**2.5 FE modeling of double walled CNT based sensor**

The Carbon Nanotubes (CNTs) are widely used for designing nano sensors, nano resonators and actuators [7]. The mass sensing characteristics of defective Double Walled Carbon nanotubes (DWNTs) were studied using FEM. Various finite element simulations covering chiral, zigzag and arm chair nanotubes with cantilever and bridged conditions using molecular [7] structural dynamics approach. The defects have been subdivided in to 6 missing atoms (A type) and 24 (B type) missing atoms on the outer wall of DWNT. COMBIN 14 element had been used for simulation of defective DWNTs with weak Vanderwaals force. The study revealed the fact that the frequency of defective DWNT reduced with increase in chiral angle. Also the frequency reduced with increase in pinhole defects.

## **2.6 Perspective on nanotips**

Numerous methods have been fabricated for developing ultra-sharp tips for scanning probe microscopy and [8] electron microscopy. It has been observed that the sharp end terminates with very single atom in field ion microscope (FIM). The last atom had been intended to form atomic channel of electrons in field emission mode which would self-collimate a coherent electron beam with an outstanding brightness. Hence nanotips are found to behave as a source of selfcollimated electron or ion beam. In this research [8] the distribution of electric field in the vicinity of nanotip apex that holds the topmost single atom had been studied analytically and numerically. The tip base was found to dominate nano protrusions which enhance electric field. The study revealed that nanotips with broad bases produce even less field than modest tips at the same voltage. This pronounced the fact that the tip base accounts for high voltages needed at imaging threshold field.

## **2.7 Axial vibration of embedded love – Bishop nanorods**

In this research, nonlocal free vibration of axial rods embedded in elastic medium had been studied using Love – Bishop rod theory with FEM. Constitutive modeling for rod formulation using kinematic relations and dynamic equilibrium had been analyzed. Equation [9] of motion and boundary conditions were obtained by varying total potential of nano rod and were solved using separation of variation. Frequency equations of 4 types of nanorods were obtained. Size dependent FEM formulation was synthesized based on weighted residual method. The four parameters mode number, non-local parameter, rod length, and slenderness ratio were used to study the frequency parameters of nanorods. The free vibration frequencies of the simple axial rods had been found to be higher than that of Love bishop rods. These were evaluated by frequencies of two rod theories in higher modes.
