Qualification: 
Ph.D, M.Tech
Email: 
b_bipin@cb.amrita.edu

Dr. Bipin Balaram currently serves as Assistant Professor (SG) at Department of Mechanical Engineering, School of Engineering, Coimbatore Campus. His areas of research include Nonlinear Dynamics, Synchronisation in mechanical systems, Non-smooth systems, Vortex induced vibrations, Nonlinear Normal Modes.

Education

DEGREE/PROGRAM INSTITUTION
Ph. D in Mechanical Engineering National Institute of Technology, Calicut
M. Tech in Engineering Design Amrita Vishwa Vidyapeetham, Coimbatore
B. Tech in Production Engineering Government Engineering College, Thrissur

Thrust Area of Research

Nonlinear Dynamics

Awards and Achievements

  • Gold medal for best academic performance at Amrita University for M. Tech Engineering Design, 2005.
  • "Excellence in Teaching" award from Amrita Vishwa Vidyapeetham, 2016-2017.

Teaching/Research Interests

Major Subjects Taught

  • Nonlinear Dynamics and Chaos
  • Mechanical Vibrations
  • Optimization Techniques
  • Engineering Mechanics

Research Interests

  • Synchronisation
  • Nonlinear Normal Modes
  • Reservoir Computing
  • Flow Induced Vibrations
  • Computational Neuroscience

Publications

Publication Type: Journal Article

Year of Publication Title

2020

Dr. Biswambhar Rakshit, Niveditha Rajendrakumar, and B. Balaram, “Dangerous Aging Transition in a Network of Coupled Oscillators”, arXiv preprint arXiv:2007.13380, 2020.[Abstract]


In this article, we investigate the dynamical robustness in a network of relaxation oscillators. In particular, we consider a network of diffusively coupled Van der Pol oscillators to explore the aging transition phenomena. Our investigation reveals that the mechanism of aging transition in a network of Van der Pol oscillator is quite different from that of typical sinusoidal oscillators such as Stuart-Landau oscillators. Unlike sinusoidal oscillators, the order parameter does not follow the second-order phase transition. Rather we observe an abnormal phase transition of the order parameter due to sudden unbounded trajectories at a critical point. We call it a dangerous aging transition. We provide details bifurcation analysis of such abnormal phase transition. We show that the boundary crisis of a limit-cycle oscillator is at the helm of such a dangerous aging transition.

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2020

Dr. Biswambhar Rakshit, Niveditha Rajendrakumar, and B. Balaram, “Abnormal route to aging transition in a network of coupled oscillators”, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 30, no. 10, 2020.[Abstract]


In this article, we investigate the dynamical robustness in a network of Van der Pol oscillators. In particular, we consider a network of diffusively coupled Van der Pol oscillators to explore the aging transition phenomena. Our investigation reveals that the route to aging transition in a network of Van der Pol oscillator is different from that of typical sinusoidal oscillators such as Stuart–Landau oscillators. Unlike sinusoidal oscillators, the order parameter does not follow smooth second-order phase transition. Rather, we observe an abnormal phase transition of the order parameter due to the sudden appearance of unbounded trajectories at a critical point. We provide detailed bifurcation analysis of such an abnormal phase transition. We show that the boundary crisis of a limit-cycle oscillator is at the helm of such an unusual discontinuous path of aging transition.
The network of coupled oscillators is an efficient model to explore various self-organizing activities of complex systems in the disciplines of physics, biology, and engineering. Having robust oscillatory dynamics is a prerequisite for the normal functioning of such complex systems. The rhythmic activities of such a large-scale system should be resilient against any local degradation or deterioration. In the absence of any rhythmic activities, the regular functioning of many natural and man-made systems may face severe disruption and this emergent phenomenon is known as aging transition. Recently, the study of the robustness of the oscillatory dynamics of a complex dynamical system has become an emerging area of research. The basic framework of such an investigation involves a network of oscillatory nodes where some components of nodes are functionally degraded but not removed. Until now, the investigation of dynamical robustness was mainly limited to coupled Stuart–Landau oscillators, which have typical sinusoidal oscillation. However, there are many natural systems that can be modeled by a network non-sinusoidal oscillators such as Van der Pol oscillator. Van der Pol oscillator has been used to model many real-life systems that includes neuronal activities in the brain cortex and cardiac rhythms. In this article, we have studied the aging transition in a network of Van der Pol oscillators. Our investigation reveals some interesting phenomena. The order parameter that represents the dynamical activities in the network goes through an abnormal phase transition and suddenly blows up to infinity. We provide detailed bifurcation analysis for such an abnormal phase transition. A blue-sky catastrophe of a limit-cycle oscillator is responsible for the unbounded dynamics of the oscillators. Our results provide significant insights into the aging transition of complex dynamical systems where individual nodes represent a Van der Pol oscillator.

