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

Bipin Balaram currently serves as Assistant Professor 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

Publications

Publication Type: Journal Article

Year of Publication Publication Type Title

2017

Journal Article

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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2017

Journal Article

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, pp. 1-12, 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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2016

Journal Article

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 »»

2016

Journal Article

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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2015

Journal Article

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

Journal Article

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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