Characterization of the Quality Factor Due to the Static Prestress in Classical Caputo and Caputo-Fabrizio Fractional Thermoelastic Silicon Microbeam.

Hamdy M Youssef,Eman A N Al-Lehaibi,Alaa A El-Bary

doi:10.3390/polym13010027

Abstract

The thermal quality factor is the most significant parameter of the micro/nanobeam resonator. Less energy is released by vibration and low damping, which results in greater efficiency. Thus, for a simply supported microbeam resonator made of silicon (Si), a thermal analysis of the thermal quality factor was introduced. A force due to static prestress was considered. The governing equations were constructed in a unified system. This system generates six different models of heat conduction; the traditional Lord–Shulman, Lord–Shulman based on classical Caputo fractional derivative, Lord–Shulman based on the Caputo–Fabrizio fractional derivative, traditional Tzou, Tzou based on the classical Caputo fractional derivative, and Tzou based on the Caputo–Fabrizio fractional derivative. The results show that the force due to static prestress, the fractional order parameter, the isothermal value of natural frequency, and the beam’s length significantly affect the thermal quality factor. The two types of fractional derivatives applied have different and significant effects on the thermal quality factor.

Highlights

Several applications are essential for micro-and nanoelectric resonator applications, such as mechanical signal processing, scanning, microscopes, and ultrasensitive mass detection
Sharma and Sharma [10] introduced the thermal damping in a circular plate of microresonators in the context of the Lord–Shulman theory of generalized thermoelasticity theory (L–S)
A force attributable to static prestress was found to create a purely assisted microbeam resonator made of silicon (Si)

Summary

Introduction

Several applications are essential for micro-and nanoelectric resonator applications, such as mechanical signal processing, scanning, microscopes, and ultrasensitive mass detection. Sun et al [9] studied the thermoelastic damping of a beam resonator based on a non-Fourier heat conduction equation. Guo et al [21,22] studied the thermoelastic damping theory of micro- and nanomechanical resonators using the DPL model. In the present study, we will construct an analytical solution of a thermal model of a silicon microbeam resonator subjected to static prestress based on two different types of fractional derivative definitions. We will calculate the thermal quality factor in the context of the new Caputo-Fabrizio fractional derivative which will supply us with new and different results. This paper introduces different and new comparisons between the Lord–Shulman (L-S) and dual-phase-lag (DPL) models and between two types of fractional derivative and the traditional derivative which has not been published before this work

Model Formulation

Descriptions of the Six Models

Conclusions