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2017

J. Velayudhan and B. Balaram, “Nonlinear normal modes of coupled Van der Pol oscillators exhibiting synchronization”, 9th EIVOC, Budapest, Hungary, 2017.[Abstract]


Summary. Nonlinear Normal Modes (NNMs), defined as two dimensional invariant manifolds in state space, have emerged as powerful analytical tools for the study of nonlinear systems. This work presents a novel approach to the study of synchronisation dynamics in mutually coupled van der Pol oscillators using the concept of NNMs. Shaw and Pierre’s method is used to arrive at the NNMs as a two dimensional manifold parameterised by the displacement and velocity of the first oscillator. It is shown that because of the synchronising property of the system the invariant manifold reduces to a one-dimensional closed curve which remains a subset of the two-dimensional manifold calculated by NNM computation. This is shown to be true for both the oscillating modes of the system which corresponds to in-phase and out of phase synchronisation. It is also shown that the one-dimensional invariant manifold coincides with the synchronised limit cycle of the system for both modes. The NNMs are further used to decouple the governing equations. The decoupled equations which capture the modal dynamics retain the form of single van der Pol equation after removal of insignificant terms. This suggests a novel approach to the study of in-phase and out of phase synchronisation using these equations.

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2017

V. Vinod, B. Balaram, Narayanan, M. D., and Sen, M., “Effect of configuration symmetry on synchronization in a Van der Pol ring with nonlocal interactions”, Nonlinear Dynamics, vol. 89, pp. 2103–2114, 2017.[Abstract]


This paper discusses the influence of configuration symmetry on synchronization of coupled Van der Pol oscillators in a ring, where the inherent symmetry in an even number ring is broken by the presence of an odd oscillator. The coupling is considered to be nonlocal represented with a particular scaling exponent which decays with distance. The effect of initial conditions on synchronization dynamics is also studied.Synchronization in such ring networks is tracked from sets of initial conditions having periodic solutions. The set of these typical initial conditions is obtained by implementing a new generalized shooting strategy in the ring model. The robustness of this new method will bypass all the transients and give a periodic orbit, if any, for a given arbitrary initial condition. From these periodic initial conditions, interesting dynamics in odd and even number ring such as waking time of odd oscillator, shifting from antiphase to inphase clusters, resurrection of the oscillators from amplitude death, etc., are discussed. Important quantitative effects due to nonlocal interactions and the presence of initial condition-based amplitude death are also detailed. © 2017 Springer Science+Business Media Dordrecht

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2017

K. Devarajan and B. Balaram, “Analytical Approximations for Stick-Slip Amplitudes and Frequency of Duffing Oscillator”, Journal of Computational and Nonlinear Dynamics, vol. 12, no. 4, 2017.[Abstract]


Linear spring mass systems placed on a moving belt have been subjected to numerous investigations. Dynamical characteristics like amplitude and frequency of oscillations and bifurcations have been well studied along with different control mechanisms for this model. But the corresponding nonlinear system has not received comparable attention. This paper presents an analytical investigation of the behavior of a Duffing oscillator placed on a belt moving with constant velocity and excited by dry friction. A negative gradient friction model is considered to account for the initial decrease and the subsequent increase in the frictional forces with increasing relative velocity. Approximate analytical expressions are obtained for the amplitudes and base frequencies of friction-induced stick-slip and pure-slip phases of oscillations. For the pure-slip phase, an expression for the equilibrium point is obtained, and averaging procedure is used to arrive at approximate analytical expressions of the periodic amplitude of oscillations around this fixed-point. For stick-slip oscillations, analytical expressions for amplitude are arrived at by using perturbation analysis for the finite time interval of the stick phase, which is linked to the subsequent slip phase through conditions of continuity and periodicity. These analytical results are validated by numerical studies and are shown to be in good agreement with them. It is shown that the pure-slip oscillation phase and the critical velocity of the belt remain unaffected by the nonlinear term. It is also shown that the amplitude of the stick-slip phase varies inversely with nonlinearity. The effect of different system parameters on the vibration amplitude is also studied. Copyright © 2017 by ASME.

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2016

C. Jacob, Eldhose, P. B., and B. Balaram, “Entrainment and Synchronization of Stick – Slip Oscillators”, Procedia Engineering, vol. 144, pp. 1015 - 1022, 2016.[Abstract]


Abstract This work investigates the entrainment and synchronisation in stick – slip oscillators. A spring – mass placed on a uniformly moving belt in the presence of friction is taken as the model and a cubic Stirbeck friction curve is considered. The entrainment of the oscillator is studied both in its stick – slip phase and pure slip phase. It is seen that entrainment in stick – slip phase is realized by gradually eliminating the stick phase; the entrained oscillator undergoes pure slip oscillations. But in pure slip phase, external force introduces a stick phase which gradually disappears on total entrainment. It is also shown that entrainment in both phases is accompanied by a decrease in oscillator amplitude. It is further shown that the critical force needed for entrainment is higher in the stick – slip phase than in the pure slip one. In coupled stick – slip oscillators, detuning is considered in belt velocities and here too mutual synchronisation is accompanied by decrease in amplitude.

