Analyses of transverse vibrations of axially pretensioned viscoelastic nanobeams with small size and surface effects

• The properties of transverse vibration of a pretensioned embedded viscoelastic nanobeam is investigated.
• The vibrational equation is formulated based on Bernoulli–Euler beam theory and Kelvin model.
• Explicit expression for the complex vibrational frequency is obtained.
• Small size and surface effects on vibrational frequency are discussed.
• Influences of structural damping, initial axial tension and surrounding medium are analyzed.

The general governing equation for transverse vibration of an axially pretensioned viscoelastic nanobeam embedded in elastic substrate medium is formulated on the basis of the Bernoulli–Euler beam theory and the Kelvin model. The factors of structural damping, initial axial tension, surrounding medium, small size, surface elasticity and residual surface tension are incorporated in the formulation. The explicit expression is obtained for the vibrational frequency of a simply supported nanobeam. The impacts of these factors on the properties of transverse vibration of the nanobeam are discussed. It is demonstrated that the dependences of natural frequency on the structural damping, surrounding medium, small size, surface elasticity and residual surface tension are significant, whereas the effect of initial axial tension on the natural frequency is limited. In addition, it can be concluded that the energy dissipation of transverse vibration of the viscoelastic nanobeam is related to the small size effect and structural damping.