## 3 Materials and Methods  
The methodology used in this study is based on the propagation of an ultrasonic wave through the material with a single frequency and the detection of the higher-order harmonic signals at the other side, for measuring the second- and third-order harmonic amplitudes. To transmit the wave through the material, a narrow bandwidth transducer was used, driven at a certain frequency f. The ultrasonic waves propagated through the material were detected using a Laser Doppler Vibrometer (LDV).The scanning vibrometry system used in this study was PSV-400 by Polytec, equipped with a digital velocity decoder, with 8 velocity ranges from 1 mm/s/V to 50 mm/s/V and a maximum bandwidth of 350 KHz and two digital displacement decoders, one with bandwidth 0-2.5 MHz and another for high frequency measurements up to 24 MHz. LDV is commonly used for nondestructive flaw detection for the calculation of structural dynamics. Using a noncontact optical detection device like a laser Doppler Vibrometry presents certain advantages such as its high resolution in velocity and out-of-plane displacement measurements. The testing sample is not affected by the light that the vibrometer uses as a sensor, making it completely noninvasive and allowing measurements to be performed on any type of structure. LDV's operating principle is based on Doppler effect. In case of a wave reflected by a moving object, detected by a Laser Doppler Vibrometer, the frequency shift f\({}_{\text{D}}\) can be expressed as:  
\[\text{f}_{\text{D}}\;=\;2\;\frac{\
u}{\lambda} \tag{6}\]  
where \(v\) is the velocity of the object. \(\lambda\) is the wavelength. In addition, based on the principle of operation of a laser interferometer, the Doppler frequency shift should be measured at a known wavelength for the velocity of an object to be determined. The LDV's laser beam is directed to the surface of interest. Because of the motion of the surface, the Doppler frequency shift of the reflected laser beam leads to extracting the frequency and amplitude of vibration. In the present study, the measurements were performed on a mold that volumes 150 \(\times\) 170 \(\times\) 50 mm\({}^{3}\). During the initial 48 h of hydration data were recorded every 4 min. In total eighteen different mixtures were used with water to cement ratio equal to 0.5, while they were all enhanced with multiwalled carbon nanotubes. Nine mixtures of cement paste, three for each concentration of 0.2, 0.4, 0.6 wt.% of cement CNTs, and respectively nine mixtures for mortar mixtures with the same nanoreinforcement percentages. The multiwalled carbon nanotubes used in this study were synthesized by catalytic chemical vapor deposition (Shenzhen Nanotech Port Co. Ltd., Shenzhen, China). Their nominal physical properties are shown in Table 1. Viscocrete Ultra 300 (Sika AG, Baar, Switzerland) was selected as dispersion agent because of its efficiency in carbon-based materials' production [48]. For the production of nanocomposite cement pastes and mortars, the superplasticizer and tubes were mixed in regular tap water at a mass ratio of 1.5/1 and then magnetically stirred for 2 min. The resulting liquid suspensions were then ultrasonicated for 90 min at room temperature using a Hielscher UP400S ultrasonicator (Hielscher Ultrasonics GmbH, Teltow, Germany) equipped with a cylindrical O22 mm sonotrode, which delivers a 4500 J/min power throughput at a frequency of 24 kHz. The ultrasonicated suspensions were next transferred into a vacuum desiccator for the complete removal of entrapped air prior to mixing with sand and cement. The suspension was placed into a rotary mixer, where it was blended according to BS EN 196-1 standard. Ordinary Portland cement (OPC type I-42.5N) was used in the case of cement paste. As it was mentioned before, the water to cement ratio was 0.5, both for pastes and mortars. Natural sand was additionally used for mortars, where sand to cement ratio equals 3.