2.3.5. Mechanical Vibration Damping Measurement

In general, vibration measurement methods are divided into contacting and contactless types [17–20]. The contactless vibration measurement methods can be performed using inductive, capacitive, optical (e.g., laser triangulation and laser interference), and ultrasonic sensors. They can be applied to measure deflections of rotary components, as well as higher vibration amplitudes and excitation frequencies compared to the contacting vibration measurements, which can be performed using piezoelectric and microelectro mechanical system (MEMS) accelerometers. The accelerometers are mounted directly on the vibrating component and are being used more widely due to the rapid development of electronic technology, accompanying secondary instrument, and low-noise cables, and their high insulation resistance and small capacitance.

The vibration damping properties of the investigated rubber composites can be examined by di fferent methods, namely using the free vibration method and by using harmonically excited vibration [21,22]. The free vibration method evaluates a material´s ability to dampen mechanical vibrations based on the logarithmic decrement δ and the damping ratio ζ. For harmonically excited vibration, which can be achieved under harmonic force or under the harmonic motion of a base, the vibration damping properties are characterized by the frequency dependencies of amplitude ratios (e.g., amplification factor or displacement transmissibility). The method involving harmonically excited vibration based on the response of a damped system under the harmonic motion of the base (so-called kinematic excitation), which is relatively simple, was applied in order to investigate the vibration damping properties of the studied rubber composites.

A material´s ability to damp mechanical vibration can be characterized by the transfer damping function *D* (dB), which is expressed by the following equation [23]:

$$D = 20 \cdot \log \frac{v\_{01}}{v\_{02}} \tag{1}$$

where *v*01 is the velocity amplitude on the input (i.e., excitation) side of the tested sample and *v*02 is the velocity amplitude on the output side of the tested sample. For harmonically excited vibration, it is also possible to express the transfer damping function as follows:

$$D = 20 \cdot \log \frac{y\_{01}}{y\_{02}} = 20 \cdot \log \frac{a\_{01}}{a\_{02}} \tag{2}$$

where *y*01 (*a*01) is the displacement (acceleration) amplitude on the input side of the tested sample and *y*02 (*a*02) is the displacement (acceleration) amplitude on the output side of the tested sample. There are three di fferent types of mechanical vibration depending on the transfer damping function value, namely damped ( *D* > 0), undamped ( *D* = 0), and resonance ( *D* < 0) vibration.

The mechanical vibration damping testing of the tested rubber composite materials was performed using the forced oscillation method. The transfer damping function was experimentally measured using the BK 4810 mini-shaker (Brüel and Kjær, Nærum, Denmark) in combination with a BK 3560-B-030 signal pulse multi-analyzer (Brüel and Kjær, Nærum, Denmark) and a BK 2706 power amplifier (Brüel and Kjær, Nærum, Denmark) at the frequency range of 2–3200 Hz (see Figure 1). Sine waves were generated by the mini-shaker. The acceleration amplitudes on the input and output sides of the investigated specimens were recorded by the BK 4393 A1 and A2 piezoelectric accelerometers (Brüel and Kjær, Nærum, Denmark). The accelerometers have these parameters: the frequency ranges from 0.5 to 16,500 Hz; the temperature range from −74 to 250 ◦C; and the weight is 2.4 g [24]. Measurements of the transfer damping function were performed for different inertial masses *m* (i.e., for 0, 90 and 500 g), which were located on the upper side of the harmonically loaded investigated samples (see Figure 1). Moreover, vibration damping properties of the investigated rubber samples with ground plane dimensions of 60 mm × 60 mm were performed for three different thicknesses (i.e., for 10, 15, and 20 mm) of these materials. The view of the experimental setup used for the vibration damping testing is shown in Figure 2. Each measurement was repeated 10 times at an ambient temperature of 22 ◦C.

**Figure 1.** Schematic diagram of the measuring device.

**Figure 2.** View of the experimental setup used for the vibration damping testing. Legend of the abbreviations: PC—personal computer; PULSE-signal pulse multi-analyzer; 2706—power amplifier; 4810—mini-shaker.
