Abstract
Background: Carbon nanotubes (CNTs) reinforced structures are the main elements of structural equipment. Hence a wide range of investigations has been performed on the response of these structures. A lot of studies covered the static and dynamic phenomenon of CNTs reinforced beams, plates and shells. However, there is no study on the free vibration analysis of a doubly-curved nano-size shell made of CNTs reinforced composite materials.
Methods: This work utilized a general third-order shear deformation theory to model the nanoshell where the general strain gradient theory is used in order to capture both nonlocality and strain gradient size-dependency. The Navier solution solving procedure is adopted to solve the partial differential equations (PDEs) and get the natural frequency of the system which is obtained through the Hamilton principle.
Results: The current study shows the importance of small-scale coefficients. The natural frequency increases with rising the strain gradient-size dependency which is because of stiffness enhancement, while the natural frequency decreases by increasing the nonlocality. In addition, the numerical examples covered the CNTs distribution patterns.
Conclusion: This work also studied the importance of shell panel’s shape. It has been observed that spherical shell panel has a higher frequency compared to the hyperbolic one. Furthermore, the frequency of the system increases with growing length-to-thickness ration.
Keywords: Carbon nanotube-reinforced nanocomposites, doubly-curved shell, free vibration, higher-order shear deformation theory, nonlocal strain gradient theory, hamilton principle.
Graphical Abstract
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