FLUTTER

Bulk Data Entry Used to specify the parameters required for aerodynamic flutter analysis.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
FLUTTER	`ID`	`METHOD`	`DENS`	`MACH`	`RFREQ`/`VEL`	`IMETH`	`NVALUE`	`EPS`

Example

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
FLUTTER	1001	K	1002	1003	1004	L	10	1.0E-6

Definitions

Field	Contents	SI Unit Example
`ID`	Unique identification number. No default (Integer > 0)
`METHOD`	Method for flutter analysis. 5 6 7 K K method. 2 PK PK method. PKNL PK method without looping. KE K method restricted for efficiency. No default (Character)
`DENS`	ID of an FLFACT Bulk Data Entry. This FLFACT entry must specify the density ratios to be used for the flutter analysis. 3 No default (Integer > 0)
`MACH`	ID of an FLFACT Bulk Data Entry. This FLFACT entry must specify the Mach numbers (M) to be used for the flutter analysis. No default (Integer > 0)
`RFREQ`/`VEL`	ID of an FLFACT Bulk Data Entry. K, KE FLFACT entry must specify the list of reduced frequencies (k) to be used for the flutter analysis. PK, PKNL FLFACT entry must specify the list of velocities to be used for the flutter analysis. No default (Integer > 0)
`IMETH`	Interpolation method for aerodynamic matrix interpolation. 9 L (Default) Linear interpolation. S Surface interpolation. (Character)
`NVALUE`	Number of Eigenvalues for the output. Default = number of modal degrees of freedom from a normal modes analysis (Integer > 0)
`EPS`	Convergence tolerance for PK and PKNL methods. K and KE methods do not involve iterations and; therefore, a tolerance is not applicable for them. Default = 1.0E-3 (Real > 0.0)

Comments

The FLUTTER Bulk Data Entry must be referenced the FMETHOD Subcase Information Entry.
When the K method is used, the CMETHOD Subcase Entry must reference a suitable EIGC Bulk Data Entry. As a general recommendation, the number of roots in EIGC must be twice the number of normal modes used in the modal flutter analysis.
Using the density ratio from the FLFACT entry and the reference density (RHOREF in AERO Bulk Data Entry), the density is:(1)
$D e n s i t y = D E N S * R H O R E F$
The reduced frequency is:(2)
$k = \frac{ω R E F C}{2 V}$

Where,

$R E F C$

Reference length for reduced frequency (from AERO Bulk Data Entry).

$ω$

Circular frequency.

$V$

Velocity.
When PK or PKNL method is used, an eigenvalue is accepted based on the following condition:
$| k - k_{e s t i m a t e} | < E P S$ , when $k_{e s t i m a t e} < 1.0$

$| k - k_{e s t i m a t e} | < E P S - k_{e s t i m a t e}$ , when $k_{e s t i m a t e} \geq 1.0$
Depending on the method, FLFACT entries will be used differently.
- For the K and KE methods – all combinations of FLFACT entries $(ρ_{i}, M_{i}, k_{i})$ will be analyzed.
- For the PK method – all combinations of FLFACT entries $(ρ_{i}, M_{i}, V_{i})$ will be analyzed.
- For the PKNL method – only ordered pairs of FLFACT entries $(ρ_{1}, M_{1}, V_{1})$ , $(ρ_{2}, M_{2}, V_{2})$ , … $(ρ_{n}, M_{n}, V_{n})$ } will be analyzed. Therefore, the number of density ratios, Mach numbers and velocities must be the same.
Let [M], [B] and [K] denote the mass, damping and stiffness matrices.
- The PK method uses only real matrix terms among the above-mentioned matrices for computing the flutter solution. Imaginary terms will be ignored, and the imaginary part of the aerodynamic matrix is added as a real matrix to the viscous damping matrix B.
- With the KE method, the B matrix is ignored while complex stiffness forms of structural damping are supported. To account for modal viscous damping (TABDMP1), PARAM, KDAMP must be set to -1.
- All forms of damping are supported with the K method.
If IMETH = L, a linear interpolation is performed on reduced frequencies at the Mach numbers specified on the FLFACT entry, using the MKAEROi entry Mach number that is closest to the FLFACT entry Mach number.
For IMETH = S, a surface interpolation is performed across Mach numbers and reduced frequencies. IMETH = S is only available for the K and KE flutter methods.

For METHOD = PK or PKNL, a special linear interpolation is performed.
For K and KE methods, at least 2 Mach numbers must be specified in MKAERO1/MKAERO2 entries, for the purpose of interpolation.