This lesson covers the concept of non-linear vibration and chaotic responses in systems. It delves into the four types of responses in a system: fixed point response, periodic response, quasi-periodic response, and chaotic response. The lesson explains how these responses are determined and how they can be manipulated. It also discusses the concept of Lyapunov exponent and its role in determining the chaotic nature of a system. The lesson further explores the application of these concepts in real-life systems such as mechanical systems, biological systems, and electrical systems. For instance, a cantilever beam subjected to base excitation is used as an example to illustrate the concepts.

- Non-linear vibration can result in different types of responses including periodic, quasi-periodic, and chaotic responses.
- The stability and bifurcation of periodic responses can be studied using the eigenvalues of the Jacobian and monodromy matrices.
- The Poincare section is a useful tool for analyzing the behavior of a system, particularly in the case of quasi-periodic responses.
- Different types of bifurcations such as cyclic fold, symmetry breaking, and transcritical bifurcation can lead to chaotic responses.
- Chaotic responses are complex and can be analyzed using various methods including the study of Feigenbaum numbers and routes to chaos.

You are being redirected to our marketplace website to provide you an optimal buying experience. Please refer to our FAQ page for more details. Click the button below to proceed further.