Free damped transverse vibration analysis of beam — Lesson 3

This lesson covers the analysis of the transverse vibration of a beam under non-classical boundary conditions. It discusses how to obtain the frequency equation and natural frequencies of the beam. The lesson also explains how non-classical boundary conditions can occur in practical problems, such as a beam carrying a concentrated mass or resting on an elastic pad. It further elaborates on how to analyze the free transverse vibration of the beam considering damping into the equation of motion. The lesson concludes with the derivation of the expression for damp free vibration response of Euler Bernoulli beam subjected to initial conditions.

Video Highlights

03:30 - Analyzing a free dam transverse vibration of the beam.
06:08 - How to formulate the boundary value problem for a beam with a lump mass at the tip.
09:10 - Modal solution for a beam with a lump mass at the tip.
30:00 - Effect of a concentrated mass on the first two natural frequencies of a beam.
57:35 - How to obtain the free vibration response of a Euler Bernoulli beam subjected to initial conditions.

Key Takeaways

- The transverse vibration of a beam can be analyzed under non-classical boundary conditions.
- Non-classical boundary conditions can occur in practical problems like a beam carrying a concentrated mass or resting on an elastic pad.
- The frequency equation and natural frequencies of the beam can be obtained under these conditions.
- The free transverse vibration of the beam can be analyzed considering damping into the equation of motion.
- The expression for damp free vibration response of Euler Bernoulli beam can be derived subjected to initial conditions.