Finite Elements for a Beam System With Nonlinear Contact Under Periodic Excitation

TL;DR

This paper models and analyzes a beam system with nonlinear contact, such as rubber snubbers, under periodic excitation, using finite element methods to study responses in time and frequency domains, with comparisons to exact solutions.

Contribution

It introduces finite element analysis for a nonlinear contact beam system with unilateral springs under periodic excitation, including response analysis and preliminary nonlinear normal mode investigation.

Findings

Numerical results match existing exact solutions.

Frequency sweep identifies maximum displacements at resonances.

Ongoing research on nonlinear normal modes.

Abstract

Solar arrays are structures which are connected to satellites; during launch, they are in a folded position and submitted to high vibrations. In order to save mass, the flexibility of the panels is not negligible and they may strike each other; this may damage the structure. To prevent this, rubber snubbers are mounted at well chosen points of the structure; a prestress is applied to the snubber; but it is quite difficult to check the amount of prestress and the snubber may act only on one side; they will be modeled as one sided springs (see figure 2). In this article, some analysis for responses (displacements) in both time and frequency domains for a clamped-clamped Euler-Bernoulli beam model with a spring are presented. This spring can be unilateral or bilateral fixed at a point. The mounting (beam +spring) is fixed on a rigid support which has a sinusoidal motion of constant frequency. The system is also studied in the frequency domain by sweeping frequencies between two fixed values, in order to save the maximum of displacements corresponding to each frequency. Numerical results are compared with exact solutions in particular cases which already exist in the literature. On the other hand, a numerical and theoretical investigation of nonlinear normal mode (NNM) can be a new method to describe nonlinear behaviors, this work is in progress.