EDUCATION
2014–Present Ph.D., Engineering Science and Mechanics
Department of Engineering Science and Mechanics, Pennsylvania State University, PA, USA.
Advisor: Dr. Joseph Cusumano.
2012–2014 M.Tech, Mechanical Engineering
Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, India.
Advisor: Dr. Anindya Chatterjee.
2008–2012 B.E., Mechanical Engineering
Department of Mechanical Engineering, Jadavpur University, West Bengal, India.
Advisors: Dr. Tarun Kanti Naskar, Dr. Arghya Nandi.
CURRENT RESEARCH EXPERIENCE
Here is a brief summary of my Ph.D. research:
Model reduction of dynamical systems subjected to impacts and discontinuity
My current research is on the model reduction of dynamical systems that are subjected to impacts and discontinuity. Model reduction is a method that provides a minimal mathematical description of any dynamical system by identifying the degrees of freedom (dofs) that primarily control the behavior of the system. Using model reduction, in principle, one formulates a simplified model that captures the principal dynamical features of the system. Such models, also known as reduced order models (ROMs), provide a simpler alternative to study the behavior of higher dimensional systems. Moreover, ROMs reduces the mathematical complexity and computational cost associated with analyzing such systems. However, the accuracy of a ROM is often not guaranteed, and it depends on how accurately its dimension is estimated. Therefore, it is important to have a thorough understanding of the dimension estimation process to formulate an accurate ROM.
In my research, I focus on a particular model reduction technique known as Proper orthogonal decomposition aka POD. It is a data-driven process that formulates ROMs using high dimensional data, obtained experimentally or by simulating high dimensional systems. Through a variance-based decomposition of the data, POD determines a small number of empirical shape functions known as proper orthogonal modes (POMs). A certain number of these POMs are chosen to form a reduced subspace onto which the high dimensional model of the system is projected to formulate a ROM. This number, which is also the dimension of the ROM, is chosen such that a predefined percentage of the data variance is captured. However, this statistical approach often fails to take into account the dynamics of the original system. As a result, while estimating dimension, dofs with small variance are often neglected. This can lead to inaccurate ROMs since the neglected dofs may be critically important to the dynamics of the original system.
My specific aim is to gain a physical understanding behind choosing the dimension of ROMs that are formulated using POD. I study dynamical systems that are subjected to nonsmooth loading conditions such as impacts, which typically excites numerous modes of vibration. While performing model reduction of such systems, it is essential to include all dynamically important modes. My study reveals that the variance-based approach for estimating dimension fails to recognize these dynamically important modes and leads to inaccurate ROMs. I studied the model reduction of an Euler-Bernoulli beam that was subjected to periodic impacts, using a semi-analytical approach. My findings demonstrate that the key to finding out the correct dimension lies in understanding the energetics of the system on the reduced subspace. For a system at a steady-state, the dimension of a ROM should be determined depending on how well the energy input to the system is in balance with the energy dissipated from the system on the reduced subspace. Such energy closure analysis provides an improved method for generating ROMs with energetics that properly reflects that of the full system, resulting in simulations that accurately represent the system’s true behavior. With variance-based mode selection, (in principle) one should always be able to formulate ROMs with any desired accuracy simply by increasing the reduced subspace dimension by trial and error. However, such an approach does not provide any insights as to why this needs to be done in specific cases. The energy closure method provides this physical insight.
After successfully implementing the energy-based approach to an Euler beam system, we are currently studying the scope of implementing this method for experimental systems.
PREVIOUS RESEARCH EXPERIENCES
A. M.tech research project
Here is a short description of my M.tech project:
Experimental study of damping enhancement in aluminium rods by knurling
This work was motivated by an interest in the damping behavior of lightly damped metal components. Prior studies have suggested that near-surface plastic deformation like shot peening can increase the damping of metallic components. Following up on that idea, we studied the damping behavior of slender aluminum rods, supported at one of the nodes of the first free-free mode, vibrating in the first mode. Three types of rods were studied. The first one was a plain aluminum rod obtained commercially from the market, the second one was the same rod but with knurling on the surface, and the third one, used purely for reference purpose, was a plain aluminum rod with electrical insulation (viscoelastic) tapes wound on it. We studied two rods of each type. We measured and recorded the free vibration response of each rod. Mitigation of the measurement noise in the data was achieved through the use of both analog and digital filters. We took ten measurements for each rod and calculated the damping coefficients for each oscillation. Results were consistent across ten measurements and two rods within each pair, but the pairs were found to be significantly different from each other. In particular, damping in the knurled rods was significantly (approximately 60%) higher than plain rods. For reference, this was not as effective as adding visco-elastic tape, which increased the damping by a factor of 2.3. However, as indicated earlier, our interest in this work remained in understanding the effect of the knurling on damping behavior. Additionally, a possible role of air damping in enhancing the dissipation for knurled rods was also investigated analytically and numerically (using FLUENT). However, our investigation revealed that air damping was not a dominant cause for the enhanced damping observed in the knurled rods. Thus, we concluded that knurling which represents a surface deformation process can have a significant effect on the damping property of metals just like shot peening, studied in previous works.
B. Undergraduate research projects
Here are brief descriptions of the two projects I completed in my undergrad.
1. Analysis of the Effect of Number of Knots in a Trajectory on Motion Characteristics of a 3R Planar Manipulator
Knots on the trajectory of a robotic manipulator are predefined points in the workspace that the end effector of the manipulator is required to pass through while moving from one position to another. To increase the accuracy of the motion of a manipulator along the desired trajectory, one is often tempted to increase the number of knots. However, the number of knots can have a significant effect on the motion characteristics of the manipulator. In this work, we studied the effect of varying the number of knots on the jerk, acceleration, and velocity of the end-effector of a 3R planar robotic manipulator. An important aspect of trajectory design is to make sure that the fluctuations in these kinematic variables are as low as possible. This is especially true for acceleration since fluctuations in the acceleration lead to a high value of jerk, which is the time derivative of acceleration. A high value of Jerk often causes unnecessary vibration in the manipulator and it adversely affects the stability of the manipulator. Considering a linear path as the target trajectory, we varied the number of knots between the start and the final positions and designed 8th order polynomial splines for describing the joint angles. Our results showed that increasing the number of knots indeed increases the accuracy of the trajectory traced by the end effector. Furthermore, we observed that as the number of knots is increased, jerk of the end-effector during travel is reduced except at the beginning and the end of the motion. With an increasing number of knots, we saw large fluctuations in velocity, acceleration, and jerk values at both ends of the trajectory at the beginning and at the end of travel leading to undesirable working condition. We thus showed a serious limitation on the use of a large number of knots for enhancing the accuracy of manipulator motion. In addition to this analysis, a simulation of the motion the end effector was also performed with the help of AutoLISP code on the AutoCAD platform.
2. Analysis of deformation and deflection of beams with channel cross section under different loading conditions
When open thin-walled cross section beams are subjected to twisting moment, they undergo large warping stress and angle of twist. The shear-centre is a point in the cross section through which if the externally applied force pass, the twisting moment becomes nil. Thus it is common practice to ensure the external force pass through the shear centre of the beam cross section in design of any assembly involving thin walled steel beams. This work provides with a simulation in ANSYS 13, how twisting deformation change with change in point of application of external load in the cross section and also concludes that the twist is nullified when load is passed through the shear centre. The MATLAB program which has been developed, is able to calculate the shear centre of any cross section with horizontal symmetry, once the geometry of the section is specified.