Special topics on the transverse vibration of beam — Lesson 3

This lesson covers the topic of beam vibrations, focusing on special topics such as the vibration of a beam on an elastic foundation, the effect of axial force on beam vibration, and the vibration of an infinitely long beam. The lesson explains how different techniques and equations are used to analyze these situations. For instance, the Hamilton principle is used to derive the equation of motion for a prismatic beam carrying an axial force. The lesson also discusses how the natural frequency of a simply supported beam changes with the presence of an axial force. An illustrative example is provided to demonstrate how Fourier transform technique can be used to analyze the free vibration of an infinitely long beam.

Video Highlights

00:47 - Special topics on the tense bars, vibration of the beam, and the need for different techniques.
01:37 - Three cases to study: vibration of the beam on an elastic foundation, the effect of axial force, and the vibration problem of a beam with infinite length.
04:34 - Vibration of a beam on an elastic foundation.
31:40 - Effect of axial force on the vibration frequencies of a beam.
62:52 - Vibration problem of a beam with infinite length.

Key Takeaways

- The vibration of a beam on an elastic foundation requires a different arrangement of equations for analysis.
- The presence of an axial force on a beam affects its natural frequency.
- The vibration of an infinitely long beam, such as a road pavement or a railway track, requires the use of Fourier transform technique for analysis.
- The Hamilton principle can be used to derive the equation of motion for a prismatic beam carrying an axial force.
- The natural frequency of a simply supported beam changes with the presence of an axial force.