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Passive suppression of parametric excitation using non-linear vibration absorber: influence of the initial condition

Grant number: 19/15046-2
Support type:Scholarships abroad - Research
Effective date (Start): December 11, 2019
Effective date (End): February 28, 2020
Field of knowledge:Engineering - Naval and Oceanic Engineering
Principal Investigator:Guilherme Rosa Franzini
Grantee:Guilherme Rosa Franzini
Host: Stefano Lenci
Home Institution: Escola Politécnica (EP). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Local de pesquisa : Università Politecnica delle Marche (UNIVPM), Italy  

Abstract

The parametric excitation problem is governed by a non-autonomous and homogeneousequation. In this case, the parameters of the mathematical model explicitly dependon time. A particular case of parametric excitation problem is that in which the stiffnessharmonically varies in time. In the latter case, the equation of motion is know as Mathieu'sequation and, depending on the values of amplitude and frequency of the stiffness variation,bounded or unbounded solutions may appear, the latter being associated with theparametric instability.There are a number of technological applications in which parametric excitationis of importance, particularly in cable dynamics. In the latter class of structures, thestiffness to the lateral motion is governed by the axial force (geometric stiffness). If anenvironmental action leads to a temporal variation of the axial force, lateral responses dueto the parametric instability may be observed.Due to its technological importance, passive suppression of parametric excitationdeserves investigations. Particularly, this project deals with the numerical study of passivesuppression of parametric excitation of a rigid cylinder mounted on an elastic support oftime-dependent stiffness. The suppression device consists of a rotative non-linear vibrationabsorber (NVA). It is important to point out that the theme has been focus of anotherproject sponsored by FAPESP (grant 2016/20929-2). In the former project, it has beenshowed that the mentioned suppressor is able to limit the response due to parametricexcitation. However, only one initial condition has been considered.Owing to the non-linear character of the mathematical model of passive suppression,the initial conditions may play an important role. Hence, the objective of the presentresearch project is to numerically investigate the influence of the initial conditions on thepassive suppression of parametric excitation using a rotative NVA. The project will becarried out at Università Politecnica delle Marche, with the group lead by Prof. StefanoLenci, a recognized researcher on the theme of sensitivity of non-linear systems withrespect to the initial conditions. At the end of the project, it is expected to obtain a setof numerical tools for investigating the influence of the initial conditions on the passive suppression of parametric excitation. Besides the numerical tools, the first results are also expected to be obtained.