Consideration of damping in a continuous medium using the rod approximation by A.R. Rzhanitsyn

Abstract

The work is focused on creating a method for accounting of internal friction, which provides frequency independence, considers the dependence of internal friction on the level of the stress state, and is suitable for physically nonlinear tasks at large and small displacements. The authors consider an approximated method of accounting the damping in plates using the rod approximation according to A.R. Rzhanitsyn. An analysis of the discrete Rzhanitsyn medium with a square cell is given in terms of isotropy of its damping properties. The exact fulfillment of the isotropic damping properties is shown for the eight specific directions in the orientation of the deformations. The solution for a test example is given, where a rod oscillating in tension is calculated according to two computational schemes. One of these schemes is a real rod, the other is a rectangular plate experiencing uniaxial tension, and for its dynamic modeling, in turn, the discrete model by A.R. Rzhanitsyn is applied. The use of the same damping parameters for the real rod and rods in the Rzhanitsyn approximation leads to close damping. An approximate approach has been developed to account for internal friction during vibrations of a two-dimensional continuous medium, as well as a variant of clarifying the damping forces in the plate. A numerical example of damping modeling is given in the case of considering geometrically and physically nonlinear oscillations.

Keywords

• frequency-independent damping
• isotropy
• dampening properties
• two-dimensional medium
• generalized prandtl diagram
• physical nonlinearity
• large displacements
• numerical solutions
• problems of dynamics