Nonlinear Vibration and Stability Analysis of Functionally Graded Nanobeam Subjected to External Parametric Excitation and Thermal Load

Analysis of vibration stability of simply supported Euler-Bernoulli functionally graded (FG) nanobeam embedded in viscous elastic medium with thermal effect under external parametric excitation is presented in this work. An attempt has been made for the first time is investigating the effect of thermal load on dynamic behavior, amplitude response, instability region and bifurcation points of functionally graded nanobeam. Thermal loads are supposed to be uniform, linear or nonlinear distribution along the thickness direction. Nonlocal continuum theory and the principle of the minimum total potential energy are applied to derive the governing equations. The partial differential equations (PDE) are transported to the ordinary differential equations (ODE) by using the Petrov-Galerkin method and the multiple time scales method are manipulated to solve the motion equation. To study the effect of external parametric excitation and thermal effect, different temperature distributions along the thickness such as uniform, linear, and nonlinear distribution are considered. Moreover, stable and unstable regions and bifurcation points are determined. It is obtained that the thermal load can affect the amplitude response of FG nanobeam. Also, it is observed that the instability of the system is affected by the detuning parameter and the parametric excitation amplitude plays great role in the instability of system. Nanobeams are used in many devices like nanoresonators, nanosensors and nanoswitches. This paper is helpful for designing and manufacturing nanoscale structures specially nanoresonators under different thermal loads.

Efficient Response Amplification of Electrothermally Driven Resonators Using Magnets

Micro/Nano-electromechanical systems, MEMS/NEMS-based resonators are presently an important part of a wide range of applications. However, many of these devices suffer from the low signal-to-noise ratio and the need for a large driving force. Different principles were proposed to enhance the sensitivity and improve their signal-to-noise ratios (SNR), such as bifurcations, jumps and higher-order excitation. However, these methods require special designs and high actuation voltages, which are not always available in the standard function generators and power supplies. Also, it increases the devices’ overall cost and power requirements. Furthermore, parametric excitation is explored as an option to amplify the signal at a lower cost and energy demand. However, this type of excitation requires specific geometrical settings, in addition to very low damping conditions. Electrothermal actuation is investigated to achieve excitation of primary resonance, which can be used for parametric excitation. This type of excitation is desirable due to its simplicity, robustness and ability to create large internal forces at low voltages. However, the time response is limited by the thermal relaxation time. In this work, we demonstrate the use of electromagnetic actuation to significantly amplify the response of electrothermally actuated clamped-clamped resonators at first mode (primary) resonance. At ambient pressure, experimental data show 18 times amplification of the response amplitude compared with electrothermal actuation only. The method is based on introducing a permanent magnetic field to induce an out-of-plane Lorentz-force. The results show the great potential of this technique being used for a variety of sensing and signal processing applications, especially, where a large signal-to-noise ratio is required while using low operational voltages.