## 2 Materials and Methods
In order to determine a parameter, more resonance frequencies must be searched [25]. This requires a lot of computational calculation time and repeated tests. The same number of normal modes for a short cylinder compared with a long cylinder requires a narrower frequency range. In the case of cylindrical samples, having diameter approximately equal with height, the first mode is the fundamental torsional mode allowing the direct determination of shear modulus. RUS involves scanning the resonance structure of a compact specimen (in our case a ceramic cylinder) with the aim of determining its mechanical properties [28; 29]. In principle, RUS is composed of three parts. Successful use of this method implies the obtaining of a resonant ultrasound spectrum, meaning obtaining the frequency answer for a certain excitation for the analyzed sample. It is necessary to develop a computing method which can help in predicting the resonant ultrasound spectrum for the estimated parameters. The third component represents the iterative refinement of the estimated parameters, in agreement with the measured spectrum. Each of the steps mentioned above have multiple solutions. In the classical RUS experiment, a sample is placed between two US transducers. The primary advantages of this contact technique are its relative simplicity and low cost. For the RUS method, the samples have been supported by two identical piezoelectric ultrasonic transducers, for emission and reception respectively, placed at the opposite ends of the cylindrical sample (see Figure 1). The measurements are carried out via transducers with contact. The coupling of the transducer with the specimen influences which modes are measured. When the sample is pinned on its edge, more modes are excited and the modes are better defined than when the transducers are placed on the ends of the cylinder. The probe is fixed between the emission and reception transducers in order to accomplish the condition of a stress free surface. The equipment allows the setting so that for the established position of the cylindrical sample, the contact on the edge assures the excitation of a maximum number of possible resonances for the fixed geometry. A Network/Spectrum/Impedance Analyzer 4395A (Agilent Technologies, Santa Clara, CA, USA), generates a sweep frequency ranging between 80 and 250 kHz with a 1 kHz step. The signal is amplified using a Power amplifier AG 1012 (T&C Power Conversion Inc., Rochester, NY, USA) and applied to the US emission transducer is applied to the B port of the 4395 A Agilent, the spectrum being acquired by a PC used to program the functioning of the equipment as well with a numerical code developed in Matlab 2012b (The MathWorks Inc., Natick, MA, USA, 2012) via a PCIB interface (National Instruments, Mopac Expwy, Austin, TX, USA). The command of the power amplifier is made using the same PC via a RS232 interface (National Instruments). For the determination of the elasticity and shear moduli of the samples, the propagation speed of the longitudinal and transversal ultrasound waves were measured using a transmission procedure. The emission transducer is applied at one base of the sample via a delay line from Perspex(r) (Perspex Acrylic Brand, Darwen, Lancashire, UK) 20 mm in length, while the reception transducer is applied on the other base. A G5 KB GE transducer (General Electric Measurement & Control, Boston, MA, USA) with a central frequency of 5 MHz has been used for the measurement of the propagation speed of the longitudinal waves, the coupling being made using a ZG-F Krautkramer (General Electric Measurement & Control, Boston, MA, USA), whereas for the transversal waves, a MB4Y GE transducer (General Electric Measurement & Control, Boston, MA, USA) was used, with a central frequency of 4 MHz, the coupling being made with honey. The generation of emission impulses and the reception of signals delivered by the reception transducer has been made using a PR 5073 Pulser Receiver former Panametrics NDT USA (Olympus Corporation Waltham, MA, USA).