Longitudinal vibrations of nano-rods by stress-driven integral elasticity

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Abstract
In elastic continuous structures defined on bounded domains, Eringen strain-driven integral model leads to ill-posed elastostatic problems since the constitutive stress field, got by convoluting the elastic strain field with an averaging kernel, conflicts with equilibrium requirements. The innovative stress-driven integral model, recently proposed in literature, is instead able to overcome inconsistencies of Eringen theory. In the present paper, size-dependent free vibrations of nano-rods are investigated by adopting the stress-driven nonlocal model equipped with Helmholtz kernel. Natural frequencies and mode shapes of nano-rods are established by an effective analytical solution strategy and are compared with those obtained by strain gradient theory.

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