Viscoelastic free vibration behavior of nano-scaled beams via finite element nonlocal integral elasticity approach

Abstract

In this paper, the free-vibration behavior of viscoelastic nano-scaled beams is studied via the finite element (FE) method by implementing the principle of total potential energy and nonlocal integral theory. The formulations are derived based on the Kelvin–Voigt viscoelastic model and Euler–Bernoulli beam theory considering the nonlocal integral theory. The eigenvalue problem of the free vibration is extracted by employing the variational relations. To the best of the authors knowledge it is the first time that the viscoelastic characteristics are implemented in the nonlocal integral FE method to study mechanical behavior of nano-scaled beams. Various boundary conditions can be properly modeled by the current method. Numerical results are compared with literature in order to validate the proposed approach. Then, the effects of nonlocal parameter, viscoelastic parameter, geometrical parameters and different boundary conditions on the complex natural frequencies of the nano-scaled Euler– Bernoulli beams are studied.