PSI- Issue 9

I. Shardakov et al. / Procedia Structural Integrity 9 (2018) 199–206 Author name / Structural Integrity Procedia 00 (2018) 000–000

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1. Introduction The reliability of the description of the deformation processes in the elements of reinforced concrete structures under dynamic loads is largely determined by the match between the elastic and dissipative characteristics of the model and the properties of the real material. The accuracy of specification the material characteristics is particularly important for concrete, since multiyear experience in civil engineering works suggests that the mechanical properties of concrete can vary considerably from one particular structure to another. It should be noted that this correlation is also important for interpreting the results of shock-vibration diagnostics of reinforced concrete structures allowing specialists to estimate their deformation state, Pandey (1991), Salawu (1997), Raghavan (2007), Wang (2009), Ng (2009), Fan (2011), Verma (2013), Stepinski (2013), Liu (2013), Bykov (2015), Quaranta (2016). There are various ways to determine the dynamic characteristics of concrete. Among them, one can distinguish methods, which are based on the measurement of the velocity of elastic wave propagation, ASTM C597/C597M-16 (2016), Lee (2017), and on the detection of decaying natural vibrations Zheng (2008), Ignat'kov (2011), ASTM C215-14 (2016). One of the main disadvantages of these methods is the idealization of the dynamic vibrational (or wave) deformation process in the mathematical interpretation of experimental measurements. As a rule, these mathematical models do not take into account a three-dimensional nature of the deformation state of a particular experimental specimen. This paper is devoted to the determination of parameters of viscoelastic concrete model, which is based on the interpretation of the results of recording the natural vibrations of a concrete specimen under impulse loading generated by an impact of the striker on the specimen. Experimental registration of velocity vibrograms on the specimen surface is performed using a laser vibrometer. The interpretation of experimental measurements is realized through the numerical solution of a three-dimensional initial-boundary problem of natural vibrations of a concrete specimen, the physical properties of which are described in the framework of a viscoelastic model. The required values of elastic and viscous properties of concrete are determined from the proposed iterative sequence of numerical solutions. 2. A mathematical model of natural vibrations of concrete specimen The model describes an impact load experiment, which is aimed at registering the natural vibrations of a concrete specimen under impulse load produced by a striker. The specimen made of concrete is shaped as a parallelepiped of length L, and square cross section with the side A (Fig. 1a). The volume of the specimen is denoted as V, and the surface of the striker- specimen contact is denoted as S  .

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Fig. 1. (a) Structural diagram of the concrete specimen; (b) pulse shape

The stress-strain state of a specimen hit by a striker is described by the following relations: – equilibrium equations in the Cartesian coordinates   1 2 3 , , x x x  x :