axial and torsional free vibrations of elastic nano-beams by stress-driven two-phase elasticity

Size-dependent longitudinal and torsional vibrations of nano-beams are examined by two-phase mixture integral elasticity. a new and efficient elastodynamic model is conceived by convexly combining the local phase with strain- and stress-driven purely nonlocal phases. the proposed stress-driven nonlocal integral mixture leads to well-posed structural problems for any value of the scale parameter. effectiveness of stress-driven mixture is illustrated by analyzing axial and torsional free vibrations of cantilever and doubly clamped nano-beams. the local/nonlocal integral mixture is conveniently replaced with an equivalent differential law equipped with constitutive boundary conditions. exact solutions of fundamental natural frequencies associated with strain- and stress-driven mixtures are evaluated and compared with counterpart results obtained by strain gradient elasticity theory. the provided numerical benchmarks can be effectively employed for modelling and design of nano- electro-mechanical-systems (nems).