Some Typical Problems in Axial and Torsional Vibrations — Lesson 3

This lesson covers the topic of axial and torsional vibrations. It delves into the differential equations that govern these vibrations and the solutions to these equations. The lesson also discusses the concept of free vibration and forced vibration, and how to solve problems related to these vibrations. It further explains how to handle non-classical boundary conditions and how to solve typical problems encountered in axial and torsional vibrations. The lesson concludes with a discussion on the torsional vibration response of a shaft subjected to a rectangular pulse.

Video Highlights

02:42 - Free vibration response of a bar which is uniformly stressed and then released.
03:39 - Problem related to the torsional vibration response of a shaft subjected to a rectangular pulse.
03:53 - Solution of a differential equation for torsional vibration.
04:48 - Explanation of how to solve a problem related to the axial vibration of a bar.
54:32 - Use of the Duhamel's integral to find the particular integral in the solution of a differential equation.

Key Takeaways

- Axial and torsional vibrations are governed by similar types of differential equations.
- The solution to these equations involves two parts: the homogeneous solution and the particular integral.
- Different boundary conditions, such as fixed-free, free-free, and fixed-fixed, can affect the solution of the vibration problem.
- The response of a system to a rectangular pulse can be split into two parts: during the pulse and after the pulse.
- The use of numerical methods and graphical solutions can aid in solving complex vibration problems.