Numerical procedure for solving the nonlinear behaviour of a spherical absorber

Abstract

The aim of the paper is to perform numerical simulations for a system of nonlinear differential equations that describe the behaviour of a spherical absorber placed in a support bowl and to describe the applied techniques. The motion of the sphere is constrained to a plane problem. The derived system of equations is numerically solved using the continuation method and the modified secant method. The absorber's response to different harmonic excitation forces is simulated to demonstrate the applicability of these techniques in its analysis. The dependence of the response amplitude on the angular frequency of excitation is presented graphically. The results also include a response stability analysis using the Routh-Hurwitz criteria.