Abstract
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.
Highlights
In recent decades, due to the rapid advancement in engineering technology and stringent training requirements, dynamics and stability and their control over mechanical vibration have gradually transformed into a fundamental and indivisible branch of study in applied mechanics and related engineering
It is imperative for micro-electro-mechanical systems (MEMSs) designers to understand the mechanical properties of elastic micro-components, considering the ultimate goal of Mathematics 2020, 8, 1128; doi:10.3390/math8071128
When an external harmonic excitation is applied to the nanobeam, the field quantities are more sensitive to the excitation frequency Ω
Summary
Due to the rapid advancement in engineering technology and stringent training requirements, dynamics and stability and their control over mechanical vibration have gradually transformed into a fundamental and indivisible branch of study in applied mechanics and related engineering. Advanced apparatuses created on the basis of resonators, modern science, microscale switches, telephones, mirrors, and pumps are cases of this approach [12,13] Both investigations and atomic reproduction calculations have established an important dimension influence in the properties of mechanical materials when the sizes of these engineering structures are very small. The proposed model and methodology introduced in this work can be applied to study and describe the thermodynamic behavior of axial nanomaterial systems, such as nanoplates or nanoscale rods with thermoelastic properties. In this investigation, the thermoelastic nonlocal theory is applied to the Euler Bernoulli beam problem subjected to a dispersed harmonic excitation load per unit length.
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