Studying free hight-frequency vibrations of an inhomogeneous nanorod based on the nonlocal theory of elasticity

Free high-frequency longitudinal vibrations of an inhomogeneous nanosized rod are studied on the basis nonlocal theory elasticity. The upper part spectrum with wavelength comparable to internal characteristic dimension a nanorod is examined. An equations in integral form Helmholtz kernel, incorporating both local and phases, used as constitutive one. original integro-differential equation reduced forth-order differential variable coefficients, pair additional boundary conditions being deduced. UsingWKB-method, solution boundaryvalue problem constructed superposition main edge effect integrals. As alternative model, we consider purely (one-phase) model which allows estimating eigen-frequencies. Considering cross-section area, revealed fair convergence eigen-frequencies found framework two models when fraction two-phase vanishes.