A rectangular wing is allowed to pitch about the leading edge at a

frequency of $5$ Hz $.$ ZONA ZAERO program was used to generate the

M$=0\mathrm{.}8$ Sea Level Generalized Forces. The MATLAB Script

"SDOF$\_$Mpt$8\_$SetUp.m$"$ contains the list of Reduced Velocities $(1/$K$)$;

the Generalized Mass, the Generalized Stiffness and the Generalized

Forces that corresponds to each Reduced Velocity $(1//$K $).$ This is

uploaded to CANVAS Files Folder $-$ Homework.

A$.$ Plot the Real part of the Generalized Force versus Reduced

Frequency $($not Reduced Velocity $1//$K $)$

B$.$ Plot the Imaginary part of the Generalized Force versus Reduced

Frequency $($not Reduced Velocity $1/$K$)$

C$.$ Make a Plot of damping versus Velocity for the one mode

D$.$ Make a Plot of frequency $($Hz$)$ versus Velocity for the one mode

E$.$ From the plots estimate: a$)$ The flutter velocity and b$)$ the flutter

freauency $($Hz$)$

Use the following MATLAB code to solve the problem and modify wherever necessary

$\%$

$\%$ K$-$Method example of Single Degree of Freedom Flutter

$\%5$Hz pitching about leading edge, Mach Number $=0\mathrm{.}8,$ Sea Level

$\%$ Homework Problem

$\%$

$\%$ Dr$.$ Dale M$.$ Pitt Oct $27,2020$

$\%$

clear all

clc

$\%$ input reduced velocitities values this is also one over K

$\%$

red$\_$vel $=[0\mathrm{.}25000$

$0\mathrm{.}33333$

$0\mathrm{.}50000$

$1\mathrm{.}00000$

$1\mathrm{.}11111$

$1\mathrm{.}25000$

$1\mathrm{.}42857$

$1\mathrm{.}66667$

$2\mathrm{.}00000$

$2\mathrm{.}50000$

$3\mathrm{.}33333$

$5\mathrm{.}00000$

$10\mathrm{.}00000$

$11\mathrm{.}11111$

$12\mathrm{.}50000$

$14\mathrm{.}28571$

$16\mathrm{.}66667$

$20\mathrm{.}00000$

$25\mathrm{.}00000$

$33\mathrm{.}33333$

$50\mathrm{.}00000$

$100\mathrm{.}00000]$

$\%$

$\%$ input generalized forces from ZONA as separate real and imaginary

$\%$

GF$\_$R $=[-10\mathrm{.}952482$;

$-21\mathrm{.}418175$;

$-31\mathrm{.}816263$;

$-38\mathrm{.}725475$;

$-39\mathrm{.}393860$;

$-39\mathrm{.}456211$;

$-38\mathrm{.}456265$;

$-36\mathrm{.}278805$;

$-33\mathrm{.}378525$;

$-30\mathrm{.}656380$;

$-28\mathrm{.}998068$;

$-29\mathrm{.}066765$;

$-32\mathrm{.}165817$;

$-32\mathrm{.}810207$;

$-33\mathrm{.}544540$;

$-34\mathrm{.}366783$;

$-35\mathrm{.}276535$;

$-36\mathrm{.}253815$;

$-37\mathrm{.}272152$;

$-38\mathrm{.}270958$;

$-39\mathrm{.}177860$;

$-39\mathrm{.}864494]$

$\%$

$\%$ Input imaginary values

$\%$

GF$\_$I $=[-268\mathrm{.}830383$;

$-198\mathrm{.}631744$;

$-130\mathrm{.}907013$;

$-68\mathrm{.}017067$;

$-62\mathrm{.}534275$;

$-57\mathrm{.}619015$;

$-52\mathrm{.}857754$;

$-47\mathrm{.}517792$;

$-40\mathrm{.}866486$;

$-32\mathrm{.}615459$;

$-23\mathrm{.}049629$;

$-12\mathrm{.}682514$;

$-2\mathrm{.}183069$;

$-1\mathrm{.}235608$;

$-0\mathrm{.}358705$;

$0\mathrm{.}422297$;

$1\mathrm{.}067442$;

$1\mathrm{.}545521$;

$1\mathrm{.}801380$;

$1\mathrm{.}808200$;

$1\mathrm{.}496766$;

$0\mathrm{.}884520]$

$\%$

$\%$ combine the real and the imaginary terms

$\%$

QQ $=$ GF$\_$R $+$ GF$\_$I$*$sqrt$(-1)$

$\%$

m $=0\mathrm{.}005476664\%$ Generalized Mass from NASTRAN F$06$ Normal Mode Solution

k $=5\mathrm{.}408388\%$ Generalized Stiffness from NASTRAN F$06$ Normal Mode Solution

L $=2/2\%$ Reference length for the ZONA AICs based on semi chord