About coefficient of dynamism of a system with a piecewice-linear stiffness characteristics

Abstract

To simplify the analysis of the strength of structural elements under the influence of impulse dynamic loads, the dynamic factor is used in engineering calculations. This coefficient does not depend either on the parameters of the system or on the magnitude of the dynamic load, and for linear systems it is equal to two. In nonlinear systems, it takes on different meanings. The value of the dynamic coefficient depends on the rigidity of the nonlinear system and in the case of a rigid power characteristic it is less than two, and in the case of a soft characteristic it is greater than two. The purpose of the paper is to calculate the dynamic coefficient of a system with a piecewise linear characteristic of elasticity under the action of an instantaneously applied constant force. In this paper we consider the definitions of the dynamical coefficient for a system with a piecewise linear stiffness characteristic. It is established that three load cases are possible from the magnitude of the applied force. The first of them corresponds to the action of a relatively "small" force. In this case we have a linear system, because the additional spring of rigidity is not deformed and the dynamic coefficient is equal to two. The second variant of the load is for the "average" force value. For it, the coefficient of dynamism is less than two, and in this case it depends on the parameters of the mechanical system and the magnitude of the applied force, which is confirmed by the calculations given. In the third case of a "comparatively large force," it is also, as in the second case, less than two. But, unlike the linear system, it depends on the coefficients of spring stiffness, the size of the gap and the magnitude of the applied force. It is proved that for each of the load variants of a system with a piecewise linear elasticity characteristic with deformation of an additional spring, the dynamic coefficient is less than two. With the increase in the instantaneously applied load, the dynamic coefficient decreases and when the additional spring is deformed it is less than two, actually nonlinear systems with a rigid power characteristic.