Important Information

Structural Dynamics Finite Element Model

A finite element model (FEM) in MSC Nastran has been generated to emulate the structural dynamics of the BSCW mounted on the PAPA system. The model was based on the structural dynamic properties reported previously. The FEM consists of a nearly rigid flat plate of the same planform dimensions as the PAPA wing, connected to a fixed point with two simulated springs at the axis of pitch rotation, as shown in the cartoon below. The axis of rotation is located at the same point at the axis of rotation for the PAPA flutter test, 8 inches from the leading edge, at the 50% chord. Fifteen grid points, form 8 CQUAD elements that are each 1 inch thick made of an invented light and stiff material. The structural grid points are laid out in a matrix: 3 chord-wise grid points; 5 span-wise grid points. Grid point 2 is located at the wing root at the axis of rotation and is constrained in 4 degrees of freedom, allowing only movement in the vertical translation and pitch rotation directions. i.e. it is constrained in the following degrees of freedom: translation in the flow-wise and span-wise directions, rotation in the yaw and roll directions, (i.e. degrees of freedom 1,2,4 and 6).

The overall mass properties and the spring constants values were specified to match the values defined in the experimental data report. The plunge spring stiffness was set to 219.75 slinch/s^2; the pitch spring stiffness was set to 35568.slinch-in^2/s^2/rad. The mass properties were established using concentrated masses at each of the grid points and a concentrated inertia at grid point 2. The distribution of the concentrated masses was generated to match the wing total mass, the wing total pitch inertia and place the center of gravity to correspond with the pitch rotational axis at the chord-wise center. From the experimental data report, the mass of the wing is 6.0237 slugs or 0.502 slinches; the pitch inertia is 2.777 slug-ft2 or 33.324 slinch-in2. Normal modes analysis of the FEM shows that the overall mass properties and the frequencies of the plunge and pitch mode match the measured values. The plunge mode has a frequency of 3.33 Hz; the pitch mode has a frequency of 5.20 Hz.

The plunge and pitch modes of the system are shown in plots below. Three levels of structural model are available for workshop participants: a detailed FEM, the FEM-extracted modal definition, and the mode shapes interpolated onto the provided grids. In addition, the organizing committee can interpolate the mode shapes onto additional grids, if requested, eliminating a possible source of differences among the solutions.