On size-dependent large-amplitude free oscillations of FGPM nanoshells incorporating vibrational mode interactions

At nanoscale, surface free energies of the atoms located on the free surfaces of structures significantly affect their mechanical characteristics. In this study, nonlinear large-amplitude free vibration response of nanoshells prepared from functionally graded porous materials (FGPM) is investigated by taking into account surface stress size effects and vibrational mode interactions. Non-classical shell model is constructed on the basis of the Gurtin-Murdoch type of the surface theory of elasticity having the capability of capturing surface stress size dependency. The accuracy of nonlinear vibration analysis is improved by incorporating the interaction of the main vibration mode and the first, third and fifth symmetric oscillation modes. Moreover, the closed-cell Gaussian-Random field scheme is put to use to extract the mechanical characteristics of FGPM nanoshell. Multiple timescales technique is then applied to achieve surface stress elastic-based nonlinear frequency of FGPM nanoshell analytically for different interactions between vibrational modes. It is revealed that by incorporating the interactions of the main vibration mode and higher symmetric oscillation modes, the behavior of the backbone curves belongs to the nonlinear free oscillation response of FGPM nanoshells changes from hardening to softening schema. It is found that when only the main vibration mode is taken into account, surface elasticity effects makes an enhancement in the significance of the hardening schema. However, by considering the interactions of higher symmetric oscillation modes, surface elasticity effects makes a reduction in the significance of the softening schema.