Nonlinear Free Vibration Analysis of Nanobeams With Nonlocal and Surface Effects

V S, Nikhil (2014) Nonlinear Free Vibration Analysis of Nanobeams With Nonlocal and Surface Effects. Masters thesis, Indian Institute of Technology Hyderabad.

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Abstract

Micro electro-mechanical system (MEMS) based sensors and actuators are widely used in almost every eld due to many advantages over the conventional devices in terms of stability, accuracy, sensitivity and operating exibility, etc. Many resonant sensors and actuators are characterized their resonant frequencies and damping. Therefore, it is essential to compute character frequency. As the size of the micro devices reduce to nanoscale, the resonance frequency become dependent of size related factors such as nonlocal eect as well as surface eects. Therefore, in this thesis, we present a detailed theory and derive resonance frequency models theoretically and numerically for the simply-supported, xed-xed, and the cantilever nanobeams. To model the nonlocal eects under axial loading, we rst obtain the governing equation by including the nonlocal eects in bending and axial terms. Subsequently, we obtain the analytical models for dierent resonance frequencies as a function of nonlocal eects. We found that higher modes are more sensitive to the nonlocal parameters. However, the nonlocal model mentioned above is valid for small amplitude oscillation. To improve its range, we modied the governing equation by including additional nonlocal eects in inertia and damping, and also geometric nonlinearity. Subsequently, we found the frequencies as a function of all the important parameters by using the method of multiple scale. To validate the models numerically, we present a linear nite element model to capture nonlocal and surface eects. However, this model does not capture geometric nonlinearity but it can be extended to complex geometries. Finally, we validate our model with each other and also present the limitation of each models. The models developed in this thesis are applicable to dierent types of beams which can be widely used in the design of senstive nanoscale sensors and actuators. However, it can be improved by extending it to Timoshenko beams.

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