2 (mode 2) become unstable at velocity around 475. The V-f plot can be created similarly by changing the Y-axis to FREQUENCY in step 4 of Figure 26.
Figure 28: V-f plot
From the above figure, the flutter instability could then be found to occur around a velocity of 475 and a frequency of 116Hz.
For more robust post processing, Compose script such as the one shown in Figure 29, could be used to convert the .flt into space delimited format. HyperGraph can then be used to create the V-g and V-f plot. In Figure 30, Templex function, intercepts() was first used to find the zero-crossing damping and the lininterp() was used to find the corresponding frequency by interpolation.
Figure 29: Compose script to convert flt file to space delimited format
Figure 30: V-g and V-f plot using HyperView
Besides the V-g and V-f plots, some other plots, such as Altitude vs Mach and EAS vs Mach are also used to check aircraft flutter stability performance. Both plots involve plotting flutter boundary lines on a flight envelope to ensure the flight envelope is clear of flutter instability. Figures 31 and 32 show the example of both types of plots. Results from OptiStruct flutter analysis can be used with HyperGraph to generate these plots.
Figure 31: Altitude vs Mach 
Figure 32: Equivalent Air Speed (EAS) vs Mach 
 Altair OptiStruct 2022.2 Help, Altair Engineering Inc, Troy MI USA
 Spivey, N., NASA Armstrong’s Structural Dynamics Airworthiness Processes for Aircraft, NESC Loads & Dynamics TDT Annual Face-to-Face Meeting San Diego, CA, 2015
 MIL-M-8856, Revision B, October 22, 1990 - MISSILES, GUIDED STRUCTURAL INTEGRITY GENERAL SPECIFICATION FOR