Novel local/nonlocal formulation of the stress-driven model through closed form solution for higher vibrations modes

In the present work, an innovative two-phases local/nonlocal constitutive mixture model based on the stress-driven model for free vibrations problems is presented. The above two-phases model has been formulated by defining a convex combination of local/nonlocal phases through a mixture parameter and the closed form solution for free vibrations problems is given. The proposed local/nonlocal model has been applied to compute the natural frequencies of four nanobeams study cases. The results are presented in terms of normalised natural frequency as function of both nonlocal and mixture parameters. First, the influence of the two parameters is studied. The effectiveness of the present model is discussed by comparing the results with those obtained by applying the Gradient Elasticity theory. Finally, the normalised natural frequencies for the second, third and fourth modes of vibrations are presented and discussed for each study case.