This paper aims to present an explicit relation for thermoelastic damping in nanobeams capturing the small-scale effects on both the continuum mechanics and heat conduction domains. To incorporate small-scale effects, the coupled equations of motion and heat conduction are obtained by employing the nonlocal elasticity theory and the dual-phase-lag heat conduction model. Adopting simple harmonic forms for transverse deflection and temperature increment and solving the governing equations, real and imaginary parts of the frequency are extracted. According to the complex frequency approach, a closed-form size-dependent expression for evaluating thermoelastic damping in nanobeams is derived. To clarify the influence of nonlocality and dual-phase-lagging on the amount of thermoelastic damping, numerical results are compared with the ones predicted in the framework of classical continuum and heat conduction theories. Findings reveal that the size effect on both the continuum mechanics and heat conduction modeling of nanobeams is not negligible. A number of parametric studies are also conducted to indicate the effect of beam dimensions, boundary conditions and type of material on the value of thermoelastic damping.

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This paper investigates the bending, buckling and free vibration behaviors of functionally graded carbon nanotubereinforced composite (FG-CNTRC) nanobeams by considering small-scale effect. The governing equations of motion of a Timoshenko beam under a general loading are derived utilizing the nonlocal elasticity theory. The equations governing bending and stretching behavior of CNTRC nanobeams are uncoupled to a fifth-order ordinary differential equation with respect to the rotation of cross-section for the static cases of bending and buckling. This uncoupling makes it possible to develop exact solutions for transverse deflection and buckling load of CNTRC nanobeams. Using differential operator method, the decoupled sixth-order differential equations in terms of the kinematic variables are obtained for vibration analysis. By setting the coefficients matrix in the corresponding system of homogenous algebraic equations to zero, an algebraic frequency equation is derived. Finally, based on the presented closed-form solutions, parametric studies are carried out to assess the effects of CNT distribution, nonlocal parameter and type of boundary conditions on the deflection, buckling and natural frequency of CNTRC nanobeams. Findings show that nonlocal effect on the mechanical behavior of nanobeams is strongly dependent on boundary conditions and loadings. It is seen that cantilever nanobeams become harder by taking into account nonlocal effect, contrary to clamped and simply supported nanobeams. In addition, the influence of CNT distribution on the mechanical behavior of cantilever beams is more significant than that of simply supported and clamped beams.

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