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Targeted energy transfer in stochastically excited system with nonlinear energy sink

Part of: Equations of mathematical physics and other areas of application Probabilistic methods, simulation and stochastic differential equations Stochastic analysis

Published online by Cambridge University Press:  18 September 2018

P. KUMAR ,
S. NARAYANAN  and
S. GUPTA
P. KUMAR
Affiliation:
Dynamic Analysis Group, Bharat Heavy Electrical Limited, Nagpur 440001, India email: pankajiit1@yahoo.co.in
S. NARAYANAN
Affiliation:
Department of Mechanical Engineering, Indian Institute of Information Technology (Design and Manufacturing), Kancheepuram, India email: drs.narayanan@gmail.com
S. GUPTA
Affiliation:
Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600036, India email: gupta.sayan@gmail.com
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Abstract

This study investigates the phenomenon of targeted energy transfer (TET) from a linear oscillator to a nonlinear attachment behaving as a nonlinear energy sink for both transient and stochastic excitations. First, the dynamics of the underlying Hamiltonian system under deterministic transient loading is studied. Assuming that the transient dynamics can be partitioned into slow and fast components, the governing equations of motion corresponding to the slow flow dynamics are derived and the behaviour of the system is analysed. Subsequently, the effect of noise on the slow flow dynamics of the system is investigated. The Itô stochastic differential equations for the noisy system are derived and the corresponding Fokker–Planck equations are numerically solved to gain insights into the behaviour of the system on TET. The effects of the system parameters as well as noise intensity on the optimal regime of TET are studied. The analysis reveals that the interaction of nonlinearities and noise enhances the optimal TET regime as predicted in deterministic analysis.

Keywords

Fokker–Planck equationstochastic differential equationstargeted energy transfernonlinear energy sinkslow flow dynamics

MSC classification

Primary: 35Q84: Fokker-Planck equations
Secondary: 60H10: Stochastic ordinary differential equations 60H30: Applications of stochastic analysis (to PDE, etc.) 60H35: Computational methods for stochastic equations 65C99: None of the above, but in this section
Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Special Issue 5: Stochastic Analysis in Applications , October 2019 , pp. 869 - 886
Copyright
© Cambridge University Press 2018 

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