Natural Frequency of longitudinal vibration using Abaqus software and Mechanical vibrations book

Project Overview

In this Abaqus tutorial, the natural frequency of longitudinal vibration of a cantilever beam with a concentrated mass is calculated using both the analytical solution and the Abaqus software.

The main objective of this tutorial is to first calculate the natural frequency of longitudinal vibration using the analytical solution, then obtain the natural frequency using Abaqus, and finally compare the results obtained from both approaches.

Model Description

In this problem, the model consists of a cantilever beam and a concentrated mass. The beam is made of steel, and the concentrated mass is equal to 20 kg.

The model is used to investigate the longitudinal vibration of the cantilever beam and to determine its natural frequency using the analytical solution and Abaqus.

Analytical Solution

First, the natural frequency of longitudinal vibration is calculated using the analytical solution. The analytical result is then used as a reference for evaluating the Abaqus simulation.

The natural frequency of longitudinal vibration obtained from the analytical solution is 594.41 Hz.

Abaqus Simulation

Following the analytical calculation, the same problem is modeled in the Abaqus software. A numerical modal analysis is performed to obtain the natural frequency of the longitudinal vibration.

The natural frequency obtained from the Abaqus software is 577.44 Hz.

Comparison of Results

The natural frequency obtained from the Abaqus software is compared with the result obtained from the analytical solution.

As observed from the results, the natural frequency obtained from Abaqus is in very good agreement with that obtained from the analytical solution, indicating that the problem has been modeled correctly in the Abaqus software.

The difference between the result obtained from the Abaqus software and that obtained from the analytical solution is approximately 2.85%.

Mechanical Vibrations Book

The problem is related to the topics covered in the Mechanical Vibrations book and provides a useful reference for studying the longitudinal vibration of mechanical systems.

The analytical result is used as a reference to evaluate the numerical result obtained from Abaqus.

What You Will Learn

• How to model a cantilever beam in Abaqus.
• How to define a concentrated mass in Abaqus.
• How to perform a natural frequency analysis.
• How to calculate the natural frequency using the analytical solution.
• How to obtain the natural frequency from Abaqus.
• How to compare Abaqus results with an analytical solution.
• How to evaluate the accuracy of a numerical vibration model.

Key Features

• Longitudinal vibration analysis.
• Cantilever beam model.
• Concentrated mass of 20 kg.
• Steel beam.
• Natural frequency calculation.
• Analytical solution.
• Abaqus numerical simulation.
• Comparison between Abaqus and analytical results.
• Approximately 2.85% difference between the results.
• Free Abaqus tutorial.