**Figure 16: Simplification of the structure with an elastic mounting of the excitation and a tuned mass-damper**

**Implementation in Simulink ^{®}:**

By this means a Simulink

^{®}simulation model due to the previous evaluated parameters for the isolation is set up. For the mass of the tuned mass-damper m

_{i}= 100 kg is used. The stiffness is set up with regards to the governing resonance in the operating range of the machine at f

_{1}= 32.3 Hz By this means a stiffness of k

_{t}=(f

_{1}2π)^2 * m

_{t}= 4.1187e6 N/m is used. The resulting Simulink® block-diagram of the damped harmonic oscillator with combination of the isolation and the tuned mass-damper is pictured in Figure 15.

**Figure 17: Simulink**

^{®}block-diagram of the damped harmonic oscillator with the combination of the elastic mounting and the tuned mass-damper**Result:**

For time-domain simulations a Simulink^{®} model is implemented as seen in Figure 17. For the parametrization the properties listed in Table 1 are used.

**[FREQ,AMPL,PHAS]=ma_frequency_response(ScopeData.time, ScopeData.signals(1).values,
ScopeData.signals(3).values,{0,50});
[FREQ_Damping,AMPL_Damping,PHAS_Damping]=ma_frequency_response(ScopeData_Damping.time,
ScopeData_Damping.signals(1).values, ScopeData_Damping.signals(3).values,{0,50});
[FREQ_Isolation,AMPL_Isolation,PHAS_Isolation]=ma_frequency_response(ScopeData_Isolation.time, ScopeData_Isolation.signals(1).values, ScopeData_Isolation.signals(3).values,{0,50});
[FREQ_Combination,AMPL_Combination,PHAS_Combination]=ma_frequency_response(ScopeData_Combination.time, ScopeData_Combination.signals(1).values, ScopeData_Combination.signals(3).values,{0,50});
**

figure

semilogy(FREQ,AMPL,’k’,’LineWidth’,2); hold on;

semilogy(FREQ_Damping,AMPL_Damping,’b’,’LineWidth’,2);

semilogy(FREQ_Isolation,AMPL_Isolation,’r’,’LineWidth’,2);

semilogy(FREQ_Combination,AMPL_Combination,’g’,’LineWidth’,2);

hold off;

grid on

xlabel(‘Frequency in Hz’)

ylabel(‘Amplitude in m/N’)

legend(‘Stiff coupling’,’Mass-damper (\xi=5%)’,’Isolation’,’Combination’,’Location’,’SouthWest’)

xlim([5 50])

Figure 18: Frequency domain results in with a mass-damper, isolation and the combination of both |

In Figure 18 the different measures are compared in the frequency domain. The tuned mass-damper results in an efficient reduction of the combined resonance of the structure and the machine. Nevertheless still either neighboring double-peaks remain or the effect is reduced. The isolation reduces the resonance better and shifts the frequency higher and still to a higher amplitude, than the stiff coupling. This resonance can reduced due to the use of an additional mass-damper tuned to the remaining resonance. This way the combination shows practical no disadvantage in regard of an increasing peak over the base level of the stiff coupling.