Large amplitude free vibration of micro/nano beams based on nonlocal thermal elasticity theory

Yong-Gang Wang,Wen-Hui Lin,Jin-Ke Wang,Hui-Fang Song

doi:10.1590/1679-78251904

Yong-Gang Wang, Wen-Hui Lin + Show 2 more

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https://doi.org/10.1590/1679-78251904

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Abstract

This paper is concerned with the nonlinear free vibration of a heated micro/nano beam modeled after the nonlocal continuum elasticity theory and Euler-Bernoulli beam theory. The governing partial differential equations are derived from the Hamilton variational principle and von Karman geometric nonlinearity, in which the effects of the nonlocality and ambient temperature are inclusive. These equations are converted into ordinary forms by employing the Kantorovich method. The solutions of nonlinear free vibration are then sought through the use of shooting method in spatial domain. Numerical results show that the proposed treatment provides excellent accuracy and convergence characteristics. The influences of the aspect ratio, nonlocal parameter and temperature rise parameter on the dimensionless radian frequency are carefully investigated. It is concluded that the nonlocal and temperature rise parameters lead to reductions of the nonlinear vibration frequency, while the influence of the nonlocal effect decreases with an increase in the aspect ratio.

Highlights

Since the initial discovery of carbon nanotubes by Iijima (1991), a new attractive topic has come under ever-increasing research scrutiny for micro/nano-sized structures
Due to the presence of small scale effects which are related to the atoms and molecules that constitute the materials at micro/nano scale, atomic modeling method, such as molecular dynamics simulation (Tuzun et al, 1996) is certainly conceptually valid for the accurate mechanical analysis
Wang et al / Large amplitude free vibration of micro/nano beams based on nonlocal thermal elasticity theory exorbitant for micro/nano structures, especially for large sized atomic systems

Summary

Introduction

Since the initial discovery of carbon nanotubes by Iijima (1991), a new attractive topic has come under ever-increasing research scrutiny for micro/nano-sized structures. The exceptional physical, chemical, mechanical, electronic and thermal properties of this structure have led to a wide range of applications (Poncharal et al, 1999; Guz et al, 2007). Due to the presence of small scale effects which are related to the atoms and molecules that constitute the materials at micro/nano scale, atomic modeling method, such as molecular dynamics simulation (Tuzun et al, 1996) is certainly conceptually valid for the accurate mechanical analysis. Y.G. Wang et al / Large amplitude free vibration of micro/nano beams based on nonlocal thermal elasticity theory exorbitant for micro/nano structures, especially for large sized atomic systems. As experiment in micro/nano scale is difficult to conduct and control, continuum modeling is becoming an alternate to atomistic method

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