Modulated linear dynamics of nanobeams accounting for higher gradient effects

We present some numerical results for the linear dynamics of nanobeams modulated by an axial force, basing on a recent proposal of literature that encompasses both the standard nonlocal elasticity, according to Eringen, and second-order strain elasticity. Three different possibilities for the elastic potential energy provide different responses that highlight the contributions of nonlocality and strain gradient, plus their combination. An axial force 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. Effects of the various elastic potentials on this modulation are investigated and thoroughly commented.