Three-dimensional free vibration analysis of multi-layered graphene sheets embedded in elastic matrix

Three dimensional vibration analysis of multi-layered graphene sheets embedded in polymer matrix is carried out employing nonlocal continuum mechanics. By using the Fourier series expansion in the in-plane axis, the governing equations in term of displacements can be obtained. By exerting the traction free surface boundary conditions to the eigenfrequency equation, natural frequencies are obtained. Accuracy of the present work is validated by comparing the numerical results with those obtained in the open literature. The effect of nonlocal parameter, length of square plate, aspect ratio, plate thickness and half wave numbers in the frequency behavior are examined.