Anindya Chatterjee

Mechanical Engineering, IIT Kanpur

Some present and past research topics:

In each case, the names of prominent students and collaborators are listed in parentheses.

**Damping:**Two automotive components (say, aluminum alloy crank cases) with similar sizes and weights and with identical material composition can have very different damping properties. Why? Can shape be chosen to maximize internal damping? We are thinking about this question theoretically, towards new constitutive relations. In the past, we have studied thermoelastic damping effects. (Anup Basak, K Nandakumar, Atanu Mohanty, Prasun Jana)**Boats:**A boat in water has a well-defined roll oscillation frequency. But oscillations are not harmonic - they decay - if the boat is in open water, because waves radiate away. We did a two-dimensional analysis of this problem, placing the boat in a finite tank. A simple boundary element method was used. (Lt Cdr Shashwat Srivastava)**Journal bearings:**In a small and cheap (demo) experimental setup, we measured pressures in a journal bearing and found the angular extent of the nonzero oil pressure to be quite small (as low as 40-50 degrees), which contradicts the usual textbook solutions. We pointed out that new combinations of old boundary conditions can actually predict such solutions, which we have not seen anywhere before. (T. Vimal and Nikhil Sharma)**Rotor dynamics:**Almost every treatment of rotor whirl considers the rotor to be made up of slender deformable beam-like or rod-like portions with bigger things like rigid disks attached. There was little done on computational approaches to finding the whirl speed of an arbitrary axisymmetric deformable rotor, like (say) a bottle or a funnel. Traditional treatments of rotor whirl use something called gyroscopic terms, which are not easy to calculate for these arbitrary shapes. We found that spin-induced prestresses, interpreted from a nonlinear elasticity viewpoint (nonlinear, but small-displacement, like Euler buckling), capture these gyroscopic effects. A new insight into an old subject. (Pradeep Mahadevan, CS Jog)**Fatigue damage evolution:**Fatigue modeling is a big remaining problem of engineering design. There are many*ad hoc*approaches to this problem, based on simple formulas for initial and approximate design. And there are many detailed studies of micromechanics, flaws, plasticity, and fracture, whose conclusions have for the most part not fed into simple design procedures (some useful exceptions exist, such as the idea of "leak before break"). Viewing damage as an evolving quantity obeying some dynamic model, we have made progress in trying to deduce in a constructive way what a useful*form*for the dynamic model might be. We are also now thinking about incorporating statistical aspects of fatigue data in new and useful ways. (Joe Cusumano, Navendu Patil, Pradeep Mahadevan, DV Rambabu)**Bicycles and motorcycles:**Bicycles, even when highly idealized in the modeling, have complicated dynamics governed by long and complicated equations. The long and scattered history of bicycle mechanics research contains many partly-erroneous treatments along with many all-correct ones. We have obtained and published some benchmark numerical results for a bicycle to provide future analysts with a basis for comparison. I am also trying to understand aspects of what makes a light motorcycle (Indian conditions) easier to handle and to ride. My student Raju has, through detailed ADAMS simulations, found some interesting correlations for steer angles and torques for realistic motorcycle models in long steady turns. (Pradipta Basu-Mandal, Jim Papadopoulos, Venkata “Raju” Karanam, David Limebeer)**Fractional order derivatives**: What time-domain operation is equivalent to multiplying by a fractional power of "s" in the Laplace domain? This question, classical, simple and yet offbeat, seems relevant to the theoretical design of innovative new control systems as well as the experimentally observed behavior of rubber-like viscoelastic materials. The time-domain operation in question involves a numerically troublesome calculation; we have found a much simpler, but quite accurate, approximate alternative. More recently, we have developed the approximation method to a slightly more general class of convolution integrals. An interesting aspect of this work is that we approximate the dynamic system and not a specific solution. Most recently, we have developed closed form expressions and hence a very compact code for generating the matrices used in this approximation. (Satwinder Jit Singh and Sambit Das)**Nonlinear oscillations:**This broad title covers an assortment of topics, some of which are separately listed below. Others include approximate implementation of asymptotic methods, the scope of seeking patterns of slow change (health monitoring, amplitude modulations, phase drift, whatever) in fast-varying (oscillating) signals, some new numerical techniques for investigation of nonlinear systems, vibrations with changing contact locations, and others. (Joe Cusumano, David Chelidze, Sovan Lal Das, Amol Marathe, K Nandakumar, Dhiman Chatterjee, Arjun Roy)**Delay differential equations:***t*depends explicitly on its states at both time*t*as well as time*t-*1, then the dynamics is governed by a delay differential equation. We have developed new analytical and numerical methods for studying and understanding such systems. (Sovan Lal Das, Pankaj Wahi)**Ion dynamics in Paul traps**: Paul traps are used in mass spectrometry. They trap and selectively eject ions in ways that tell chemists things about these ions. The motion of these ions is governed by weakly nonlinear equations with parametric forcing. We have studied such dynamics, and also developed new approximate techniques for the same. (Amol Marathe, N Rajanbabu, AG Menon, Atanu Mohanty, Pawan Tallapragada)**Health monitoring of equipment**: This work was done during my postdoc days at Penn State, prior to 2000. (David Chelidze, Joe Cusumano)**Passive walking machines:**This was work with fellow PhD students at Cornell, prior to 1998. (Mike Coleman, Mariano Garcia, Andy Ruina)**Rigid body impact models:****Odd topics:**Solitary waves in a chain of elastic spheres; indirect measurement of contact forces in vibration-dominated impacts; the short-time impulse response of Euler-Bernoulli beams; an optimization problem that arises in trying to do high-dimensional PODs with a few sensor measurements at a time; active noise control using a feedforward algorithm; stress analysis of flanges;*sub-exponential*attenuation of waves in a periodic structure (with Ishita Chakraborty and Atanu Mohanty; this is a surprising new result in a mature subject); oscillations of an inextensible catenary using a Rayleigh-Ritz method (somehow never done by others, apparently; with Indrasis Chakraborty); and some other such diversions.