Title : Effect of curvature on the dynamic behavior of carbon nanotube reinforced FGM shells
Abstract:
In the present paper an analytical model was developed to study the non?linear vibrations of Functionally Graded Carbon Nanotube (FG-CNT) reinforced doubly-curved shallow shells using the Multiple Scales Method (MSM). The nonlinear partial differential equations of motion are based on the FGM shallow shell hypothesis, the non?linear geometric Von-Karman relationships, and the Galerkin method to reduce the partial differential equations associated with simply supported boundary conditions. The novelty of the present model is the simultaneous prediction of the natural frequencies and their mode shapes versus different curvatures (cylindrical, spherical, conical, and plate) and the different types of FG-CNTs. The results obtained showed that the curvature and the number of modes have considerable effects on the variation of the effective nonlinearity αe as well as the displacement a. The frequency response of the shallow shells of the FG-CRNTC showed two types of nonlinear behaviors (hardening and softening) which are strongly influenced by the change of the curvatures of the shallow shells.
Audience Take Away Notes:
- The analytical model used allows vibration analysis
- Modulation equations have been developed and solved to represent the frequency-response curves as a function of the number of modes retained in our approximation
- The behavior of the shell in the vicinity of the resonance was valued by the effective nonlinearity and the displacement
- Our study is based on the effects of the curvature on the natural frequencies of the shell with low curvatures reinforced by CNTs
- It has been shown that the non-dimensional frequencies depend on the number of modes retained and the shell curvature, the variation of the latter leads to a significant change in the stiffness of the shell
