Numerical Methods in Dynamic System Analysis

This course covers the application of numerical methods in solving dynamic equations, with a focus on the Duhamel Integral and direct integration methods. It begins with an understanding of the Duhamel Integral and its role in determining the response of a dynamic system to arbitrary input. For instance, a single degree Freedom system subjected to an arbitrary input is used to illustrate the numerical procedure for evaluating the Duhamel Integral. The course also explores the application of the Duhamel Integral to a continuous system. Further, it delves into the use of direct integration methods in numerical analysis, discussing different methods like the Central Defense Method and Numark Method. The concept of convergence in solutions and its relation to the time step chosen in numerical integration is also explained. Lastly, the course introduces the spectral method of analysis for structures subjected to random excitation, using a single storage building model subjected to earthquake acceleration as an example.