Determination of modal mass and stiffness in longitudinal vibrations of the rod.

In this work, the problem of determining the analytical expressions of modal mass and stiffness in the longitudinal vibrations of the rod under the influence of kinematic and random excitations, depending on the system parameters and variables, was considered. The elastic dissipative characteristics of the rod material are hysteresis type. Expressions of the non-one-valued functional based on the Pisarenko-Boginich hypothesis obtained by the methods of harmonic linearization for kinematic excitations and statistical linearization for random excitations were used. The importance of the analytical expressions of determined modal mass and stiffness in solving the problems of mathematical modeling of longitudinal vibrations of the rod using the method of bond graph, study of dynamics and exploring of the absolute stability of nonlinear stationary vibrations is substantiated. [ABSTRACT FROM AUTHOR]