Solving Dynamic Equations Using Duhamel Integral — Lesson 1

This lesson covers the numerical methods of solving dynamic equations, specifically focusing on the Duhamel Integral. The lesson begins with an explanation of the Duhamel Integral and its applications in finding the response of a dynamic system subjected to any type of arbitrary input. The lesson then delves into the numerical procedure for evaluating the Duhamel Integral, using the example of a single degree Freedom system subjected to an arbitrary input. The lesson also discusses the application of the Duhamel Integral to a continuous system. The lesson concludes with a detailed explanation of how to use the Duhamel Integral to solve a numerical problem involving a simply supported beam.

Video Highlights

02:10 - Numerical procedure for evaluating the Duhammed integral.
05:20 - Explanation of the impulse response function and its importance in the Duhammed integral.
13:18 - Trapezoidal rule and Simpson rule for numerical integration.
53:25 - Application of the Duhammed integral in solving a numerical problem involving a simply supported beam.

Key Takeaways

- The Duhamel Integral is a powerful tool for finding the response of a dynamic system subjected to any type of arbitrary input.
- The numerical procedure for evaluating the Duhamel Integral involves developing a numerical procedure for vibration analysis of a single degree Freedom system and applying it to a continuous system.
- The Duhamel Integral can handle any type of function, including simple harmonic functions, mathematically well-defined functions, and even samples of random functions.
- The Duhamel Integral can be used to solve numerical problems involving systems like a simply supported beam.