Analysis of small oscillations of a pendulum partially filled with a viscoelastic fluid

Hilal Essaouini ¹

Pierre Capodanno ²

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Department of Physics, Abdelmalek Essaadi University, Faculty of Sciences, Energy Laboratory, 93030 Tetuan, Morocco |

Université de Franche-Comté, 2B - Rue des jardins, F- 25000 Besançon, France |

Publication type: Journal Article

Publication date: 2023-07-12

American Institute of Mathematical Sciences (AIMS)

Journal: Communications in Analysis and Mechanics

SJR: —

CiteScore: 0.7

Impact factor: —

ISSN: 28363310

DOI: 10.3934/cam.2023019

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Abstract

<abstract><p>This paper focuses on the spectral analysis of equations that describe the oscillations of a heavy pendulum partially filled with a homogeneous incompressible viscoelastic fluid. The constitutive equation of the fluid follows the simpler Oldroyd model. By examining the eigenvalues of the linear operator that describes the dynamics of the coupled system, it was demonstrated that under appropriate assumptions the equilibrium configuration remains stable in the linear approximation. Moreover, when the viscosity coefficient is sufficiently large the spectrum comprises three branches of eigenvalues with potential cluster points at $ 0 $, $ \beta $ and $ \infty $ where $ \beta $ represents the viscoelastic parameter of the fluid. These three branches of eigenvalues correspond to frequencies associated with various types of waves.</p></abstract>