Effect of tendon structural control on the appearance of horseshoes chaos on a cantilever beam due to seismic action

TL;DR

This paper develops an analytical model for a cantilever beam with tendon-based control to suppress horseshoe chaos caused by seismic forces, using Melnikov methods to identify effective control parameters.

Contribution

It introduces a mathematical framework for active tendon control on cantilever beams and analyzes stability and chaos suppression mechanisms.

Findings

Identification of critical control gain parameters

Demonstration of chaos suppression via tendon control

Analytical stability analysis of the controlled system

Abstract

This paper deals with the problem of improving the seismic strength of mechanical structures by using a tendon system as actuation device. It consists of a pair of tension cables transmitting a control torque to the structure at the moment arm position. The purpose of the paper is to, establish the analytical framework consisting of mathematical modelling of cantilever beam under active tendon structural control, analyze the stability and, determine the physical characteristics of tendon system leading to the suppression of horseshoes chaos. The control efficiency is found by analyzing the behavior of the controlled system through the Melnikov methods. We also provide the critical control gain parameters leading to the efficiency of the control process.