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2016

R. Rajeev, Govind, M., and B. Balaram, “Effect of External Force on the Dynamics of Nonlinearly Coupled Self Excited Oscillators”, Procedia Engineering, vol. 144, pp. 1007 - 1014, 2016.[Abstract]


Abstract This work deals with effect of external force on the dynamics of mutually coupled self-excited oscillators. Self-excited oscillators with linear and non-linear coupling are considered. The phase-amplitude equations or Adler equations are obtained analytically in both cases with Krylov and Bogoliubov method of averaging and these equations are used to analyze the effect of external force on their synchronization dynamics. Computational results are obtained by numerical integrations to validate the analytical results. For linearly coupled oscillators, the effect of external force on synchronization are studied. For nonlinear coupling, it's shown that in-phase synchronization is not possible even if the coupling values are varied. Such a system is brought into synchronization with effect of external force. Also, for both cases, non-synchronized cases are brought into synchronization with the aid of external force. This work shows that, even small amplitude of external disturbances, can produce considerable effect on the synchronization dynamics of coupled systems and thus should be given due importance in practical scenarios More »»

2015

V. Vinod, B. Balaram, Narayanan, M. D., and Sen, M., “Effect of Oscillator and Initial Condition Differences in the Dynamics of a Ring of Dissipative Coupled Van Der Pol Oscillators”, Journal of Mechanical Science and Technology, vol. 29, pp. 1931–1939, 2015.[Abstract]


This paper investigates the dynamical behavior of coupled van der Pol oscillators in a ring to understand vibrations that may occur in systems such as turbine blades mounted on a single shaft. The objective is to investigate the effect of spatial differences in oscillator parameters and initial conditions that occur in realistic systems. The coupling between the neighboring oscillators is modeled as a linear dissipative element, and the mathematical model is analyzed asymptotically and numerically. Synchronization of self excited oscillators in mechanical systems has been predominantly investigated in recent literature by focusing on its parameter dependence. This work investigates the dependence of dynamics of such systems on initial conditions. The analysis is conducted for identical oscillators as well as oscillators with a frequency mismatch, along with three different sets of initial conditions. The dynamics of the system is discussed based on time plots, frequency plots, instantaneous dynamics of each oscillator by Hilbert transform and the phase equation obtained by asymptotic expansion. The study reveals interesting phenomena like amplitude death, oscillation suppression, oscillation resurrection, frequency locking and beat frequency in the model when subjected to the different set of initial conditions.

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2012

B. Balaram, Narayanan, M. D., and Rajendrakumar, P. K., “Optimal design of multi-parametric nonlinear systems using a parametric continuation based Genetic Algorithm approach”, Nonlinear Dynamics, vol. 67, pp. 2759–2777, 2012.[Abstract]


In this paper, a procedure for the optimal design of multi-parametric nonlinear systems is presented which makes use of a parametric continuation strategy based on simple shooting method. Shooting method is used to determine the periodic solutions of the nonlinear system and multi-parametric continuation is then employed to trace the change in the system dynamics as the design parameters are varied. The information on the variation of system dynamics with the value of the parameter vector is then used to find out the exact parameter values for which the system attains the required response. This involves a multi-parametric optimisation procedure which is accomplished by the coupling of parameter continuation with different search algorithms. Genetic Algorithm as well as Gradient Search methods are coupled with parametric continuation to develop an optimisation scheme. Furthermore, in the coupling of continuation and Genetic Algorithm, a ``norm-minimising'' strategy is developed and made use of minimising the use of continuation. The optimisation procedure developed is applied to the Duffing oscillator for the minimisation of the system acceleration with nonlinear stiffness and damping coefficient as the parameters and the results are reported. It is also briefly indicated how the proposed method can be successfully used to tune nonlinear vibration absorbers.

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Publication Type: Conference Paper

Year of Publication Title

2019

V. Vigneshvar, Vishwanth, S. R., Venkateshwaran, S., and B. Balaram, “A comparative study of wake oscillator models for flow induced vibrations”, in AIP Conference Proceedings, 2019, vol. 2134.[Abstract]


This paper analyzes the existing structure-wake oscillator models which are used to model the vortex induced vibrations occurring in an elastically supported rigid circular cylinder in a uniform fluid stream. The wake region, a consequence of the fluctuating nature of the vortex shedding, has been modeled using the classical van der Pol equation, and a single degree of freedom oscillator has been used for the structure. The parameters used for the numerical simulations have been taken from experimental literature, which estimated them based on the results of experimental studies. The inclusion of nonlinearity in the structural oscillator, to see if it would give better results compared to the existing models, has also been investigated. © 2019 Author(s).

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2017

Alwin Thomas, B. Balaram, and Dr. Santhosh B., “Entrainment in multi degree of freedom discontinuous system with application to disc brakes”, in Int. Conference on Vibration problems (ICOVP 2017), IIT Guwahati, 2017.

List of Ph. D. Students

  • Rony Philip, Power flow analysis of nonlinear energy harvesting systems using Nonlinear Normal Modes, Ongoing, Co-guide.

Key Responsibilities at Amrita Vishwa Vidyapeetham

  • Member – Academic Audit Committee
  • Class Advisor