A FINITE-DEGREES-FREE MODEL OF A BODY-BAR

Abstract

This article examines a mathematical model of a tooled rod with a periodic structure and a finite number of degrees of freedom, used to analyze the vibration-induced separation of castings from casting blocks. The authors propose a simplified numbering system for the associated masses and derive analytical relationships for determining two spectra of natural frequencies and vibration modes under various boundary conditions. Using the principal coordinate method, a detailed methodology for finding unknown parameters of the general solution to differential equations of motion for the case of a longitudinal rod impact on a rigid barrier is described.