Analytical solution of free vibration of viscoelastic perforated nanobeam

This article presented an enhanced mathematical formulated model and well-defined closed-form solutions to explore the dynamic vibration response of perforated viscoelastic nanostructure thin/thick nanobeam with size-dependent continuum model with different boundary conditions for the first time. The thin and thick kinematic assumptions are presented by Euler-Bernoulli and Timoshenko theories, respectively. The perforation is assumed to be arranged in symmetric array with equal space and holes geometry. The nanoscale size is included in the model by using the differential form of nonlocal Eringen model. The governing equations and their associated boundary conditions are developed by using Hamilton principle. The Kelvin/Voigt viscoelastic constitutive relation is exploited to consider the viscoelastic and energy dissipation of nanostructure. Analytical solutions in closed forms are derived and verified with respectable previous works. The numerical and parametric analyses are illustrated the influence of viscoelastic parameter, nonlocal softening coefficient, supporting conditions and filling/spacing ratio on the vibration response. The developed model and solutions can be used simply in the analysis and design of perforated viscoelastic nanobeam and perforated viscoelastic NEMS structures.