In this article thermoelastic damping in nano-beam resonators is investigated based on nonlocal theory of elasticity and the Euler-Bernoulli beam assumptions. The governing equation of deflection of the beam is obtained from shear and moment resultants and stress–strain relationship of the nonlocal elasticity model and also the governing equations of thermoelastic damping are established by usi...

We show that a non-dissipative feedback that has been shown in the literature to exponentially stabilize an Euler-Bernoulli beam makes a Rayleigh beam and a Timoshenko beam unstable.

This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equati...

In this paper, a relatively new method, namely variational iteration method (VIM), is developed for free vibration analysis of a Timoshenko beam with different boundary conditions. In the VIM, an appropriate Lagrange multiplier is first chosen according to order of the governing differential equation of the boundary value problem, and then an iteration process is used till the desired accuracy ...

Carbon nanotubes with their outstanding mechanical, physical and electrical properties have stimulated a significant amount of scientific technological research due to uniqueness compared conventional materials. As result, an extensive study on mechanical has been conducted, the static dynamic behavior single- walled multi-walled carbon examined using Euler-Bernoulli Timoshenko beam models. The...

A consistent nonlocal viscoelastic beam model is proposed in this paper. Specifically, a Timoshenko bending problem, where size- and time-dependent effects cannot be neglected, investigated. In order to inspect scale phenomena, stress-driven formulation used, whereas simulate effects, fractional linear viscoelasticity considered. These two approaches are adopted develop new model. Analytical so...

In this paper we further develop the theory of the extended Timoshenko beam model, as first introduced in Part I [5] of this work, with particular emphasis on applications of the model in formation theory [11], [12]. We begin with formal development of the equilibrium equations of static formation theory in the context of the extended Timoshenko model, giving a rigorous discussion of existence,...

The scale effect of carbon nanotubes (CNTs) in the macro CNT-reinforced composites (CNTRCs) is analyzed, and free vibration characteristics a composite beam resting on viscoelastic foundation were studied. By combining nonlocal theory with Eshelby–Mori–Tanaka (EMT) method, EMT constitutive equation considering CNTs CNTRCs proposed. Based Timoshenko theory, governing equations corresponding boun...

The thermal vibration of a single-walled carbon nanotube (SWCNT) is investigated by using the models of Euler beam and Timoshenko beam with quantum effects taken into consideration when the law of energy equipartition is unreliable. The relation between temperature and the root of mean-squared (RMS) amplitude of thermal vibration at any cross section of the SWCNT is derived via the beam models ...