## 7 Conclusions  
The harmonic response of a beam supported at the ends with the FG viscoelastic bars is considered. The harmonic force is applied at the centre of the beam. The FG viscoelastic bars are connected to the end points of a beam by rotary joints to ensure that they work only in the axial direction. The effects of the length-varying material properties and internal damping of the FG bars on the force transmission \(\mathrm{T_{R}}\) and frequency parameters \(\lambda\) are examined in detail. No study has been found in the literature on the vibration of FG viscoelastic bar-supported beams subjected to a harmonic force at the centre point. The functional variation of the internal damping property between two different materials is defined depending on the Young's modulus and material damping. This study show that the longitudinally varying bar properties and the longitudinally varying internal damping coefficient are very effective on the dynamic behaviour of the beam. In the light of all the findings, the following observations can be made. It is seen that the longitudinal variation of the internal damping significantly reduces the responses compared to the normal internal damping which is naturally present in all materials. By selecting the appropriate material distribution with material distribution coefficient, better force transmission can be achieved from the pure material. The internal damping effect varies according to whether the vibration mode is bar-dominated or beam-dominated for the bar-supported beam. The internal damping ratio of the viscoelastic support bar has a significant effect on insulation. This is achieved by increasing the ratio for ratio > 1 and by decreasing the ratio for ratio < 1. The force transmission values are lower when ratio > 1 than when ratio < 1. The force transmission ratio (\(T_{R}\)) is lower when the part pressing on the ground has a larger internal damping. The transmission of force in bars with the material pairs _Al/Pb_ and _Pb/Al_ is an example of this situation. Between material pairs (as in the case of Pb/St and Al/Pb pairs), the force transfer characteristics change as the ratio of Young's modulus and internal damping coefficient closes to zero. By controlling the values of the internal damping ratio and material distribution coefficient of the bar, the system's frequency parameters can be increased or decreased, or a constant value can be maintained within certain ranges at high frequencies. The frequency parameters can remain nearly constant locally despite the changing value of the material distribution coefficient value. The frequency parameters generally increase with the increase in bar area. However, this situation is reversed after the bar effect is seen as a frequency parameter in the system. The effect of the bar area on force transmission depends on the vibration mode. The force transmission decreases with the increase in the bar area for the bar-dominant vibration mode. The force transmission gives minima at different area values for the beam dominant vibration mode. Experimental studies on material damping indicate that the damping is independent of velocity and increases in proportion to the square of the displacement. Therefore, in the case of material-dependent damping, the damping occurs at the same frequency. In the AFG viscoelastic bar, the effect of the material damping change is considered together with the specific mass and Young's modulus. The effect of material damping, which is only seen as a change in amplitude at the same frequency, begins to change based on frequencies. It is possible to minimise the force transmission for a certain frequency parameter by adjusting the stiffness, mass and internal damping distribution with the material coefficient in the frame of dynamic absorber logic. In future studies, the application of viscoelastic FG bars to functionally graded beams can be investigated. The ratios of the material change coefficients of two FG structures in isolation can provide important practical data.