Free vibration of doubly-curved panels reinforced by carbon nanotubes: New analytic solutions under non-Lévy-type boundary conditions

Abstract

Existing analytic solutions for the free vibration of functionally graded carbon nanotube reinforced doubly-curved panels primarily address the cases with two parallel simply supported boundaries, known as Lévy-type boundary conditions (BCs). However, doubly-curved panels with non-Lévy-type BCs are more commonly encountered in practical engineering applications, yet their analytic solutions are rarely available due to significant mathematical challenges. This gap motivates us to develop new analytic free vibration solutions under these more complex BCs. The nanocomposites’ material properties are first computed according to the rule of mixture. The Hamiltonian-system governing equation for the free vibration of doubly-curved panels is then formulated from the Donnell-Mushtari theory, and is solved by adopting the analytic symplectic superposition method. The obtained analytic solutions are derived without requiring predefined solution forms, and have been thoroughly validated by comparison with the results from the finite element method. By utilizing the accurate analytic solutions, the effects of aspect ratios, BCs, types of CNT distributions, and volume fractions of CNT on the free vibration behaviors are further analyzed. The present solution procedure and the resulting analytic solutions are expected to be useful for dynamic modeling of composite shell panels, supporting both future research and practical applications.