Continuing the Simulations

When we are in simulation mode the model editing is restricted. We can open any component for inspecting e.g. by double-clicking its title (or in other way), but changing the model including its parameters is disabled. The only exceptions to this rule are the input components - Source Effort, Source Flow and signal Input Generator. We can freely edit their constitutive relations and the local parameters (i.e. the parameter defined inside the component, not in the documents). When we close the component by clicking OK button the program automatically update the built in model and informs us on this by a message in Output window. In this way it is possible to continue the simulation to study the model behavior under different input conditions. If we wish to make the other changes in the model we must to close the simulation session by clicking the “stop” toolbar button, or select End Simulation command in Simulation menu, change the model and rebuild it. 

As an example we continue analyzing the behavior of Body Spring Damper Problem under a different external excitation. We assume the input force is sinusoidal, i.e.

Continuing the Simulations

where F0 is the force amplitude and ω the circular frequency of the applied harmonic force.  We will analyze the system response under different force's frequencies. We start by setting frequency equal to the natural frequency of the system (evaluated in Running Simulations) ω = 150 rad/s. This corresponds to the resonance and we expect that the amplitudes of body vibrations (after the transients has died out) rise to a rather high value, much larger than the static one,

Continuing the Simulations 

In order to find the response to such an input we double-click the SE port and type in the editing box (see Editing Project, Source Effort port dialog) F0*sin(w*t). The edit box accepts only ASCII characters, and thus, we use F0 for the amplitude of the driving force and instead of common symbol ω for the circular frequency we write “w”. We have to define the values of theses parameters. We do it in a similar way as we set parameters earlier. We click the Parameter button and in the Edit Parameters dialog windows that opens we type in the edit box at the top the symbol F0 and then click insert. In the dialog box that opens we type in the 500.0 as the value of the force amplitude (in N). We close the dialog by pressing OK button. Next, we type in w, insert it, and as the value we write 150.0; we close it again by OK button. Finally, we close Edit Parameter dialog by OK button, and Source Effort Port dialog also by OK. If we didn’t make errors in typing the new force constitutive relation is accepted and the program upgrades the built-in model and informs us on this.

Now we can repeat the simulation by pressing the Run command. We check the Restart button and as the simulation interval choose 1.0 s and set the output interval to 0.001 s for a better resolution. The results are shown in the figure below.

Response to harmonic driving force at the resonance (150 rad/s)
Continuing the Simulations

We see that the outputs now oscillate trying to follow the input. There is a transient in the amplitudes, which settle after about 0.3. The steady-state position amplitude has a large value, which is about five times of the static value found earlier.

We repeat the simulations using a much lower input frequency, e.g. w = 15 rad/s. Because the input frequency is now much lower we increase the simulation interval to e.g. 5s, retaining the other parameters values. The results are shown in the figure below on the left. Now we see that the body follows well the input force with the amplitude practically equal to the static value.

We repeat the simulation again by using this time much higher input frequency, e.g. w = 1500 rad/s. The results are shown in the figure below on the right. We see now that steady-state amplitude is very low (about 0.0444 mm), and thus the body cannot follows the input well. Because it is difficult to observe such a low value it appears as the body is not moving at all.

Responses to harmonic driving force at the frequencies: 15 rad/s (left)  and 1500 rad/s( right)
Continuing the SimulationsContinuing the Simulations