Large-amplitude oscillations of composite conical nanoshells with in-plane heterogeneity including surface stress effect. (English) Zbl 1481.74301
Summary: In the current investigation, a new formulation for nonlinear vibration behaviors of functionally graded (FG) composite conical nanoshells are constructed using Gurtin-Murdoch elasticity theory based on higher-order shear deformation shell theory (HSDFST) framework. Both W. Voigt [Wiedemann Ann. 38, 573–587 (1888; JFM 21.1039.01)] and A. Reuss [Z. Angew. Math. Mech. 9, 49–58 (1929; JFM 55.1110.02)] homogenization procedures are considered for the estimation of the mechanical characteristics of FG materials. Using generalized differential quadrature method (GDQM) together with Galerkin technique, the surface elastic-based nonlinear frequency-responses of FG composite conical nanoshell are obtained. It has been illustrated that the decrease of material property gradient index or transformation of boundary condition from full simply supported to full clamped, surface stress effect on the nonlinear frequency of a FG composite conical nanoshell reduces. Also, decreasing semi-vertex angle increases the frequency ratio of \(\omega_{NL} / \omega_L\) which reveals higher geometrical nonlinearity. However, it is seen that surface elasticity effect on the nonlinear vibration behavior of FG composite conical nanoshells is not significant.
Keywords:
conical shells; functionally graded composites; Gurtin-Murdoch elasticity theory; nonlinear dynamics; homogenizationReferences:
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