Exact solution of the Mass Spring system in the Abaqus software

Product Overview

In this example, we intend to simulate the exact solution of the mass-spring system using the Abaqus software.

The steel bar is hinged at point O, and two springs are connected to the top of the bar. Therefore, the bar can only rotate about point O.

The whole bar starts rotating with an initial angular velocity of 7 rad/s.

Equation of Motion

The purpose of this analysis is to obtain the equation of motion of the mass-spring system using Abaqus and compare the numerical results with those obtained from the exact solution.

The dynamic behavior of the system is investigated based on the rotational motion of the steel bar and the restoring forces generated by the springs.

Exact Analytical Solution

The mass-spring system is also solved using an exact analytical solution. This solution is used as a reference for evaluating the numerical results obtained from Abaqus.

The analytical formulation provides the theoretical response of the system and allows the Abaqus results to be directly compared with the exact solution.

Abaqus Simulation

The same mass-spring system is modeled in Abaqus to obtain its numerical dynamic response.

The initial angular velocity of 7 rad/s is applied to the bar, and the resulting rotational response is obtained from the Abaqus simulation.

Abaqus Validation

The mass-spring system is solved independently using the exact analytical solution, and the same system is simulated in Abaqus. The numerical results are then compared with the analytical results.

The agreement between the Abaqus results and the exact solution provides a verification of the numerical model and demonstrates that the mass-spring system has been correctly implemented in Abaqus.

Results

The dynamic response obtained from Abaqus is compared with the theoretical response calculated using the exact solution.

The comparison shows good agreement between the numerical and analytical results, confirming the accuracy of the Abaqus model.

What You Will Learn

• How to model a mass-spring system in Abaqus.
• How to model a hinged steel bar with rotational motion.
• How to define springs in Abaqus.
• How to apply an initial angular velocity.
• How to obtain the equation of motion of the system.
• How to obtain the exact analytical solution.
• How to compare Abaqus results with an exact solution.
• How to verify an Abaqus model using an analytical solution.

Key Features

• Mass-spring system analysis in Abaqus.
• Hinged steel bar.
• Two springs connected to the bar.
• Rotational motion about point O.
• Initial angular velocity of 7 rad/s.
• Equation of motion calculation.
• Exact analytical solution.
• Comparison between Abaqus and exact analytical results.
• Analytical verification of the numerical model.