Vibration analysis of two-phase local/nonlocal viscoelastic nanobeams with surface effects

According to defects of the differential form of pure nonlocal elasticity, two-phase nonlocal elasticity has recently attracted the attention of researchers for studying the size-dependent mechanical behaviors of nanostructures. Given this, in present work, damping vibration behavior of two-phase local/nonlocal viscoelastic nanobeams in conjunction with surface effects is studied. The governing equation of Euler-Bernoulli nanobeam and corresponding constitutive boundary conditions are presented. Using analytical solution, the influences of viscoelastic parameter, surface effects, local phase fraction and nonlocal parameter on the size-dependent damping vibration behavior of nanobeams are investigated. From the results, it can be observed in all boundary conditions that not only the real part but also the imaginary part of the complex frequencies of nanobeams decreases, while the impact of nonlocal elasticity is raised by increasing the nonlocal parameter ratio or decreasing the local phase fraction. Also, the variation of frequency ratios of nanobeams with different dimensions reveals that the influence of surface elasticity on the both parts of complex frequencies depends on the size of cross section and length of nanobeam.