Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive govern...

Bending, buckling and vibration behaviors of nonlocal Timoshenko beams are investigated in this research using a variational approach. At first, the governing equations of the nonlocal Timoshenko beams are obtained, and then the weak form of these equations is outlined in this paper. The Ritz technique is selected to investigate the behavior of nonlocal beams with arbitrary boundary conditions ...

Abstract Free vibration of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium is studied on the basis nonlocal Timoshenko beam model. Influences slenderness ratios, boundary conditions, atomic structures and stiffness natural frequencies mode shapes SWCNT are examined. The effect significant for higher modes with small ratio soft medium, it softens except fundamental frequenc...

Nonlocal vibration of double-smart nanobeam-systems (DSNBSs) under a moving nanoparticle is investigated in the present study based on Timoshenko beam model. The  two  smart  nanobeams (SNB) are  coupled  by  an  enclosing  elastic  medium  which  is  simulated  by  Pasternak foundation. The energy method and Hamilton’s principle are used to establish the equations of motion. The detailed param...

In this study, free vibration analysis of carbon nanotubes is investigated based on Timoshenko beam theory. Discrete singular convolution (DSC) method is used for free vibration problem of numerical solution of carbon nanotubes. Numerical results are presented and compared with that available in the literature. It is shown that reasonable accurate results are obtained. Keywords-Carbon Nanotubes...

In this paper we develop highly flexible Timoshenko beam model for tracking large deformations in noisy data. We demonstrate that by neglecting some physical properties of Timoshenko beam, classical energy beam can be derived. The comparison of these two models in terms of their robustness and precision against noisy data is given. We demonstrate that Timoshenko beam model is more robust and pr...

In this paper, a numerical solution procedure is presented for the free and forced vibration of a piezoelectric nanowire under thermo-electro-mechanical loads based on the nonlocal elasticity theory within the framework of Timoshenko beam theory. The influences of surface piezoelectricity, surface elasticity and residual surface stress are taken into consideration. Using Hamilton’s principle, t...

Non-prismatic beams have received great attention from engineers due to their capability in optimizing the strength and weight of the structure. In recent years, many researchers have worked on engineering problems related to static and dynamic analysis of either Euler–Bernoulli [1–3] or Timoshenko [4,5] beams. For short thick beams and rotating machineries, the Timoshenko beam theory presents ...

This work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. The Legendre orthogonal polynomials are used as the beam eigenfunctions. N...

Analytical relations between the critical buckling load of a functionally graded material (FGM) Timoshenko beam and that of the corresponding homogeneous Euler–Bernoulli beam subjected to axial compressive load have been derived for clamped–clamped (C–C), simply supported–simply supported (S–S) and clamped–free (C–F) edges. However, no such relation is found for clamped–simply supported (C–S) b...