# Role of Piezoelectric Elements in Finding the Mechanical Properties of Solid Industrial Materials
## Using Piezoelectricity to Calculate Solid-Material Properties
### Shear Modulus of Elasticity  
For materials subjected to shear force, an important parameter that must be taken into account is the shear modulus of elasticity, which is defined as the ratio between shear stress to shear strain. Instead of using direct shear forces to excite the three samples of granular materials (Fontainebleau sand, first and second class of natural alluvial deposits of the Seine River) to measure the shear modulus of elasticity (\(G_{w}\)), refs. [103; 104] used a PE (bender elements) to generate and receive a shear wave. Moreover, they calculated the propagation time \(t_{w}\) (the time that the wave took to pass through the sand specimens) by recording the input and output electric signal on an oscilloscope. The equations below were used to calculate the shear modulus where \(L_{w}\) is the length between the tips of the bender elements and \(m\) is the unit mass of the materials.  
\[C_{S}\ =\ L_{w}/t_{w}\to G_{w}\ =\ m\ \times\ C_{S}^{2}.\]  
Then, the authors in [105] used PE as an emitter (1 and 10 MHz) and receiver of a shear wave but it was placed at opposite corners in the cubic and cylindrical specimens with the length of an isotropic cube side or cylinder height L\({}_{1}\) (10.1 mm brass cube of mass 8.175 g). This procedure was performed for many reasons, such as to provide a weak elastic couple (torsional couple) on the piezoelectric pieces and for minimum parasitic damping. Resonant ultrasound spectroscopy was also employed, which involved scanning the resonance structure (\(\gamma\)) for a compact specimen and then by using Equation (9) the shear modulus was calculated:  
\[G_{w}\ =\ \frac{\rho(\mathrm{L}_{1}\pi\mathrm{.}\gamma)^{2}}{2} \tag{9}\]  
The authors in [106] utilized PE(LiNbO\({}_{3}\)) to generate a wave from 300 kHz to 1 MHz with the Curie temperature at 1200 \({}^{\circ}\)Cto calculate \(G_{w}\) for metallic glass under this condition equation.  
An interesting study was conducted by [107; 108] to study the difference between the static and dynamic factors. Two couples of piezoelectric transducers were used as an actuator, which required a trigger with dimensions of 10 mm \(\times\) 10 mm \(\times\) 20 mm and an actual frequency of 69 kHz to generate a compressive wave (longitudinal wave (\(C_{L}\))) and shear waves \(C_{S}\). Three couples of piezoelectric transducers were used as a cylindrical accelerometer of 60 kHz with a diameter of 3.6 mm and a thickness of 3 mm to receive these waves. Two small piezoelectric-type bender elements was fixed first at the top of the cylindrical specimen (Toyoura sand, 5 cm in diameter and 10 cm in thickness), as shown in Figure 13, and the other at the bottom. The equation \(E_{D}=\rho\ \times\ C_{S}^{2}\) was considered as the equation of dynamic modulus of elasticity and \(G_{D}=\rho\ \times\ C_{L}^{2}\) as the equation of dynamic shear modulus of elasticity. For shear modulus, the results were in good agreement with the results from those that used \(C_{L}\) and \(C_{S}\) waves. However, for the dynamic modulus of elasticity, the results revealed  
Figure 12: [102] (**a**) Top view of all test systems. (**b**) Frame of the test system.  
a large difference between the dynamic and static values and the difference increased with increasing specimen density. Using the similar technique, the authors in [109] utilized three plate transducers of 3.9, 7.8, and 15.9 kHz to calculate G\({}_{\mathrm{D}}\) from the equation \(G_{D}=\rho\ \times\ C_{\mathrm{s}}^{2}\) for a soil.  
The authors in [2] reported using torsional resonant frequencies as a recent technique in this field to measure shear modulus for isotropic bars.  
\[f_{r}\ =\ \frac{C_{\mathrm{s}}}{2l}\ =\ \frac{\sqrt{(G_{w}/\rho)}}{2l}\]  
where \(f_{r}\) is the fundamental frequency of torsional resonance. PE has been used as an actuator (electro-mechanic) driver to excite both flexural and torsional vibrations in isotropic bars [110; 111; 112].