Frequency Analysis of Simulation Data

1 Fourier Analysis

1.1 The Model

Consider a weak axis excited by a torque pulse train. The axis is modeled by three segments joined by two torsion springs. The following diagram is imported from the MathModelica Lite Graphic Editor where the model was defined. (See Section 15.8 in the Modelica Book).

Diagram: WeakAxis

loadModel(Modelica)
model WeakAxis import Modelica.Mechanics.Rotational; import Modelica.Blocks.Sources; Rotational.Sources.Torque torque1; Rotational.Components.Inertia inertia1(J = 1.0, phi(fixed = true), w(fixed = true)); Rotational.Components.Spring spring1(c=0.7); Rotational.Components.Inertia inertia2(J = 1.0, phi(fixed = true), w(fixed = true)); Rotational.Components.Spring spring2(c=1); Rotational.Components.Inertia inertia3(J = 1.0, phi(fixed = true), w(fixed = true)); Sources.Pulse pulse1(width=1,period=200); equation connect(pulse1.y, torque1.tau); connect(torque1.flange, inertia1.flange_a); connect(inertia1.flange_b,spring1.flange_a); connect(spring1.flange_b, inertia2.flange_a); connect(inertia2.flange_b,spring2.flange_a); connect(spring2.flange_b, inertia3.flange_a); end WeakAxis;

1.2 Simulation of WeakAxis

We simulate the model in 100 seconds ...

simulate( WeakAxis, stopTime=100 )

and plot the angular velocity of the rightmost axis-segment.

plot( { inertia3.w, torque1.tau } )