On the nonlinear dynamics of porous composite nanobeams connected with fullerenes

In this study, an attempt is made to investigate the large-amplitude nonlinear vibration response of symmetric porous functionally graded (FG) nanobeams carrying several fullerenes. The influence of various porosity distributions as well as position and mass of fullerenes on the nonlinear vibrational behaviour is particularly studied. To model size effects on the vibration response, a nonlocal elasticity and strain gradient theory in conjunction with the Euler-Bernoulli beam theory is used. Using Hamilton's variational principles, the strain energy, external work and kinetic energy of the ultrasmall system are formulated. The governing nonlinear equations and the associated boundary conditions that incorporate geometrical nonlinearity are derived. Inhomogeneity in the material parameters of the FG porous nanobeam is modelled according to the power-law mixture of constituent materials with cosine function. A discretization technique based on Galerkin's approach and a perturbation solution method are employed to estimate the shift in the nonlinear frequencies of the nanobeams due to the attached fullerene. The nonlinear frequency shift of the complex coupled nanosystem is calculated for various boundary conditions. The validity of the estimated results is evaluated by performing several comparison studies with available data in the literature. Several system parameters such as porosity distribution, material index, the number, position and mass of attached fullerenes, as well as size parameters including the length scale and nonlocal coefficients are taken into consideration in the nonlinear vibration analysis.