# Investigating various nonlinear vibration problems using VIBRANT: A tool based on Abaqus and Python

## TL;DR

This paper introduces VIBRANT, a Python-Abaqus tool for analyzing nonlinear vibrations in mechanical systems, validated through benchmark examples.

## Contribution

VIBRANT introduces an automated, efficient tool for modeling diverse nonlinearities in mechanical systems using Abaqus and Python.

## Key findings

- VIBRANT successfully models geometric nonlinearities in a Timoshenko beam with large displacements.
- The tool accurately captures stiffness nonlinearities in a bar with frictional clamps using Jenkins contact elements.
- VIBRANT demonstrates damping nonlinearities via Coulomb friction in an Euler-Bernoulli beam.

## Abstract

This paper investigates nonlinear vibration problems using VIBRANT (VIbration BehaviouR ANalysis Tool), a tool based on Python and Abaqus for the detailed analysis of complex mechanical systems. VIBRANT employs time-marching algorithms to perform time domain finite element simulations under harmonic excitation, predicting frequency domain behaviour. It addresses a significantly large range of nonlinearities, including contacts and large displacements, as it uses a commercial finite element software package Abaqus, while reducing computational time through parallelisation. The tool’s capabilities are examined through three academic benchmark examples. The first example examines a geometrically nonlinear Timoshenko beam subjected to large displacements, which highlights the nonlinear behaviour due to significant deformation associated with stiffness nonlinearities. The second example is a bar forced to move in axial direction by its frictional clamps that are modelled using Jenkins contact elements. This example is also a demonstration of a stiffness nonlinearity. The third example involves an Euler-Bernoulli beam with a frictional contact element, which demonstrates the effects of damping nonlinearities by the application of a localised Coulomb friction element. All examples serve to validate VIBRANT’s accuracy and efficiency in capturing the characteristics of nonlinear systems, emphasising its potential for industrial applications, particularly in aerospace engineering. VIBRANT’s capacity to model a wide range of nonlinearities and to automate frequency sweep analysis with minimal manual intervention represents a significant advantage, providing a reliable and efficient approach to modelling and analysing dynamic responses in engineering structures.