Examples Set 1 — Lesson 5

This lesson covers the evaluation of the response of a system with one degree of freedom when excited by a sinusoidal forcing function. The lesson provides a detailed walkthrough of three examples: a portal frame made of steel, a beam supporting a machine, and an automobile mounted on springs. The lesson explains how to calculate the natural frequency, frequency ratio, dynamic magnification factor, and maximum steady state response of these systems. It also discusses the impact of factors such as mass, stiffness, damping ratio, and driving frequency on the system's response.

Video Highlights

Explanation of the components of the system, including the mass, spring, and damper - 0:38
Explanation of the transient response and steady state response of the system - 1:45
Discussion on the concept of dynamic amplification and its calculation - 2:35
Explanation of the concept of resonance and its impact on the system response - 3:26
Introduction to the technique of logarithmic decrement for quantifying damping - 5:21
Explanation of the concept of dynamic magnification factor and its calculation - 6:08
Discussion on the concept of bandwidth and its calculation - 9:12
Explanation of the half power bandwidth technique for measuring damping - 23:43

Key Takeaways:

- The natural frequency of a system can be calculated using the effective stiffness and mass of the system.
- The frequency ratio is the ratio of the driving frequency to the natural frequency.
- The dynamic magnification factor, which indicates the amplitude of the response, can be calculated using the frequency ratio and the critical damping ratio.
- The maximum steady state response can be found by multiplying the dynamic magnification factor by the static deformation.
- The response of a system to a harmonic force is also harmonic and has a phase lag.