Fundamental Frequency of the Lateral Vibration of a Shaft carrying one mass using the Abaqus software and Analytical Solution

Project Overview

This Abaqus tutorial focuses on calculating the fundamental frequency of the lateral vibration of a shaft carrying one mass using the Analytical Solution and the Abaqus software.

In this training, we first calculate the fundamental frequency using the Analytical Solution. Then, the same problem is analyzed 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 includes a beam and a concentrated mass. The concentrated mass is located exactly at the center of the beam.

The length of the beam is 1 meter, and its cross-section is circular with a radius of 0.01 meter.

A hinged support is used at both ends of the beam.

Analytical Solution

First, the fundamental frequency of the lateral vibration is calculated using the Analytical Solution.

The fundamental frequency obtained from the Analytical Solution is equal to 6.806 Hertz.

Abaqus Simulation

In the next step, the same problem is modeled and analyzed using the Abaqus software to calculate the fundamental frequency of the lateral vibration.

The fundamental frequency obtained from the Abaqus software is equal to 6.806 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 fundamental frequency obtained from the Abaqus software is exactly concordant with the result obtained from the Analytical Solution.

The fundamental frequency obtained from both the Abaqus software and the Analytical Solution is 6.806 Hz.

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 shaft with a concentrated mass in Abaqus.
• How to define hinged supports at both ends of a beam.
• How to model a circular beam cross-section.
• How to perform a natural frequency analysis in Abaqus.
• How to calculate the fundamental frequency using the Analytical Solution.
• How to obtain the fundamental frequency using Abaqus.
• How to compare Abaqus results with the Analytical Solution.

Key Features

• Lateral vibration analysis.
• Shaft carrying one concentrated mass.
• Beam length of 1 meter.
• Circular cross-section with a radius of 0.01 meter.
• Hinged supports at both ends.
• Fundamental frequency calculation.
• Analytical Solution.
• Abaqus numerical simulation.
• Exact agreement between Abaqus and Analytical Solution.
• Free Abaqus tutorial.