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.

Free vibration characteristics of nonlocal viscoelastic nano‐scaled plates with rectangular cutout and surface effects

“…[33] for the tension of elastic plates, Taghizadeh et al. [34, 35] for bending and buckling of elastic beams and Naghinejad and Ovesy [37, 38, 47] for vibration of beams and plates. In the present study, the nonlocal finite element method is formulated, for studying the vibration behavior of nano‐scaled plates, containing cutouts, by implementing the principle of total potential energy based on nonlocal integral theory, taking into account the viscoelastic properties and various boundary conditions.…”

Transverse Vibration of Functionally Graded Tapered Double Nanobeams Resting on Elastic Foundation

“…Moreover, Zhang et al [13] applied Eringen's elasticity theory to present the scale parameter coefficients for the natural vibrations and buckling behavior of simply supported rectangular plates. Further studies about this topic were examined by other authors [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

Torsional Vibration Analysis of Carbon Nanotubes Using Maxwell and Kelvin-Voigt Type Viscoelastic Material Models

“…Wang and Shen [26] used the nonlocal strain gradient theory in nonlinear vibration analysis of axially moving viscoelastic nanobeam. Naghinejad and Ovesy [27] used the finite element formulation and nonlocal integral elasticity in free vibration analysis of viscoelastic CNTs. Martin [28] proposed a nonlocal fractional Zener model for dynamic analysis of viscoelastic nanotubes.…”