Non-stationary vibrations of mechanical systems with slowly varying natural frequencies during acceleration through resonance ( Approximate analytic solution)

Abstract

The paper presents an approximate analytical solution for investigation of vibration responses in linear Single-Degree-of-Freedom-Systems (SDOF) with slowly varying natural frequency subjected to a transient excitalion force with constant amplitude. The solution employs the WBKJ-approximation method, the method of Variation of the constants and in the final analysis using error functions with complex variables. This has been used to study systems -with an ideal energy source, the excitation frequency changes linearly as function of time, the natural frequency changes slowly and linearly with time and the damping remains constant. The influence of the changing parameters on the non-stationary resonance response with special emphasis on the maximum amplitude and the speed are presented.