Free vibration analysis of nanocones embedded in an elastic medium using a nonlocal continuum shell model

The effect of elastic foundation on the free vibration characteristics of embedded nanocones is investigated in this paper. The nanocone is modeled as a thin shell and the nonlocal elasticity theory is used to derive the governing equations of motion. Also the elastic medium is simulated using Winkler and Pasternak foundation models. Based on the modal analysis technique and applying the Galerkin method the governing equations are solved to obtain the natural frequencies. The drawn results emphasis the effects of geometry and small-scale parameter on the natural frequencies of nanocone. Also the effect of elastic foundation modulus on the resonance frequencies of the nanocones are studied and some conclusions are outlined.