## 2 Overview of Theoretical and Experimental Methods  
Currently, there are many methods of non-destructive testing of concrete characteristics, including strength properties [1; 2; 3; 4; 5; 6; 7; 8]. Non-destructive research methods can be divided into direct methods for calculating a linear response of material structure, reflecting its properties, for example, hardness or elasticity under pressure, and indirect methods, implying the transmission of various wave pulses of energy through the body, functionally reflecting its characteristics. In these studies, various types of wave sources of oscillations can be used, including the transmitting and receiving of elements of the sensors. Based on the excitation type of oscillation sources, the methods of non-destructive testing can be characterized as (i) X-ray methods; (ii) electromagnetic methods; (iii) acoustic methods; (iv) impact methods; and (v) combined methods. Some of them are presented in reviews of works [5; 6; 7]. Most often in practice, acoustic and shock methods of non-destructive testing are used. The resonance and ultrasonic methods of non-destructive research of structural materials are examples of acoustic research methods. The resonance method is based on measuring and calculating the amplitudes and spectral characteristics of a structure, and also the damping decrement of small vibrations. The longitudinal, bending and torsional oscillations of a simple rod construction can be considered as idealized ones [6; 7; 8; 9; 10; 11; 12; 13]. The method consists of the following stages: (i) The vibration amplitudes are measured at several points of the construction at its stationary oscillations with the obtainment of dynamic images of the construction vibrations as output characteristics; (ii) the data of the vibration patterns are processed by using the analytical Fourier transform, and the vibration resonances are selected; (iii) using the application of inverse methods for restoring properties using analytical dependences, for example, based on the Bernoulli beam theory, one can calculate the elastic modulus \(E\), shear modulus \(G\) and Poisson's ratio \(\
u\) of the considered structure. The use of indirect analysis of the dependences of material properties, defectiveness, stiffness of individual nodes on the amplitudes \(E\sim f(A)\) and frequencies \(E\sim f(\omega_{n})\) can be obtained on the basis of analytical functional dependencies of regression analysis [14; 15; 16; 17]. The analytical and numerical methods of the oscillation theory allow us study the vibrations of elastic solids with a more complex shape [18; 19; 20]. A simpler method is the use of an acoustic non-destructive testing method based on measuring the speed of a propagating oscillation wave between two points, which in turn can be classified in the dependence on the relative position of the transmitting and receiving transducers of acoustic waves. The frequencies between 20 and 200 kHz represent the most commonly used frequency range for ultrasonic frequency analysis, applicable in practice. Practical approaches of various authors show the positive aspects of using ultrasonic scanning of materials [21; 22; 23]. Their applicability under certain conditions is determined by such details as access to the surface of the sample from only one or both sides, as well as the ability to test the required material properties (strength, presence or absence of defects, etc.). The physical quantities that must be measured in acoustic methods are wave velocity, damping and frequency spectrum composition. In this case, the most sensitive measurements are the direct changes in the wave, propagating from a vibration source to a receiver. The longitudinal \(V_{L}\) and the transverse \(V_{T}\) velocities of sound are measured between the amplitude peaks of the propagation of the excited wave with the corresponding oscillation mode through two points. A review of works on the estimation of the dependences of strength of concrete \(R_{c}\) on velocity parameters is presented in [24; 25].