This element is used to model an aerodynamic modal element, i.e. an unsteady aerodynamic model that inherits the structural motion from a modal element Its definition is very similar to that of the pure modal element, but it also includes some data representing unsteady aerodynamics in the time domain trough the residualization matrices. This element is defined as follows:
<element_type> ::= aeromodal
<element_arglist> ::= <label> ,
<modal node> ,
<reference modal joint> ,
(Mat3x3)<orientation> ,
<reference chord> ,
<number of aerodynamic states> ,
[ rigid , ]
<state space modal matrices file>
With this formulation, anytime an aeromodal element is defined,
the user needs to declare the number of modal aerodynamic elements
in use in the control data section.
An air properties
card definition is also required.
The keyword rigid indicates that the generalized aerodynamic forces provided by the model include global forces and moments associated to the rigid body motion of the underlying modal element (FIXME: untested).
There is also an optional gust model which is totally undocumented; for further information, please contact the Author(s).
The .fea file includes the state space model in form of matrices A, B, C, D0, D1 and D2, according to the representation
| = Ax + Bq | ||
| f | = q |
The file is formatted as follows:
*** MATRIX A
(<na> x <na> coefficients)
*** MATRIX B
(<na> x <ns> coefficients)
*** MATRIX C
(<ns> x <na> coefficients)
*** MATRIX D0
(<ns> x <ns> coefficients)
*** MATRIX D1
(<ns> x <ns> coefficients)
*** MATRIX D2
(<ns> x <ns> coefficients)
aeromodal: Wing, Wing, Wing,
eye,
131.25, 10, "ha145b.fea";
The aeromodal element is declared with the label Wing.
This element is attached to a modal node, also labeled
with the name Wing, and the reference modal joint
it is referred to is named Wing as well.
The orientation of the aerodynamic reference with respect
to the nodal reference is here expressed by the matrix eye.
The aerodynamic element chord is 131.25 (inches!).
This quantity must be consistent with the system chosen to define
the whole model (S.I., for example; in this case, British Units).
The next field, 10, indicates the number of states needed to use
the aerodynamic model.
The string ha145b.fea is the name of the file that contains
the state space model matrices, obtained with an approximation
chosen by the user.
In this particular case, a 10 states Padé approximation
has been chosen.
This example is taken from the Bisplinghoff Ashley Halfman
(BAH) Jet Transport Wing cantilevered wing with modal aerodynamic
frequency responce, computed by a double-lattice method at Mach 0.0.
Data were extracted from the MSC-NASTRAN aeroelastic example file,
named ha145b, while the aerodynamic state-space fitting
has been computed using a Padé polynomial approximation
(by Pasinetti & Mantegazza).
All quantities are expressed in inches and pounds.