Numerical Procedure for Solving the Nonlinear Behaviour of a Spherical Absorber

Authors

  • Marek Kawulok
    Affiliation
    Department of Structural Mechanics, Faculty of Civil Engineering, VSB-Technical University of Ostrava, Ludvíka Podéště 1875/17, 708 00 Ostrava-Poruba, Czech Republic
    Institute of Theoretical and Applied Mechanics of the Czech Academy of Sciences, Prosecká 809/76, 190 00 Prague 9, Czech Republic
  • Martin Čermák
    Affiliation
    Department of Mathematics, Faculty of Civil Engineering, VSB-Technical University of Ostrava, Ludvíka Podéště 1875/17, 708 00 Ostrava-Poruba, Czech Republic
  • Stanislav Pospíšil
    Affiliation
    Department of Structural Mechanics, Faculty of Civil Engineering, VSB-Technical University of Ostrava, Ludvíka Podéště 1875/17, 708 00 Ostrava-Poruba, Czech Republic
    Institute of Theoretical and Applied Mechanics of the Czech Academy of Sciences, Prosecká 809/76, 190 00 Prague 9, Czech Republic
  • David Juračka
    Affiliation
    Department of Structural Mechanics, Faculty of Civil Engineering, VSB-Technical University of Ostrava, Ludvíka Podéště 1875/17, 708 00 Ostrava-Poruba, Czech Republic
https://doi.org/10.3311/PPci.25903

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.

Keywords:

nonlinear dynamic, modified secant method, continuation method, ball vibration absorber, bifurcation portraits

Citation data from Crossref and Scopus

Published Online

2024-07-22

How to Cite

Kawulok, M., Čermák, M., Pospíšil, S., Juračka, D. “Numerical Procedure for Solving the Nonlinear Behaviour of a Spherical Absorber”, Periodica Polytechnica Civil Engineering, 68(4), pp. 1367–1377, 2024. https://doi.org/10.3311/PPci.25903

Issue

Section

Review Article