- A list of my publications is here.
- Here is my Ph.D dissertation.
Introduction:
The broad area of my research for the last 4 years has been ‘ultrasonic guided waves’. I used to work on simulation and modeling but for the last 1.5 years I have concentrated on the theoretical aspects of guided waves. In the following paragraphs I have made an attempt at explaining my research to someone who might only have a basic understanding of the physics involved.
‘Sound’ is the interaction of material disturbance, travelling in the air, with the eardrum. This material disturbance is known as a ’stress wave’. Same stress wave also travels in any other material when it is struck with a hammer or insonified with a transducer. In an infinite 3 dimensional medium these waves travel unhindered and both the solution and analysis of such waves are easy. But when these waves are constrained by boundaries , like in the case of a thin plate or a circular pipe, their behavior becomes very complex. Such constrained waves are called ‘guided waves’. They continue to generate a lot of research interest because they can travel long distances with little attenuation. Hence they are ideal for long range inspection of defects in structures such as rails and aircraft wings. There is a rule of thumb that the higher the frequency of the wave (or smaller the wavelength), the smaller the defects it is sensitive to. Therefore, high frequency (ultrasonic) guided waves are the craze.
The caveat here is that guided waves are very complex to analyze. Even in the simplest of structures, they exhibit what is called multimodal-dispersive behavior. Multimodal means that at a given frequency, more than 1, typically thousands of modes potentially exist in the structure and dispersive means that most of those modes, at least all which are of any interest usually, travel at velocities which are in turn dependent upon frequency. So any attempt at using guided waves requires that this behavior be well understood.
Simulation and modeling:
My initial research (first 2-2.5 years) consisted of computer modeling of such guided waves in complex structures. One way to do this is by using the Finite Element method but it is highly computationally intensive and there is virtually no physical insight in the end. So we used what’s called a Semi Analytical Finite Element (SAFE) method. My contribution till this point was small. Later though, I was able to join SAFE and FE in a tool that had the advantages of both methods. This hybrid method (unimaginatively called Global-Local) had the computational efficiency and physical insight of SAFE and the versatility of FE and still remains a useful tool.
Nonlinear guided waves:
At this point I became interested in the nonlinear aspects of guided waves. I also wanted to do some theoretical work but frankly speaking, the kind of physics I work in has been around for so long that it appears that most of the fundamental problems have already been solved and what all remain, if any, are excruciatingly difficult. So I was surprised to find that there was a very fundamental physical phenomenon in nonlinear plate waves (Lamb waves) that was neither known nor had a mathematical explanation. Part of the problem lay in the unbearably cumbersome mathematics of the solution. It was possible to solve the problem, but owing to the mathematical complexity, it wasn’t possible to find meaningful physical implications of the solution. Fortunately though, I was able to find a workaround wherein the underlying physics could be understood without going into the complete solution. This reasoning was subsequently extended to rod waves for other results.
Further Research
I am going to be joining Dr. Nemat Nasser’s group and my research would focus on (verbatim from the offer letter) modeling and characterization of composite metamaterials and wave propagation in anisotropic media with spatially changing material axis using theoretical and numerical approaches.
At this point I have no idea what that means 
!