Nigam & Jennings and Central Difference Method — Lesson 1

This lesson covers the concept of numerical solution techniques, focusing on the equation of motion and how to solve it under different conditions. It introduces the Nigam and Jennings method, Central Difference method, Wilson Theta, and New Mark Beta. The lesson explains how to numerically solve differential equations and how to use inbuilt options in MATLAB that use another numerical technique called OD solver. It also discusses how to model the variation of a forcing function linearly and how to derive the total response from free vibration, constant force, and ramp force. The lesson concludes with the importance of setting the right time period for accurate results.

Video Highlights

Discussion on the equation of motion and its different types of solutions - 0:41
Explanation of how to numerically solve the differential equation of motion - 1:27
Introduction to different numerical techniques including Neigum and Jins method, Central difference method, Wilson Theta, and New Mark Beta - 1:52
Explanation of how to model the variation of the forcing function linearly - 4:24
Derivation of the expression for total response - 9:57
Explanation of how to derive the expressions for displacement and velocity at time point to - 13:50
Discussion on how to use the information available at the i th time point to find the solution at time point - 24:35
Introduction to the Central difference technique and how to use it to solve the equation of motion - 25:38
Explanation of how to find the solution at t using the Central difference technique - 32:38
Discussion on the importance of setting the correct time point for accurate results - 38:39

Key Takeaways:

- The Nigam and Jennings method, Central Difference method, Wilson Theta, and New Mark Beta are different numerical solution techniques.
- The equation of motion can be solved numerically under different conditions.
- The variation of a forcing function can be modeled linearly for a small time step.
- The total response is derived from free vibration, constant force, and ramp force.
- The accuracy of the method depends on the time delta T and for a SOP system, delta T by TN should be less than 1 by 5.
- In earthquake analysis, a time point of 0.2 or 0.1 seconds is usually set for response analysis of structures.