# Role of Piezoelectric Elements in Finding the Mechanical Properties of Solid Industrial Materials
## Using Piezoelectricity to Calculate Solid-Material Properties
### Longitudinal Velocity of Sound
In addition, they illustrated a behavior of longitudinal and transfer waves with a different molar ratio of silica aerogels, where, silica aerogels was a function of molar ratios of tetramethylasilane (TMOS) precursor, ammonia (NH4 OH) catalyst, methanol (MeOH) solvent, and water, as shown in Figure 7.  
Authors in [73; 74] studied an air-coupling technique to explain the effect of velocities of transferred longitudinal waves on different samples of paper as shown in Figure 8. These paper samples involved differences in density from 80 g/m\({}^{3}\) to 300 g/m\({}^{3}\) and difference in magnitudes of angles for the paper (angle of inclination of the paper). Two pairs of specially designed air-coupled piezoelectric transducers were used as emitters and receivers. The center frequency was 0.9 MHz for one pair and 1.7 MHz for the other. The active elements were 1 to 3 piezocomposite disks made by the dice and filling technique (PZ-26, Ferroperm and Araldite-D), which were 2-mm thick for the 0.9 MHz transducers and 1 mm thick for the 1.7 MHz transducers. Figure 7: Sound velocity in silica aerogel versus: (**a**) NH4 OH/TMOS molar ratio, (**b**) MeOH/TMOS molar ratio, and (**c**) H2O/TMOS molar ratio [72]. Using the same technique (air coupled), authors in [75] PE 750 kHz to show a good match between the theoretical calculations and the experimental results of the longitudinal behavior of the waves for the following materials(1) copper sheets with 0.35 mm width and 0.45 mm thickness (2) 0.1 mm width and 0.5 mm thickness, and finally (3) CW508L copper with width 0.0762 mm and thickness of 0.381 mm). PE with a resonance frequency of 7 MHz was employed by [76] as a transducer to investigate and measure the longitudinal sound waves in liquid and selenium. The authors in [77] succeeded to replace the disturbance force effects on a steel square plate (19 mm \(\times\) 19 mm \(\times\) 305 mm) by a PE with a center frequency of 2.2 MHz and attached it by using cyanoacrylate adhesive to create longitudinal sound waves. The transducer was driven by a five-cycle windowed sinusoid voltage waveform [78] where the used pulses generator in [76] was arbitrary. Waveform generatorscan produce waves of any shape such as the function in Equation (4). They noted the first arrival of the wave at 52.6 \(\upmu\)s, and this corresponded to the group velocity of sound in the steel (5.8 km/s). Equation (4) represents two sine waves multiplied together with the deference phase angle for producing modulated waves (Ton berst wave). \[C(t)\ =\ \left( \begin{array}{cc}c_{o}\sin(2\pi ft).\Big{(}\sin\frac{ft}{20 \pi}\Big{)}^{2}t\ <\frac{5}{7}\\ 0\ t\ \geq\ \frac{5}{7}\end{array} \right). \tag{4}\]  
The authors in [79] used longitudinal velocity, which was measured by utilizing two pieces of PE (one as an emitter and the other as a sensor) for a set of various Fe\({}_{4}\)Sb\({}_{12}\) and Co\({}_{4}\)Sb\({}_{12}\)-based skutterudites filled by mischmetal, didmium, or alkaline earths (Ca, Sr, and Ba) in order to calculate some of the mechanical properties which are: modulus of elasticity, transfer velocity, shear modulus of elasticity, bulk modulus, and Poisson's ratio for the above materials, where time-of-flight sound pulse measurements were performed on cylinders (height = 10 mm, diameter = 10 mm) with a frequency of 10 MHz were also measured. Recently, many researchers have considered piezoelectric shunt damping techniques as a renewable technology in this field, where the periodic arrays of shunted piezoelectric patches are utilized to control the wave host plate. The tunable characteristics that belong to shunted piezo-patches allow the band gaps to be tuned over desired frequency ranges. The authors in [80] used this technology to explain the mechanism of resonant piezoelectric shunt scan to be tuned over desired frequency ranges.