Dynamic characteristics of damped viscoelastic nonlocal Euler–Bernoulli beams

• Dynamic characteristics of damped viscoelastic nonlocal beams are investigated.
• The Kelvin–Voigt and three-parameter standard viscoelastic models, velocity-dependent external dampings are considered.
• A transfer function method (TFM) is employed to obtain closed-form solution.
• The nonlocal parameters reduces the sensitivity of the viscoelastic parameter on the damped natural frequencies

The dynamic characteristics of damped viscoelastic nonlocal beams are studied in this paper. The Kelvin–Voigt and three-parameter standard viscoelastic models, velocity-dependent external damping and nonlocal Euler–Bernoulli beam theory are employed to establish the governing equations of motion for the bending vibration of nanobeams. A transfer function method (TFM) is developed to obtain closed-form and uniform solution for the vibration analysis of Euler–Bernoulli beams with different boundary conditions. New analytical expressions for critical viscoelastic parameters, damping parameters and limiting frequencies are obtained. Considering a carbon nanotube as a numerical example, the effects of the nonlocal and viscoelastic constants on the natural frequencies and damping factors are discussed. The results demonstrate the efficiency of the proposed modeling and analysis methods for free vibration analysis of viscoelastic damped nonlocal Euler–Bernoulli beams.