PSI - Issue 28

Liudmila Igusheva et al. / Procedia Structural Integrity 28 (2020) 1303–1309 L. Igusheva, Y. Petrov / Structural Integrity Procedia 00 (2019) 000–000

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There are many models that describe the interaction of bodies with the medium, but the calculation of deformations and stresses under dynamic load takes a special place since many materials exhibit non-classical behavior under dynamic loads. It is also important to calculate critical stresses to prevent unplanned structural failure under dynamic operating conditions. This work is devoted to the study of the effects resulting from dynamic deformation of a rod in contact with an elastic environment. A one-dimensional model is used to calculate the stresses and strains that occur in the rod. Elastic and viscoelastic models of longitudinal vibrations of the rod are considered. A detailed description of the analytical solutions made, as well as the results of computer modeling, is given. Deformations and stresses in the rod are investigated. The critical values of stresses that cause rod fracture are studied. The simulation results are compared with the effects obtained in the course of known experiments. A good correspondence between the results of the theoretical calculation and the experiment was found, which confirms the possibility of using the model in question for applied purposes. 2. Rods in environments Rods are the main elements of a huge number of engineering structures. Often structures are located in different environments. Therefore, when calculating the strength of structures, it is necessary to take into account the influence of the environment on the deformations and stresses that occur in the rods. There is a large number of papers devoted to static problems of rod theory (Svetlitskiy, 1987; Slepyan, 1972; Nikitin, 1998; Akulenko and Nesterov, 2012). But it should be taken into account that in real conditions, dynamic loads also act on the rods, which lead to fluctuations. It is known that vibrations in rods can have a significant impact on the strength of structures (Svetlitskiy, 1987). Therefore, the calculation of deformations and stresses that occur in rods under dynamic loads is a very important application task. One-dimensional models are often used to describe the longitudinal vibrations of rods. Despite the fact that these models do not fully account for all the processes occurring in the rods interacting with the medium, they have their advantages. One-dimensional models differ in their simplicity and at the same time allow us to study the effects associated with rod structures, so the use of the assumption of one-dimensionality of the system for such problems is often found in the scientific literature. Filippov, 1983 considers the propagation of longitudinal elastic waves in a semi-infinite rod of constant circular cross-section, which interacts with its environment of the Winkler type according to the law of dry friction. To find a solution to the problem, the Laplace transform method is used. A solution to this equation is found. It is worth noting that in this formulation of the problem, it is assumed that in dry friction, the resistance force acting from the medium on the rod is directly proportional to the deformations that occur in the rod. But there are other variations of the description of environmental impact, one of which will be considered in this paper. In this paper, we consider a one-dimensional model of a rod that performs longitudinal vibrations. The paper uses the assumption that the forces acting on the rod from the environment are directly proportional to the movement of the surface material particles alongside the rod. In addition, it is assumed that the cross-section of the rod is constant along its entire length. The purpose of this work is to develop a model describing the longitudinal vibrations that occur in a rod located in the environment under dynamic loading. 3. Longitudinal vibrations of the rod in an elastic medium Consider a one-dimensional model of a viscoelastic rod in an elastic environment. Let the stresses arising in the rod be related to deformations according to the Kelvin-Voigt model (1)       (1) where  is the viscosity coefficient. The equation of longitudinal vibrations of a viscoelastic rod in an elastic environment has the following form: