Longitudinal vibrations of rods from dynamic and kinematic perturbations

Abstract

Objective. In modern technology, elastic structures of structures, machines, and technical devices are widespread. In real conditions, the rods experience oscillations from dynamic and kinematic disturbances. The aim of the work is to develop methods and algorithms for solving problems of oscillations under dynamic and kinematic disturbances.Method. The study is based on the application of the hypothesis of flat sections and the d'Alembert principle.Result. The problem of longitudinal free and forced vibrations of rods is considered. As a result, the displacement function of transverse sections in the longitudinal direction of the rod was found, the spectra of natural forms jn and natural frequencies wn of vibrations were obtained.Conclusion. A set of calculation programs has been created, which makes it possible to solve problems of rod vibrations. Spectra of eigenfrequencies wn and eigenmodes jn(x) of vibrations are obtained, and u(x, t) is found, the function of displacement of cross sections in the longitudinal direction of the rod.

Keywords

• homogeneous steel rod
• vibration amplitude
• longitudinal vibrations
• free and forced vibrations
• dynamic and kinematic perturbations
• dalamber principle
• differential equations
• boundary conditions
• matlab computer complex
• cross-sections
• longitudinal force
• normal stresses