Stability - Lesson 4

In this lesson, we perform the analysis, and the analysis is based on the eigenvalue problem. Modal equations are written with explanations for natural frequency and eigenvector terms. The modal damping ratio is defined. The time-discretized problem in modal form is written.

Reduction from second-order ODE to two first-order ODEs is performed and shown at the start of the video. The amplification factor is shown along with one more parameter which indicates the Newmark algorithm. Stability results are discussed. Conditional and unconditional stability are discussed along with Undamped Critical frequency is defined. Table for different methods, types, beta and gamma parameters used, undamped critical frequency, and the order of accuracy is shown.