Somnath Dey
Ph.D. Student
Research
Somnath Dey is a research associate, in the Department of Mechanical Engineering at Indian Institute of Technology Bombay. His primary research interests are in the areas of Vibrations, Nonlinear Dynamics, Dynamics and Control, and MEMS. He has recently submitted his Ph.D. thesis titled “High-Speed Dynamics of Cantilevers in Video-Rate Scanning Probe Microscopy”. The motivation behind the study is ‘Video-Rate’ SPM, which can be used to image temporally evolving phenomena, or to visualize rapidly changing topographies, such as those encountered in several biological processes.
The analysis has been performed in two parts: first, at the macro-scale, by neglecting the micro-scale forces, but which provides insight into the cantilever's dynamics due to the intermittent impacts; and at the micro-scale, considering the nonlinear interaction forces. An expression was derived for the maximum surface excitation frequency at which contact loss can occur, which provides an estimate of the upper limit of the achievable scanning speed (Fig. 1). An upscaled (macro-scale) experimental setup (Fig. 2) was designed to investigate the cantilever's dynamics due to the intermittent impacts, at high scan speeds. Several interesting phenomena were observed in the cantilever's responses, such as modal transition, beating, grazing, and possible chaotic behaviour.
Figure 1. Variation of contact loss frequency ΩCL with stiffness ratio Κ and mass ratio μm.
Figure 2. Photograph of the macro-scale experimental model.
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Figure 3. Simulated and experimentally-obtained Poincare maps of the responses of the cantilever’s end (w|x=1) for different Ω's |
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The micro-scale experiments were performed on a commercial SPM setup. At low scan speeds, the nonlinear forces excite several cantilever eigenmodes. Interestingly, these frequencies appear as combination frequencies in the spectra (Fig. 4). At high scan speeds the overshooting and parachuting phenomena are clearly observed, and the cantilever dynamics resembles intermittent contact mode behaviour. The image resolution is found to be sensitive to the excited eigenmodes and the achievable imaging speed (or resolution) is directly dependent on the surface feature excitation frequency.
Next, in order to improve the scan-speed range and force sensitivity of the microscope, a stepped profile geometry of the cantilever was designed and fabricated. The dimensions for each section of the cantilever were selected to maximize the first eigenfrequency (Fig. 5) even while lowering its flexural stiffness. This in turn significantly increases the contact loss frequency, and also reduces the effect of the scanner's oscillations upon the image resolution. Certain passive techniques, such as electrostatic pre-stressing, and piezo-electric damping, were also explored to mitigate the high amplitude oscillations of the cantilever and to suppress the effects of higher eigenmodes, possibly excited due to the nonlinear forces and intermittent impacts at such high scan speeds. Ω
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Figure 4. Frequency spectra of the simulated responses at two different locations x = L, 0.5L of the cantilever for different (constant) scan speeds. |
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Figure 5. Variation of the first eigenfrequency of the cantilever with the length ratio L̅ and width ratib b̅. |
Figure 6. Variation of the frequency ratio of the first two eigenfrequencies of the cantilever. |
Publications
Journal Publications
S. Dey, and V. Kartik, “Intermittent Impact Dynamics of a Cantilever Scanning a Surface at High Speed,” Journal of Applied Physics, 123, 124904 (2018).
Chatterjee, S., and Dey, S., 2013. “Nonlinear dynamics of two harmonic oscillators coupled by Rayleigh type self-exciting force”. Nonlinear Dynamics, 72 (1-2), pp. 113-128.
S. Dey, and V. Kartik, “Dynamics of Scanning Probe Microscope Micro-Cantilevers in High-Speed Constant-Height Contact Mode Imaging.” (Upcoming)
S. Dey, and V. Kartik, “High-Speed Imaging Using Stepped Micro-Cantilevers in Contact Mode Scanning Probe Microscopy.” (Upcoming)
Conference Proceedings
S. Dey, and V. Kartik, “Energy Harvesting from an Intermittent Impact Macro-Cantilever with Remote Sensor Applications,” 10th National Symposium and Exposition on Aerospace and Defence Related Mechanisms (ARMS 2016), Thiruvananthapuram, India, 18th-19th November 2016.
S. Dey, and V. Kartik, “Micro-cantilever Vibration with Non-linear Interaction Forces at High Imaging Speeds in AFM,” Proceedings of the 12th International Conference on Vibration Problems (ICOVP-2015), Indian Institute of Technology, Guwahati, India, 14th-17th December 2015.
S. Dey, and V. Kartik, “Intermittent Contact Dynamics of a Micro-Cantilever in High Speed Contact Mode Scanning Probe Microscopy", ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE), Houston, USA, 13th-19th November 2015.
Biography
Somnath is a currently working as a Research Associate in the Mechanical Engineering Department at IIT Bombay. He has recently submitted his Ph.D. thesis for external review. He completed his Master’s (M. Engineering) in Machine Design from the Indian Institute of Engineering Science and Technology (IIEST) Shibpur in the year 2012. During his Master’s he worked in the area of non-linear coupled oscillators, with a thesis titled “Nonlinear dynamics of two harmonic oscillators coupled by Rayleigh type self-exciting force”. He graduated in the year 2010, with a B. Technology in Mechanical Engineering from Tezpur University, Assam.