# The Sonic Resonance Method and the Impulse Excitation Technique: A Comparison Study
## 1 Introduction  
[PERSON]'s modulus is a mechanical quantity of great importance for solid materials. It depends on different external influences, in addition to the intrinsic properties of the measured material. Therefore, [PERSON]'s modulus allows an indirect study of, for example, the microstructure (porosity, texture) and the influences of some technological steps (drying or sintering) on ceramic materials. [PERSON]'s modulus is also a necessary quantity in some engineering calculations, e.g., in the determination of the critical rate of heating a ceramic body. The most commonly used methods for determining Young's modulus of metals, ceramics, concrete, glass, composites, and biological materials are dynamical methods. [PERSON] et al. [1] studied [PERSON]'s modulus of concrete containing basaltic aggregates using static and dynamic methods, such as the ultrasonic pulse velocity (UPV) and impulse excitation technique (IET). They found out that the dynamic [PERSON]'s moduli had higher values than the static moduli by approximately 16% for IET and 28% for UPV. Using IET, [PERSON] et al. [2] determined [PERSON]'s modulus of samples from basalt and diabase mines used as aggregates in the construction industry. Their results showed that values of [PERSON]'s modulus had high repeatability and agreed with those reported in the literature for the same material. Using IET, [PERSON] et al. [3] studied the dynamic Young's modulus of ZrB\({}_{2}\)-based composites containing MoSi\({}_{2}\) as a secondary phase up to 1430 \({}^{\circ}\)C. [PERSON] et al. [4] used IET to compare the microstructures of several glasses by measuring [PERSON]'s modulus and the internal friction as a function of temperature. [PERSON] et al. [5] investigated the validity of using the frequency and decay rate of free-free beam vibrations, which were measured by IET, to characterize the viscoelastic properties of glass in the temperature range of glass transition. [PERSON] et al. [6] used a traditional compression test and the ultrasonic and impulse excitation of vibration methods to compare and analyze [PERSON]'s modulus, [PERSON]'s modulus, and Poisson's ratio using alumina foam/tri-functional epoxyresin composites with an interpenetrating network structure. [PERSON] et al. [7] compared four different experimental techniques, namely, resonant ultrasound spectroscopy (RUS), impulse excitation, nanoindentation, and the four-point bending test to determine Young's and shear moduli of 99.9% pure Al\({}_{2}\)O\({}_{3}\), 7075 aluminum, 4140 steel, and Pyrex glass. They found that dynamic methods (RUS and IET) have superior precision and repeatability, and the differences between the results of RUS and IET were not statistically significant. [PERSON] et al. [8] compared the results from a resonance flexure method and from four-point static flexure tests for wood samples. Dynamical methods based on measurement of the resonant frequency of a vibrating sample are relatively simple and produce very low mechanical stress that does not initiate inelastic processes in tested material. Under such a low stress, the assumptions of the elastic theory of vibration are well fulfilled. Another advantage of these methods is their applicability for high temperature measurements [9; 10]. If resonant frequency is measured in a defined temperature regime, e.g., during heating/cooling with a constant rate, such measurement falls under thermal analysis and is called dynamical thermomechanical analysis (D-TMA). A rectangular prism or a rod with a circular cross-section, both having free ends, are commonly used for determination of Young's modulus. The longitudinal vibration or flexural vibration of such samples are possible for measurement purposes, but the flexural vibration is preferable because it can be easily excited, gives more intense amplitude, and the resonant frequency is lower compared to the longitudinal vibration. Two kinds of vibrations are used [11; 12]:  
1. Driven vibrations with a known frequency.