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research-article

Response of a Harmonically Forced Dry Friction Damped System under Time Delayed State Feedback

[+] Author and Article Information
Ranjan Kumar Mitra

Department of Mechanical Engineering, National Institute of Technology, Durgapur, West Bengal, Pin-713209, India
rkmitra.me@gmail.com

A. K. Banik

Department of Civil Engineering, National Institute of Technology, Durgapur, West Bengal, Pin-713209, India
akbanik@gmail.com

Shyamal Chatterjee

Department of Mechanical Engineering, Indian Institute of Engineering Science and Technology, Shibpur, West Bengal, Pin-711103, India
shychat@gmail.com

1Corresponding author.

ASME doi:10.1115/1.4038445 History: Received February 17, 2017; Revised October 27, 2017

Abstract

Nonlinear dynamics, control and stability analysis of dry friction damped system under state feedback control with time delay are investigated. The dry friction damped system is harmonically excited and the nonlinearities in the equation of motion arise due to nonlinear damping and spring force. In this paper a frequency domain based method, viz. incremental harmonic balance method along with arc-length continuation technique (IHBC) is first employed to identify the primary responses which may be present in such system. The IHBC is then reformulated in a manner to treat the dry friction damped system under state feedback control with time delay and is applied to obtain control of responses in an efficient and systematic way. The stability of uncontrolled responses is obtained by Floquet's theory using Hsu' scheme and the stability of the controlled responses is obtained by applying a semi-discretization method for delay differential equation.

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