Continuation Sparselizard

Academic Year 2024 – 2025

Author: Victor Renkin s2306326

Table of Contents

• Introduction

• Requirements

• Usage

• Project Structure

• AI Integration

Introduction

This project focuses on implementing a parallel Harmonic Balance Method within the Sparselizard framework for the analysis of a nonlinear mechanical system. The primary objective is to accurately trace the system's nonlinear frequency responses (NLFR). This is achieved through the application of a continuation method based on a robust predictor-corrector scheme.

Requirements

This repository relies on Sparselizard. Please refer to the official documentation at this link for proper installation instructions. Additionally, this project requires specific Python packages, which are listed in the requirements.txt file. To install these dependencies, ensure that both Python and pip are installed on your system, then execute the following command:

pip install -r requirements.txt

Usage

For all computations, it is essential to precisely define the physical regions of the system. This includes the entire volume, any clamped surfaces, and the specific point (or surface) of excitation.

Nonlinear Frequency Response (NLFR) Computation

To compute the nonlinear frequency response of the system, execute the following command:

python3 src/main_NLFR.py

Nonlinear Normal Mode (NNM) / Frequency Response Function (FRF) Computation

To compute the Nonlinear Normal Mode (NNM) run:

python3 src/main_NNM.py

Project Structure

The codebase is predominantly organized around a class-based architecture, distinguishing between the NLFR and NNM functionalities. Each of these main functionalities is encapsulated within a class that incorporates abstract methods. These abstract methods serve as guidelines for implementing custom predictor and corrector schemes, allowing for flexible extension of the framework.

The core of the code follows the continuation loop, which is represented by the continuation_loop_NNM and continuation_loop_NLFR functions. The adaptive adjustment of the predictor step size is managed by the StepSizeRule function, enabling efficient convergence. Furthermore, a dedicated function is implemented to store previous solutions, typically maintaining a history equivalent to the predictor's order plus one, which is crucial for the continuation process.

AI Integration

Artificial intelligence tools are utilized periodically throughout this project. Their primary roles include code correction and rephrasing sentences within the accompanying report to enhance clarity and conciseness.