Experimental verification of the frequency method for evaluating the axial load and imperfection of boundary conditions in reinforcing bars

Evaluation of the forces and stiffness of joints is of fundamental importance for the control of rod elements of fastenings of the roof of mines, bridges, mesh shells and other structures. Existing evaluation methods are divided into static and dynamic. The paper considers a method for dynamic estimation of the longitudinal force and angular stiffness coefficients of the embedment of an imperfectly fixed rod according to the spectrum of its bending vibrations by comparing the experimentally recorded vibration frequencies with the theoretical frequency spectrum generated on the basis of the models of the Timoshenko beams. To match the results of the theoretical model with a set of experimental frequencies, a combination of well-known optimization algorithms based on global search and local minima is used. This approach is actively used, in particular, to analyze the working conditions of reinforcing bars in historical stone structures. In this work, an experimental verification of the dynamic technique was carried out on rod models with known values of the longitudinal force and the angular stiffness of the embedment. For this, two rods are considered as model samples. In one of them, predetermined longitudinal forces were created during tension in a testing machine. The other beam had the form of a cantilever with an end threaded fastening, according to the degree of tightening of which, controlled by the static deflection of the cantilever, the angular stiffness coefficient of the fastening was determined. As a result, depending on the parameters of the beam, the minimum number of recorded natural frequencies of its oscillations is determined, which is necessary for the dynamic estimation of the longitudinal force with an acceptable error. Also demonstrated is the dependence of the critical frequency of the Timoshenko beam from the internal force factor - the tensile force.