Modulated linear dynamics of functionally graded nanobeams with nonlocal and gradient elasticity

In this contribution some numerical results are presented for the linear dynamics of nanobeams modulated by an axial force. The beam model was recently proposed and encompasses both Eringen's usual nonlocal elasticity and second-gradient strain elasticity. Three different combinations of such aspects provide elastic potential energies that give responses highlighting the various levels of contributions of nonlocality and strain gradient. We suppose that these elastic properties are functionally graded on the beam cross-section according to a power law, thus turning some interesting aspects on. A traction affects the linear stationary dynamics of such nanobeams, inducing suitable variation of the natural angular frequencies for benchmark cases, until static buckling occurs when the natural angular frequency vanishes. The effects of the functional grading and of the different elastic potentials on this modulation are investigated and thoroughly commented.