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

Project Overview

In this training, we first calculate the natural frequency of transverse vibration using the Analytical Solution. In the next step, the natural frequency is calculated using the Abaqus software. Finally, the results obtained from Abaqus are compared with those obtained from the Analytical Solution.

Model Description

As shown in the model, the system consists of a cantilever beam and a concentrated mass. The beam is made of steel, and the concentrated mass is equal to 20 kg.

Analytical Solution

First, the natural frequency of transverse vibration is calculated using the Analytical Solution.

The natural frequency of transverse vibration obtained from the Analytical Solution is equal to 11.887 Hertz.

Abaqus Simulation

In the next step, the same problem is modeled and analyzed using the Abaqus software to obtain the natural frequency of transverse vibration.

The natural frequency of transverse vibration obtained from the Abaqus software is equal to 11.877 Hertz.

Comparison of Results

The results obtained from the Abaqus software are compared with those obtained from the Analytical Solution.

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

The natural frequency obtained from Abaqus is 11.877 Hz, while the value obtained from the Analytical Solution is 11.887 Hz.

Mechanical Vibrations

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 using Abaqus.
• How to compare Abaqus results with the Analytical Solution.
• How to evaluate the accuracy of a numerical vibration model.

Key Features

• Transverse vibration analysis.
• Cantilever beam model.
• Steel beam.
• Concentrated mass of 20 kg.
• Natural frequency calculation.
• Analytical Solution.
• Abaqus numerical simulation.
• Comparison between Abaqus and Analytical Solution.
• Free Abaqus tutorial.