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

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

Abstract

The parametric excitation problem is governed by a non-autonomous and homogeneous equation. In this case, the parameters of the mathematical model explicitly depend on time. A particular case of parametric excitation problem is that in which the stiffness harmonically varies in time. In the latter case, the equation of motion is know as Mathieu's equation and, depending on the values of amplitude and frequency of the stiffness variation, bounded or unbounded solutions may appear, the latter being associated with the parametric instability.There are a number of technological applications in which parametric excitation is of importance, particularly in cable dynamics. In the latter class of structures, the stiffness to the lateral motion is governed by the axial force (geometric stiffness). If an environmental 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 excitation deserves investigations. Particularly, this project deals with the numerical study of passive suppression of parametric excitation of a rigid cylinder mounted on an elastic support of time-dependent stiffness. The suppression device consists of a rotative non-linear vibration absorber (NVA). It is important to point out that the theme has been focus of another project sponsored by FAPESP (grant 2016/20929-2). In the former project, it has been showed that the mentioned suppressor is able to limit the response due to parametric excitation. 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 present research project is to numerically investigate the influence of the initial conditions on the passive suppression of parametric excitation using a rotative NVA. The project will be carried out at Università Politecnica delle Marche, with the group lead by Prof. Stefano Lenci, a recognized researcher on the theme of sensitivity of non-linear systems with respect to the initial conditions. At the end of the project, it is expected to obtain a set of 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. (AU)