The Size-Dependent Thermoelastic Vibrations of Nanobeams Subjected to Harmonic Excitation and Rectified Sine Wave Heating

Abstract

<jats:p>In this article, a nonlocal thermoelastic model that illustrates the vibrations of nanobeams is introduced. Based on the nonlocal elasticity theory proposed by Eringen and generalized thermoelasticity, the equations that govern the nonlocal nanobeams are derived. The structure of the nanobeam is under a harmonic external force and temperature change in the form of rectified sine wave heating. The nonlocal model includes the nonlocal parameter (length-scale) that can have the effect of the small-scale. Utilizing the technique of Laplace transform, the analytical expressions for the studied fields are reached. The effects of angular frequency and nonlocal parameters, as well as the external excitation on the response of the nanobeam are carefully examined. It is found that length-scale and external force have significant effects on the variation of the distributions of the physical variables. Some of the obtained numerical results are compared with the known literature, in which they are well proven. It is hoped that the obtained results will be valuable in micro/nano electro-mechanical systems, especially in the manufacture and design of actuators and electro-elastic sensors.</jats:p>

Viscoelastic stressed microbeam analysis based on Moore–Gibson–Thompson heat equation and laser excitation resting on Winkler foundation

“…If integration is done along the microbeam thickness to equation (22), after multiplying with 12z=h 3 , it results in 1 þ τ 0 ∂ ∂t…”

“…Many researchers have considered the mechanism of heat transfer and microbeam vibration. [13][14][15][16][17][18][19][20][21][22] The inclusion of different field effects, such as temperature or initial stress field effects, also represents an important problem in the simulation of microstructures and microscale systems. Initial stress is generated in the medium due to various factors, resulting from a tightening phase, temperature difference, shot pinning, varieties of gravity, differential forces external, etc.…”

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“…Mathematics 2021, 9, x FOR PEER REVIEW 3 of 21 more specially, it is equally important to analyze the thermoelastic behavior of engineering structures, for example, the thermoelasticity behaviors of nanobeams [26], microbeams [27], composite beams [28], and laminated beams [29]. Of course, the bimodular material beams should also be included in the thermoelastical analysis of structures.…”

“…It should be emphasized that Green and Lindsay's theory has been addressed for many types of media, in which Marin et al [25] used this theory in the context of the dipolar thermoelastic bodies. On the other hand, besides the development of the theory itself, it is also very important to apply the theory to the analysis of the engineering components, or more specially, it is equally important to analyze the thermoelastic behavior of engineering structures, for example, the thermoelasticity behaviors of nanobeams [26], microbeams [27], composite beams [28], and laminated beams [29]. Of course, the bimodular material beams should also be included in the thermoelastical analysis of structures.…”

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“…Due to their unique properties and functions, micro/nanoelectromechanical systems (MEMS and NEMS) have been of great research interest. These systems are widely used in many areas of technology and engineering, including vehicles and electronics 15 . Some micro and nano structures, as well as length and width differences that have a significant impact on the properties and performance of those structures, may have geometric irregularities during production, assembly and packaging.…”